首页 期刊 论文 学科刊群 资讯 加盟 关于
EN
image
Article(id=1246028561321144525, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246028557319783390, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2023.058, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1701792000000, receivedDateStr=2023-12-06, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1775005959109, onlineDateStr=2026-04-01, pubDate=1719244800000, pubDateStr=2024-06-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1775005959109, onlineIssueDateStr=2026-04-01, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1775005959109, creator=13701087609, updateTime=1775005959109, updator=13701087609, issue=Issue{id=1246028557319783390, tenantId=1146029695717560320, journalId=1241755870837649424, year='2024', volume='45', issue='3', pageStart='289', pageEnd='426', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1775005958156, creator=13701087609, updateTime=1775006058227, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1246028977123471371, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246028557319783390, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1246028977123471372, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246028557319783390, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=341, endPage=351, ext={EN=ArticleExt(id=1246028561665077458, articleId=1246028561321144525, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Free Vibration Analysis for Anisotropic Plates Based on Peridynamic Operator Method, columnId=1244229834482757770, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

Anisotropic materials find widespread applications across various engineering domains. The investigation on vibrational properties of anisotropic materials holds significance for structural vibration mitigation and safety design. This paper introduces a novel approach, the peridynamic operator method (PDOM), to construct a non-local anisotropic model and applies it to the analysis of free vibrations in anisotropic plates. The model incorporates the unique feature of PDOM, which transforms local differentials and their products into non-local integrals, thereby reformulating the strain energy density from its local form to a non-local form within classical anisotropic theory. Additionally, the paper employs a variational principle and introduces the free vibration equation to develop a PDOM solution for anisotropic free vibration problems. Three numerical examples are provided, including the free vibrations of a thin anisotropic rectangular plate, an anisotropic rectangular plate with cracks, and an anisotropic rectangular plate with holes. The results are compared with finite element results, showcasing the model's convergence, stability, and high computational accuracy in dealing with free vibrations of anisotropic plates with defects and discontinuities.

, correspAuthors=Dan Huang, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Yanzhou Lu, Zhiyuan Li, Dan Huang, Xuehao Yao), CN=ArticleExt(id=1246028575707607771, articleId=1246028561321144525, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=基于近场动力学算子方法的各向异性板自由振动分析, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

各向异性材料广泛应用于诸多工程领域，研究其振动特性对结构减振与安全设计具有重要意义. 本文基于一种新的近场动力学算子方法（Peridynamic operator method，PDOM）构建非局部各向异性模型，并应用于各向异性板的自由振动分析. 该模型结合了PDOM将局部微分及其乘积转化为非局部积分的特点，将经典各向异性理论中的应变能密度从局部形式重构为非局部形式. 同时，采用变分原理并引入自由振动方程，构建了适用于各向异性自由振动问题的PDOM求解方案. 通过三个数值算例：各向异性矩形薄板、各向异性矩形含裂纹板、各向异性矩形含孔板的自由振动，并将计算结果与有限元结果比较，说明了模型在计算含缺陷以及不连续的各向异性板自由振动问题时具有收敛性、稳定性以及高计算精度.

, correspAuthors=黄丹, authorNote=null, correspAuthorsNote=
** E-mail：.
, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=CdwDkb+aq3rnUV5PQ5xCOA==, magXml=gYz+9Ove0nufI/0cCFDjdA==, pdfUrl=null, pdf=10iqt8j2ljL+mVQcd8vbyg==, pdfFileSize=4907260, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=Hb5IUwtC1MYVRr5vPMg3+Q==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=4V8mmAEluioiIrZSIB69ew==, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=陆炎洲, 李志远, 黄丹, 姚学昊)}, authors=[Author(id=1246028576152204008, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=null, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1246028576257061612, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, authorId=1246028576152204008, language=EN, stringName=Yanzhou Lu, firstName=Yanzhou, middleName=null, lastName=Lu, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=Department of Engineering Mechanics, Hohai University, Nanjing, 211100, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1246028576332559086, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, authorId=1246028576152204008, language=CN, stringName=陆炎洲, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=河海大学工程力学系，南京，211100, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null)}, companyList=[AuthorCompany(id=1246028576009597667, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, xref=null, ext=[AuthorCompanyExt(id=1246028576017986276, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Department of Engineering Mechanics, Hohai University, Nanjing, 211100), AuthorCompanyExt(id=1246028576030569189, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=河海大学工程力学系，南京，211100)])]), Author(id=1246028576424833776, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, orderNo=1, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=null, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1246028576508719861, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, authorId=1246028576424833776, language=EN, stringName=Zhiyuan Li, firstName=Zhiyuan, middleName=null, lastName=Li, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=Department of Engineering Mechanics, Hohai University, Nanjing, 211100, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1246028576605188855, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, authorId=1246028576424833776, language=CN, stringName=李志远, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=河海大学工程力学系，南京，211100, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null)}, companyList=[AuthorCompany(id=1246028576009597667, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, xref=null, ext=[AuthorCompanyExt(id=1246028576017986276, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Department of Engineering Mechanics, Hohai University, Nanjing, 211100), AuthorCompanyExt(id=1246028576030569189, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=河海大学工程力学系，南京，211100)])]), Author(id=1246028576710046461, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, orderNo=2, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=danhuang@hhu.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=1, authorType=1, ext={EN=AuthorExt(id=1246028576806515454, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, authorId=1246028576710046461, language=EN, stringName=Dan Huang, firstName=Dan, middleName=null, lastName=Huang, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=**, address=Department of Engineering Mechanics, Hohai University, Nanjing, 211100, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1246028576869430016, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, authorId=1246028576710046461, language=CN, stringName=黄丹, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=**, address=河海大学工程力学系，南京，211100, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null)}, companyList=[AuthorCompany(id=1246028576009597667, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, xref=null, ext=[AuthorCompanyExt(id=1246028576017986276, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Department of Engineering Mechanics, Hohai University, Nanjing, 211100), AuthorCompanyExt(id=1246028576030569189, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=河海大学工程力学系，南京，211100)])]), Author(id=1246028576940733187, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, orderNo=3, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=null, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1246028577024619271, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, authorId=1246028576940733187, language=EN, stringName=Xuehao Yao, firstName=Xuehao, middleName=null, lastName=Yao, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=Department of Engineering Mechanics, Hohai University, Nanjing, 211100, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1246028577095922442, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, authorId=1246028576940733187, language=CN, stringName=姚学昊, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=河海大学工程力学系，南京，211100, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null)}, companyList=[AuthorCompany(id=1246028576009597667, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, xref=null, ext=[AuthorCompanyExt(id=1246028576017986276, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Department of Engineering Mechanics, Hohai University, Nanjing, 211100), AuthorCompanyExt(id=1246028576030569189, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=河海大学工程力学系，南京，211100)])])], keywords=[Keyword(id=1246028577200780045, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, orderNo=1, keyword=free vibration), Keyword(id=1246028577276277519, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, orderNo=2, keyword=anisotropic), Keyword(id=1246028577364357905, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, orderNo=3, keyword=PDOM), Keyword(id=1246028577511158547, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, orderNo=4, keyword=non-local), Keyword(id=1246028577616016148, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, orderNo=5, keyword=variational principle), Keyword(id=1246028577733456662, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, orderNo=1, keyword=自由振动), Keyword(id=1246028577800565527, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, orderNo=2, keyword=各向异性), Keyword(id=1246028577880257306, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, orderNo=3, keyword=近场动力学算子方法), Keyword(id=1246028577955754779, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, orderNo=4, keyword=非局部), Keyword(id=1246028578027057949, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, orderNo=5, keyword=变分原理)], refs=[Reference(id=1246028580514280275, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2020, volume=188, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=Mandal T K, Nguyen V P, Wu J Y, journalName=International Journal of Mechanical Sciences, refType=null, unstructuredReference=Mandal T K, Nguyen V P, Wu J Y. A length scale insensitive anisotropic phase field fracture model for hyperelastic composites[J]. International Journal of Mechanical Sciences, 2020, 188: 105941., articleTitle=A length scale insensitive anisotropic phase field fracture model for hyperelastic composites, refAbstract=null), Reference(id=1246028580585583443, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2021, volume=40, issue=22, pageStart=216, pageEnd=220+266, url=null, language=null, rfNumber=[2], rfOrder=1, authorNames=王久法, journalName=振动与冲击, refType=null, unstructuredReference=王久法. 正交各向异性声源膜板的自由振动特性分析[J]. 振动与冲击, 2021, 40(22): 216-220+266., articleTitle=正交各向异性声源膜板的自由振动特性分析, refAbstract=null), Reference(id=1246028580665275221, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2021, volume=40, issue=22, pageStart=216, pageEnd=220+266, url=null, language=null, rfNumber=[2], rfOrder=2, authorNames=Wang J F, journalName=Journal of Vibration and Shock, refType=null, unstructuredReference=(Wang J F. Free vibration characteristics analysis of orthotropic sound source plates[J]. Journal of Vibration and Shock, 2021, 40(22): 216-220+266. (in Chinese)), articleTitle=Free vibration characteristics analysis of orthotropic sound source plates, refAbstract=null), Reference(id=1246028580736578391, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=28, issue=1-2, pageStart=3, pageEnd=16, url=null, language=null, rfNumber=[3], rfOrder=3, authorNames=Su X, Bai E, journalName=Journal of Vibration and Control, refType=null, unstructuredReference=Su X, Bai E. Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method[J]. Journal of Vibration and Control, 2022, 28(1-2): 3-16., articleTitle=Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method, refAbstract=null), Reference(id=1246028580803687257, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2023, volume=40, issue=6, pageStart=1330, pageEnd=1350, url=null, language=null, rfNumber=[4], rfOrder=4, authorNames=Su X, Bai E, Hai G J, journalName=Engineering Computations, refType=null, unstructuredReference=Su X, Bai E, Hai G J. Unified solution of some problems of rectangular plates with four free edges based on symplectic superposition method[J]. Engineering Computations, 2023, 40(6): 1330-1350., articleTitle=Unified solution of some problems of rectangular plates with four free edges based on symplectic superposition method, refAbstract=null), Reference(id=1246028580883379035, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=10.1080/15397734.2023.2193623, pmid=null, pmcid=null, year=2023, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[5], rfOrder=5, authorNames=Kumar V, Singh S J, Saran V H, Harsha S P, journalName=Mechanics Based Design of Structures and Machines, refType=null, unstructuredReference=Kumar V, Singh S J, Saran V H, Harsha S P. Vibration response of the exponential functionally graded material plate with variable thickness resting on the orthotropic Pasternak foundation[J]. Mechanics Based Design of Structures and Machines, 2023,, articleTitle=Vibration response of the exponential functionally graded material plate with variable thickness resting on the orthotropic Pasternak foundation, refAbstract=null), Reference(id=1246028580946293597, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2023, volume=13, issue=1, pageStart=2601, pageEnd=null, url=null, language=null, rfNumber=[6], rfOrder=6, authorNames=Hu Z Y, Du J Y, Liu M F, Li Y H, Wang Z X, Zheng X R, Bui T Q, Li R, journalName=Scientific Reports, refType=null, unstructuredReference=Hu Z Y, Du J Y, Liu M F, Li Y H, Wang Z X, Zheng X R, Bui T Q, Li R. Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions[J]. Scientific Reports, 2023, 13(1): 2601., articleTitle=Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions, refAbstract=null), Reference(id=1246028581009208159, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2023, volume=188, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[7], rfOrder=7, authorNames=Hou S X, Li M H, Luo J J, Kiani Y, journalName=Thin-walled Structures, refType=null, unstructuredReference=Hou S X, Li M H, Luo J J, Kiani Y. Numerical modeling of vibration and damping of higher-order magnetorheological elastomer polar orthotropic composite sectorial/annular plates[J]. Thin-walled Structures, 2023, 188: 110825., articleTitle=Numerical modeling of vibration and damping of higher-order magnetorheological elastomer polar orthotropic composite sectorial/annular plates, refAbstract=null), Reference(id=1246028581105677153, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=10.1007/s00419-023-02453-w, pmid=null, pmcid=null, year=2023, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[8], rfOrder=8, authorNames=Bai Y, Li H, journalName=Archive of Applied Mechanics, refType=null, unstructuredReference=Bai Y, Li H. Vibration characteristics analysis of anisotropic metal rubber medium-thick cylindrical shells[J]. Archive of Applied Mechanics, 2023,, articleTitle=Vibration characteristics analysis of anisotropic metal rubber medium-thick cylindrical shells, refAbstract=null), Reference(id=1246028581156008803, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=146, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[9], rfOrder=9, authorNames=Strozzi M, Smirnov V V, Pellicano F, Kovaleva M, journalName=International Journal of Non-linear Mechanics, refType=null, unstructuredReference=Strozzi M, Smirnov V V, Pellicano F, Kovaleva M. Nonlocal anisotropic elastic shell model for vibrations of double-walled carbon nanotubes under nonlinear van der Waals interaction forces[J]. International Journal of Non-linear Mechanics, 2022, 146: 104172., articleTitle=Nonlocal anisotropic elastic shell model for vibrations of double-walled carbon nanotubes under nonlinear van der Waals interaction forces, refAbstract=null), Reference(id=1246028581214729061, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2000, volume=48, issue=null, pageStart=175, pageEnd=209, url=null, language=null, rfNumber=[10], rfOrder=10, authorNames=Silling S A, journalName=Journal of the Mechanics and Physics of Solids, refType=null, unstructuredReference=Silling S A. Reformulation of elasticity theory for discontinuities and long-range forces[J]. Journal of the Mechanics and Physics of Solids, 2000, 48: 175-209., articleTitle=Reformulation of elasticity theory for discontinuities and long-range forces, refAbstract=null), Reference(id=1246028581290226535, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2010, volume=40, issue=4, pageStart=448, pageEnd=459, url=null, language=null, rfNumber=[11], rfOrder=11, authorNames=黄丹, 章青, 乔丕忠, 沈峰, journalName=力学进展, refType=null, unstructuredReference=黄丹, 章青, 乔丕忠, 沈峰. 近场动力学方法及其应用[J]. 力学进展, 2010, 40(4): 448-459., articleTitle=近场动力学方法及其应用, refAbstract=null), Reference(id=1246028581353141097, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2010, volume=40, issue=4, pageStart=448, pageEnd=459, url=null, language=null, rfNumber=[11], rfOrder=12, authorNames=Huang D, Zhang Q, Qiao P Z, Shen F, journalName=Advances in Mechanics, refType=null, unstructuredReference=(Huang D, Zhang Q, Qiao P Z, Shen F. A review on peridynamics (PD) method and its applications[J]. Advances in Mechanics, 2010, 40(4): 448-459. (in Chinese)), articleTitle=A review on peridynamics (PD) method and its applications, refAbstract=null), Reference(id=1246028581432832875, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2023, volume=283, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[12], rfOrder=13, authorNames=Wu L W, Wang H, Huang D, Cai X, Guo J B, journalName=Engineering Fracture Mechanics, refType=null, unstructuredReference=Wu L W, Wang H, Huang D, Cai X, Guo J B. A reformulated non-ordinary state-based peridynamic method for dynamic failure of ductile materials[J]. Engineering Fracture Mechanics, 2023, 283: 109196., articleTitle=A reformulated non-ordinary state-based peridynamic method for dynamic failure of ductile materials, refAbstract=null), Reference(id=1246028581495747437, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=290, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[13], rfOrder=14, authorNames=Ma Q P, Wu L W, Huang D, journalName=Composite Structures, refType=null, unstructuredReference=Ma Q P, Wu L W, Huang D. An extended peridynamic model for dynamic fracture of laminated glass considering interfacial debonding[J]. Composite Structures, 2022, 290: 115552., articleTitle=An extended peridynamic model for dynamic fracture of laminated glass considering interfacial debonding, refAbstract=null), Reference(id=1246028581571244911, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=270, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[14], rfOrder=15, authorNames=Yao X H, Huang D, journalName=Computers and Structures, refType=null, unstructuredReference=Yao X H, Huang D. Coupled PD-SPH modeling for fluid-structure interaction problems with large deformation and fracturing[J]. Computers and Structures, 2022, 270: 106847., articleTitle=Coupled PD-SPH modeling for fluid-structure interaction problems with large deformation and fracturing, refAbstract=null), Reference(id=1246028581646742385, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=54, issue=12, pageStart=3333, pageEnd=3343, url=null, language=null, rfNumber=[15], rfOrder=16, authorNames=姚学昊, 陈丁, 武立伟, 黄丹, journalName=力学学报, refType=null, unstructuredReference=姚学昊, 陈丁, 武立伟, 黄丹. 流固耦合破坏分析的多分辨率PD-SPH方法[J]. 力学学报, 2022, 54(12): 3333-3343., articleTitle=流固耦合破坏分析的多分辨率PD-SPH方法, refAbstract=null), Reference(id=1246028581739017076, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=54, issue=12, pageStart=3333, pageEnd=3343, url=null, language=null, rfNumber=[15], rfOrder=17, authorNames=Yao X H, Chen D, Wu L W, Huang D, journalName=Chinese Journal of Theoretical and Applied Mechanics, refType=null, unstructuredReference=(Yao X H, Chen D, Wu L W, Huang D. A multi-resolution PD-SPH coupling approach for structural failure under fluid-structure interaction[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3333-3343. (in Chinese)), articleTitle=A multi-resolution PD-SPH coupling approach for structural failure under fluid-structure interaction, refAbstract=null), Reference(id=1246028581831291764, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2019, volume=40, issue=7, pageStart=2873, pageEnd=2881, url=null, language=null, rfNumber=[16], rfOrder=18, authorNames=张钰彬, 黄丹, journalName=岩土力学, refType=null, unstructuredReference=张钰彬, 黄丹. 页岩水力压裂过程的态型近场动力学模拟研究[J]. 岩土力学, 2019, 40(7): 2873-2881., articleTitle=页岩水力压裂过程的态型近场动力学模拟研究, refAbstract=null), Reference(id=1246028581931955061, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2019, volume=40, issue=7, pageStart=2873, pageEnd=2881, url=null, language=null, rfNumber=[16], rfOrder=19, authorNames=Zhang Y B, Huang D, journalName=Rock and Soil Mechanics, refType=null, unstructuredReference=(Zhang Y B, Huang D. State-based peridynamic study on the hydraulic fracture of shale[J]. Rock and Soil Mechanics, 2019, 40(7): 2873-2881. (in Chinese)), articleTitle=State-based peridynamic study on the hydraulic fracture of shale, refAbstract=null), Reference(id=1246028581994869622, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2020, volume=234, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[17], rfOrder=20, authorNames=Zhang Y B, Huang D, Cai Z, Xu Y P, journalName=Engineering Fracture Mechanics, refType=null, unstructuredReference=Zhang Y B, Huang D, Cai Z, Xu Y P. An extended ordinary state -based peridynamic approach for modelling hydraulic fracturing[J]. Engineering Fracture Mechanics, 2020, 234: 107086., articleTitle=An extended ordinary state -based peridynamic approach for modelling hydraulic fracturing, refAbstract=null), Reference(id=1246028582116504439, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2019, volume=159, issue=null, pageStart=336, pageEnd=344, url=null, language=null, rfNumber=[18], rfOrder=21, authorNames=Wang H, Xu Y P, Huang D, journalName=International Journal of Mechanics Sciences, refType=null, unstructuredReference=Wang H, Xu Y P, Huang D. A non-ordinary state-based peridynamic formulation for thermo-visco-plastic deformation and impact fracture[J]. International Journal of Mechanics Sciences, 2019, 159: 336-344., articleTitle=A non-ordinary state-based peridynamic formulation for thermo-visco-plastic deformation and impact fracture, refAbstract=null), Reference(id=1246028582271693689, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2023, volume=305, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[19], rfOrder=22, authorNames=He D W, Huang D, Wu L W, Xu Y P, journalName=Composite Structures, refType=null, unstructuredReference=He D W, Huang D, Wu L W, Xu Y P. Investigation on thermal failure of functionally graded materials using fully coupled thermo-mechanical peridynamics[J]. Composite Structures, 2023, 305: 116454., articleTitle=Investigation on thermal failure of functionally graded materials using fully coupled thermo-mechanical peridynamics, refAbstract=null), Reference(id=1246028582330413946, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2019, volume=160, issue=null, pageStart=140, pageEnd=155, url=null, language=null, rfNumber=[20], rfOrder=23, authorNames=Diana V, Casolo S, journalName=International Journal of Mechanics Sciences, refType=null, unstructuredReference=Diana V, Casolo S. A full orthotropic micropolar peridynamic formulation for linearly elastic solids[J]. International Journal of Mechanics Sciences, 2019, 160: 140-155., articleTitle=A full orthotropic micropolar peridynamic formulation for linearly elastic solids, refAbstract=null), Reference(id=1246028582393328507, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2021, volume=42, issue=4, pageStart=467, pageEnd=475, url=null, language=null, rfNumber=[21], rfOrder=24, authorNames=吴林潮, 吴志渊, 张文明, journalName=固体力学学报, refType=null, unstructuredReference=吴林潮, 吴志渊, 张文明. 基于近场动力学的梁结构振动特性分析方法研究[J]. 固体力学学报, 2021, 42(4): 467-475., articleTitle=基于近场动力学的梁结构振动特性分析方法研究, refAbstract=null), Reference(id=1246028582473020284, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2021, volume=42, issue=4, pageStart=467, pageEnd=475, url=null, language=null, rfNumber=[21], rfOrder=25, authorNames=Wu L C, Wu Z Y, Zhang W M, journalName=Chinese Journal of Solid Mechanics, refType=null, unstructuredReference=(Wu L C, Wu Z Y, Zhang W M. Vibration analysis method of beam structure in peridynamics[J]. Chinese Journal of Solid Mechanics, 2021, 42(4): 467-475. (in Chinese)), articleTitle=Vibration analysis method of beam structure in peridynamics, refAbstract=null), Reference(id=1246028582531740541, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2019, volume=213, issue=null, pageStart=72, pageEnd=81, url=null, language=null, rfNumber=[22], rfOrder=26, authorNames=Jafari A, Ezzati M, Atai A A, journalName=Computers and Structures, refType=null, unstructuredReference=Jafari A, Ezzati M, Atai A A. Static and free vibration analysis of Timoshenko beam based on combined peridynamic-classical theory besides FEM formulation[J]. Computers and Structures, 2019, 213: 72-81., articleTitle=Static and free vibration analysis of Timoshenko beam based on combined peridynamic-classical theory besides FEM formulation, refAbstract=null), Reference(id=1246028582586266494, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2020, volume=15, issue=1, pageStart=220, pageEnd=229, url=null, language=null, rfNumber=[23], rfOrder=27, authorNames=Heo J, Yang Z H, Xia W X, Oterkus S, Oterkus E, journalName=Ships and Offshore Structures, refType=null, unstructuredReference=Heo J, Yang Z H, Xia W X, Oterkus S, Oterkus E. Free vibration analysis of cracked plates using peridynamics[J]. Ships and Offshore Structures, 2020, 15(1): 220-229., articleTitle=Free vibration analysis of cracked plates using peridynamics, refAbstract=null), Reference(id=1246028582657569663, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2016, volume=304, issue=null, pageStart=408, pageEnd=451, url=null, language=null, rfNumber=[24], rfOrder=28, authorNames=Madenci E, Barut A, Futch M, journalName=Computer Methods in Applied Mechanics and Engineering, refType=null, unstructuredReference=Madenci E, Barut A, Futch M. Peridynamic differential operator and its applications[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 408-451., articleTitle=Peridynamic differential operator and its applications, refAbstract=null), Reference(id=1246028582733067136, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2019, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[25], rfOrder=29, authorNames=Madenci E, Barut A, Dordunce M, journalName=Peridynamic differential operator for numerical analysis, refType=null, unstructuredReference=Madenci E, Barut A, Dordunce M. Peridynamic differential operator for numerical analysis[M]. Switzerland: Springer Nature Switzerland AG, 2019., articleTitle=null, refAbstract=null), Reference(id=1246028582783398785, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2020, volume=367, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[26], rfOrder=30, authorNames=Ren H L, Zhuang X Y, Rabczuk T, journalName=Computer Methods in Applied Mechanics and Engineering, refType=null, unstructuredReference=Ren H L, Zhuang X Y, Rabczuk T. A higher order nonlocal operator method for solving partial differential equations[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 367: 113132., articleTitle=A higher order nonlocal operator method for solving partial differential equations, refAbstract=null), Reference(id=1246028582837924738, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2020, volume=358, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[27], rfOrder=31, authorNames=Ren H L, Zhuang X Y, Rabczuk T, journalName=Computer Methods in Applied Mechanics and Engineering, refType=null, unstructuredReference=Ren H L, Zhuang X Y, Rabczuk T. A nonlocal operator method for solving partial differential equations[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 358: 112621., articleTitle=A nonlocal operator method for solving partial differential equations, refAbstract=null), Reference(id=1246028582900839299, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=10.1007/s00366-022-01763-x, pmid=null, pmcid=null, year=2022, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[28], rfOrder=32, authorNames=Li Z Y, Huang D, Ren H L, Rabczuk T, journalName=Engineering with Computers, refType=null, unstructuredReference=Li Z Y, Huang D, Ren H L, Rabczuk T. Weak form of bond-associated peridynamic differential operator for solving differential equations[J]. Engineering with Computers, 2022,, articleTitle=Weak form of bond-associated peridynamic differential operator for solving differential equations, refAbstract=null), Reference(id=1246028582963753860, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=14, issue=5, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[29], rfOrder=33, authorNames=Zhou B L, Li Z Y, Xu Y P, Huang D, journalName=International Journal of Applied Mechanics, refType=null, unstructuredReference=Zhou B L, Li Z Y, Xu Y P, Huang D. Analysis of nonlinear heat conduction problems with temperature-dependent conductivity using peridynamic differential operator[J]. International Journal of Applied Mechanics, 2022, 14(5): 2250047., articleTitle=Analysis of nonlinear heat conduction problems with temperature-dependent conductivity using peridynamic differential operator, refAbstract=null), Reference(id=1246028583035057029, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=43, issue=6, pageStart=660, pageEnd=668, url=null, language=null, rfNumber=[30], rfOrder=34, authorNames=周保良, 李志远, 黄丹, journalName=应用数学与力学, refType=null, unstructuredReference=周保良, 李志远, 黄丹. 二维瞬态热传导的PDDO分析[J]. 应用数学与力学, 2022, 43(6): 660-668., articleTitle=二维瞬态热传导的PDDO分析, refAbstract=null), Reference(id=1246028583198634886, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=43, issue=6, pageStart=660, pageEnd=668, url=null, language=null, rfNumber=[30], rfOrder=35, authorNames=Zhou B L, Li Z Y, Huang D, journalName=Applied Mathematics and Mechanics, refType=null, unstructuredReference=(Zhou B L, Li Z Y, Huang D. PDDO analysis of 2D transient heat conduction problems[J]. Applied Mathematics and Mechanics, 2022, 43(6): 660-668. (in Chinese)), articleTitle=PDDO analysis of 2D transient heat conduction problems, refAbstract=null), Reference(id=1246028583257355143, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2021, volume=93, issue=null, pageStart=294, pageEnd=313, url=null, language=null, rfNumber=[31], rfOrder=36, authorNames=Li Z Y, Huang D, Xu Y P, Yan K H, journalName=Applied Mathematical Modelling, refType=null, unstructuredReference=Li Z Y, Huang D, Xu Y P, Yan K H. Nonlocal steady-state thermoelastic analysis of functionally graded materials by using peridynamic differential operator[J]. Applied Mathematical Modelling, 2021, 93: 294-313., articleTitle=Nonlocal steady-state thermoelastic analysis of functionally graded materials by using peridynamic differential operator, refAbstract=null), Reference(id=1246028583353824136, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2022, volume=279, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[32], rfOrder=37, authorNames=Li Z Y, Huang D, Yan K H, Xu Y P, journalName=Composite Structures, refType=null, unstructuredReference=Li Z Y, Huang D, Yan K H, Xu Y P. Large deformation analysis of functionally graded beam with variable cross-section by using peridynamic differential operator[J]. Composite Structures, 2022, 279: 114788., articleTitle=Large deformation analysis of functionally graded beam with variable cross-section by using peridynamic differential operator, refAbstract=null), Reference(id=1246028583479653257, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2020, volume=216, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[33], rfOrder=38, authorNames=Gao Y, Oterkus S, journalName=Ocean Engineering, refType=null, unstructuredReference=Gao Y, Oterkus S. Multi-phase fluid flow simulation by using peridynamic differential operator[J]. Ocean Engineering, 2020, 216: 108081., articleTitle=Multi-phase fluid flow simulation by using peridynamic differential operator, refAbstract=null), Reference(id=1246028583588705162, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2021, volume=239, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[34], rfOrder=39, authorNames=Nguyen C T, Oterkus S, Oterkus E, Amin I, Ozdemir M, El-Aassar A H, Shawky H, journalName=Ocean Engineering, refType=null, unstructuredReference=Nguyen C T, Oterkus S, Oterkus E, Amin I, Ozdemir M, El-Aassar A H, Shawky H. Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator[J]. Ocean Engineering, 2021, 239: 109815., articleTitle=Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator, refAbstract=null), Reference(id=1246028583685174155, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2023, volume=55, issue=07, pageStart=1593, pageEnd=1603, url=null, language=null, rfNumber=[35], rfOrder=40, authorNames=李志远, 黄丹, Rabczuk T, journalName=力学学报, refType=null, unstructuredReference=李志远, 黄丹, Rabczuk T. 近场动力学算子方法[J]. 力学学报, 2023, 55(07): 1593-1603., articleTitle=近场动力学算子方法, refAbstract=null), Reference(id=1246028583752283020, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2023, volume=55, issue=07, pageStart=1593, pageEnd=1603, url=null, language=null, rfNumber=[35], rfOrder=41, authorNames=Li Z Y, Huang D, Rabczuk T, journalName=Chinese Journal of Theoretical and Applied Mechanics, refType=null, unstructuredReference=(Li Z Y, Huang D, Rabczuk T. Peridynamic operator method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(07): 1593-1603. (in Chinese)), articleTitle=Peridynamic operator method, refAbstract=null), Reference(id=1246028583823586189, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, doi=null, pmid=null, pmcid=null, year=2023, volume=411, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[36], rfOrder=42, authorNames=Li Z Y, Huang D, Rabczuk T, journalName=Computer Methods in Applied Mechanics and Engineering, refType=null, unstructuredReference=Li Z Y, Huang D, Rabczuk T. Peridynamic operator method[J]. Computer Methods in Applied Mechanics and Engineering, 2023, 411: 116047., articleTitle=Peridynamic operator method, refAbstract=null)], funds=[Fund(id=1246028580375868238, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, awardId=B240201144, language=CN, fundingSource=中央高校基本科研业务费专项资金(B240201144), fundOrder=null, country=null), Fund(id=1246028580430394192, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, awardId=12071204, language=CN, fundingSource=国家自然科学基金项目(12071204), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1246028576009597667, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, xref=null, ext=[AuthorCompanyExt(id=1246028576017986276, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Department of Engineering Mechanics, Hohai University, Nanjing, 211100), AuthorCompanyExt(id=1246028576030569189, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, companyId=1246028576009597667, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=河海大学工程力学系，南京，211100)])], figs=[ArticleFig(id=1246028578136109855, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.1, caption=Interaction domain of PDOM points, figureFileSmall=ZnvB7boQlev86Yupsr/JgA==, figureFileBig=Hb5IUwtC1MYVRr5vPMg3+Q==, tableContent=null), ArticleFig(id=1246028578207413025, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图1, caption=PDOM物质点相互作用域, figureFileSmall=ZnvB7boQlev86Yupsr/JgA==, figureFileBig=Hb5IUwtC1MYVRr5vPMg3+Q==, tableContent=null), ArticleFig(id=1246028578387768100, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.2, caption=Global and material coordinate systems, figureFileSmall=Rp0GmGnPVkDIsxEmhw4IaA==, figureFileBig=QHK9qrKCzXp/OQ5C9astlQ==, tableContent=null), ArticleFig(id=1246028578454876965, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图2, caption=整体坐标系和材料坐标系, figureFileSmall=Rp0GmGnPVkDIsxEmhw4IaA==, figureFileBig=QHK9qrKCzXp/OQ5C9astlQ==, tableContent=null), ArticleFig(id=1246028578563928871, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.3, caption=Flowchart of numerical algorithm, figureFileSmall=FL7JXCTydqoBaIEzedZyXQ==, figureFileBig=VXBtMa1dYSFroBlf7zHLJA==, tableContent=null), ArticleFig(id=1246028578639426345, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图3, caption=数值算法流程图, figureFileSmall=FL7JXCTydqoBaIEzedZyXQ==, figureFileBig=VXBtMa1dYSFroBlf7zHLJA==, tableContent=null), ArticleFig(id=1246028578727506731, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.4, caption=Relative error of first 3 frequencies for different discrete distance, figureFileSmall=j8fkx+liwGv7gLH37JBoYg==, figureFileBig=wlYVthDb4QBnQIuB7e0U/Q==, tableContent=null), ArticleFig(id=1246028578807198509, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图4, caption=不同离散间距下前3阶频率的相对误差, figureFileSmall=j8fkx+liwGv7gLH37JBoYg==, figureFileBig=wlYVthDb4QBnQIuB7e0U/Q==, tableContent=null), ArticleFig(id=1246028578874307375, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.5, caption=Geometry conditions of anisotropic rectangular cracked plate, figureFileSmall=c54K0Jp9Qpa/wdac6aZ/6w==, figureFileBig=fidIwyk/PQpXZYVngnLz7w==, tableContent=null), ArticleFig(id=1246028578941416240, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图5, caption=各向异性矩形含裂缝板几何条件, figureFileSmall=c54K0Jp9Qpa/wdac6aZ/6w==, figureFileBig=fidIwyk/PQpXZYVngnLz7w==, tableContent=null), ArticleFig(id=1246028579000136497, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.6, caption=First 3 order displacement modes of the anisotropic cracked plate under off-angle φ=π/3 (PDOM results on the left, FEM results on the right), figureFileSmall=+Ak2aEzhPypAla/MOSJKlw==, figureFileBig=9310Nc34jsv6CEKop9b79g==, tableContent=null), ArticleFig(id=1246028579071439667, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图6, caption=各向异性偏角φ=π/3时含裂缝板前3阶全位移模态（左栏为PDOM结果，右栏为FEM结果）, figureFileSmall=+Ak2aEzhPypAla/MOSJKlw==, figureFileBig=9310Nc34jsv6CEKop9b79g==, tableContent=null), ArticleFig(id=1246028579134354229, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.7, caption=Geometry conditions of anisotropic rectangular plate with a hole, figureFileSmall=uBcW1vc8GFR3A3HbswKVhA==, figureFileBig=Y12yWQq5BiB8USGBzC3Ezg==, tableContent=null), ArticleFig(id=1246028579218240311, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图7, caption=各向异性矩形含孔板几何条件, figureFileSmall=uBcW1vc8GFR3A3HbswKVhA==, figureFileBig=Y12yWQq5BiB8USGBzC3Ezg==, tableContent=null), ArticleFig(id=1246028579285349177, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.8, caption=First 3 order displacement modes obtained with FEM and PDOM at r=0.07 m (φ=π/2), figureFileSmall=6zC1I3jBO2YoquCvfVpwFA==, figureFileBig=LnbjA7gYuWDZ1rlJU00Wkw==, tableContent=null), ArticleFig(id=1246028579381818171, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图8, caption=FEM和PDOM求得的前3阶位移模态在r=0.07 m处分布（φ=π/2）, figureFileSmall=6zC1I3jBO2YoquCvfVpwFA==, figureFileBig=LnbjA7gYuWDZ1rlJU00Wkw==, tableContent=null), ArticleFig(id=1246028579453121341, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.9, caption=Third-order displacement modes obtained with FEM and PDOM at r=0.07 m under different anisotropic off-angle φ, figureFileSmall=Ou+z+HiLFZdI8NJ0sQ4BIw==, figureFileBig=9Vbp8vZB7AFvri3e5KEA/Q==, tableContent=null), ArticleFig(id=1246028579520230205, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图9, caption=不同各向异性偏角φ下FEM和PDOM求得的第3阶位移模态在r=0.07 m处分布, figureFileSmall=Ou+z+HiLFZdI8NJ0sQ4BIw==, figureFileBig=9Vbp8vZB7AFvri3e5KEA/Q==, tableContent=null), ArticleFig(id=1246028579587339071, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Fig.10, caption=First 3 order displacement modes of the anisotropic plate with a hole under off-angle φ=π/6 (PDOM results on the left, FEM results on the right), figureFileSmall=MCGRvj7SCLvRIRgmqtk+wA==, figureFileBig=JBLYMXelu8CZuHT17sy7wA==, tableContent=null), ArticleFig(id=1246028579641865025, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=图10, caption=各向异性偏角φ=π/6时含孔板前3阶全位移模态（左栏为PDOM结果，右栏为FEM结果）, figureFileSmall=MCGRvj7SCLvRIRgmqtk+wA==, figureFileBig=JBLYMXelu8CZuHT17sy7wA==, tableContent=null), ArticleFig(id=1246028579721556802, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Table 1, caption=

Frequencies of the rectangular plate (φ=π/2)

, figureFileSmall=null, figureFileBig=null, tableContent=
阶次fPDOM（Hz）fFEM（Hz）相对误差（%）
1259.43260.240.311
2892.41884.850.854
31141.41136.80.405
42473.92460.00.565
52674.12650.90.875
63558.93545.10.389
74383.64369.50.323
84431.14392.40.881
), ArticleFig(id=1246028579822220100, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=表1, caption=

矩形板自振频率（φ=π/2）

, figureFileSmall=null, figureFileBig=null, tableContent=
阶次fPDOM（Hz）fFEM（Hz）相对误差（%）
1259.43260.240.311
2892.41884.850.854
31141.41136.80.405
42473.92460.00.565
52674.12650.90.875
63558.93545.10.389
74383.64369.50.323
84431.14392.40.881
), ArticleFig(id=1246028579889328966, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Table 2, caption=

Natural frequencies of the anisotropic rectangular cracked plate

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数φfPDOM（Hz）fFEM（Hz）相对误差（%）
1阶0368.53371.920.911
π/6333.18336.611.019
π/3269.06268.020.388
π/2234.40236.971.085
2阶01476.41476.70.020
π/61277.01272.70.338
π/3981.59984.720.318
π/2882.74884.360.183
3阶01493.21508.81.033
π/61418.81427.50.609
π/31188.31180.90.627
π/21048.91048.40.048
), ArticleFig(id=1246028579956437832, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=表2, caption=

各向异性矩形含裂缝板自振频率

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数φfPDOM（Hz）fFEM（Hz）相对误差（%）
1阶0368.53371.920.911
π/6333.18336.611.019
π/3269.06268.020.388
π/2234.40236.971.085
2阶01476.41476.70.020
π/61277.01272.70.338
π/3981.59984.720.318
π/2882.74884.360.183
3阶01493.21508.81.033
π/61418.81427.50.609
π/31188.31180.90.627
π/21048.91048.40.048
), ArticleFig(id=1246028580061295434, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=EN, label=Table 3, caption=

Natural frequencies of the anisotropic rectangular plate with a hole

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数φfPDOM（Hz）fFEM（Hz）相对误差（%）
1阶0387.88387.030.220
π/6352.15352.690.153
π/3283.87285.100.431
π/2251.29253.050.696
2阶01377.31379.40.152
π/61238.11236.60.121
π/3942.66940.470.233
π/2834.08832.010.249
3阶01591.61584.00.480
π/61459.21455.50.254
π/31263.01262.20.063
π/21160.01161.20.103
), ArticleFig(id=1246028580191318860, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246028561321144525, language=CN, label=表3, caption=

各向异性矩形含孔板自振频率

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数φfPDOM（Hz）fFEM（Hz）相对误差（%）
1阶0387.88387.030.220
π/6352.15352.690.153
π/3283.87285.100.431
π/2251.29253.050.696
2阶01377.31379.40.152
π/61238.11236.60.121
π/3942.66940.470.233
π/2834.08832.010.249
3阶01591.61584.00.480
π/61459.21455.50.254
π/31263.01262.20.063
π/21160.01161.20.103
)], attaches=null, journal=Journal(id=1241752460218384393, delFlag=0, nameCn=固体力学学报, nameEn=Chinese Journal of Solid Mechanics, nameHistory1=null, nameHistory2=null, issn=0254-7805, eissn=null, cn=42-1250/O3, coden=null, periodic=1, language=CN, oaType=null, ccby=null, superviseOffice=null, ownerOffice=null, pubOffice=null, editorOffice=null, officeType=null, aims=null, clcCode=null, officeProv=null, officeCity=null, officeAddr=null, officeZip=null, officeEmail=null, officePhone=null, editDirector=null, officeDirector=null, officeDirectorPhone=null, officeStaffNum=null, officeEmpNum=null, coverPicUrl=QijUwme6mcFRwEfHnJkyaw==, journalPrice=null, startedYear=null, abbrevIsoEn=Chinese Journal of Solid Mechanics, journalRemark=null, publicationField=null, createdTime=1773986457163, updatedTime=1773987385031, createdBy=18614031015, updatedBy=13701087609, firstLetterCn=C, firstLetterEn=C, subjectCode=Engineering, subjectName=null, subjectCodeEn=Engineering, subjectNameEn=null, picCn=QijUwme6mcFRwEfHnJkyaw==, picEn=3rj3gh183UJiEfa2LeH0yw==, jcr=null, cjcr=null, exts=[JournalExt(id=1241756352066941240, language=CN, name=固体力学学报, nameHistory1=null, nameHistory2=null, managedBy=, sponsoredBy=, publishedBy=, editorOffice=, officeProv=null, officeCity=null, officeAddr=, officeZip=, editDirector=, officeDirector=null, officePhone=null, coverPicUrl=null, journalRemark=, submitArticleUrl=null, websiteUrl=, createdTime=1773987385050, updatedTime=1773987385050, createdBy=13701087609, updatedBy=13701087609, submissionGuidelinesUrl=, submissionAuthorUrl=http://manu39.magtech.com.cn/Journalx_gtlxxb/authorLogOn.action, submissionEditorUrl=http://manu39.magtech.com.cn/Journalx_gtlxxb/editorLogOn.action, submissionReviewUrl=http://manu39.magtech.com.cn/Journalx_gtlxxb/expertLogOn.action, submissionCeEditorUrl=, submissionAeEditorUrl=, option={"copyright":""}), JournalExt(id=1241756352121467193, language=EN, name=Chinese Journal of Solid Mechanics, nameHistory1=null, nameHistory2=null, managedBy=, sponsoredBy=, publishedBy=, editorOffice=, officeProv=null, officeCity=null, officeAddr=, officeZip=, editDirector=, officeDirector=null, officePhone=null, coverPicUrl=null, journalRemark=, submitArticleUrl=null, websiteUrl=, createdTime=1773987385063, updatedTime=1773987385063, createdBy=13701087609, updatedBy=13701087609, submissionGuidelinesUrl=, submissionAuthorUrl=http://manu39.magtech.com.cn/Journalx_gtlxxb/authorLogOn.action, submissionEditorUrl=http://manu39.magtech.com.cn/Journalx_gtlxxb/editorLogOn.action, submissionReviewUrl=http://manu39.magtech.com.cn/Journalx_gtlxxb/expertLogOn.action, submissionCeEditorUrl=, submissionAeEditorUrl=, option={"copyright":""})], databaseList=null, tenantJournalId=1241755870837649424, websiteList=[Website(id=1241757301007242027, webName=null, webTitle=null, webDomain=null, webCopyrigh=null, webIpcNo=null, seoTitle=null, seoKeywords=null, seoDescription=null, tenantJournalId=null, journalId=1241755870837649424, journalNameCn=null, journalNameEn=null, grayFlag=null, tenantId=1146029695717560320, platformId=null, journalGroupId=null, journalGroupNameCn=null, journalGroupNameEn=null, type=1, domain=https://castjournals.cast.org.cn/joweb/gtlxxb/CN, language=CN, createTime=1773987611295, createBy=18614031015, updateTime=1773987633317, updateBy=18614031015, name=固体力学学报-中文, tplId=1146099689490845704, title=固体力学学报, delFlag=0, indexPage=/home, props=[WebsiteProps(id=1241757704407012157, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=articleTextType, value=kx, createTime=1773987707473, updateTime=1773987707473, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704386040634, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=banner, value=null, createTime=1773987707468, updateTime=1773987707468, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704427983680, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=grayFlag, value=0, createTime=1773987707478, updateTime=1773987707478, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704381846329, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=logo, value=https://castjournals.cast.org.cn/joweb/gtlxxb/CN/file/pic?fileId=gh/BtLvApxKS7pGvgd4faA==, createTime=1773987707467, updateTime=1773987707467, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704453149506, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=minRunFlag, value=0, createTime=1773987707484, updateTime=1773987707484, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704398623548, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=picServerUrl, value=https://castjournals.cast.org.cn/joweb/gtlxxb/CN/file/pic, createTime=1773987707471, updateTime=1773987707471, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704436372289, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=silenceFlag, value=0, createTime=1773987707481, updateTime=1773987707481, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704394429243, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=staticResourcePath, value=https://castjournals.cast.org.cn/joweb/cast_kjdb_cn_619/, createTime=1773987707470, updateTime=1773987707470, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704415400766, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=themeColor, value=null, createTime=1773987707475, updateTime=1773987707475, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757704423789375, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301007242027, code=themeStyle, value=null, createTime=1773987707477, updateTime=1773987707477, creator=18614031015, updator=18614031015)]), Website(id=1241757301070156588, webName=null, webTitle=null, webDomain=null, webCopyrigh=null, webIpcNo=null, seoTitle=null, seoKeywords=null, seoDescription=null, tenantJournalId=null, journalId=1241755870837649424, journalNameCn=null, journalNameEn=null, grayFlag=null, tenantId=1146029695717560320, platformId=null, journalGroupId=null, journalGroupNameCn=null, journalGroupNameEn=null, type=1, domain=https://castjournals.cast.org.cn/joweb/gtlxxb/EN, language=EN, createTime=1773987611311, createBy=18614031015, updateTime=1773987648333, updateBy=18614031015, name=固体力学学报-英文, tplId=1146101810881728533, title=Chinese Journal of Solid Mechanics, delFlag=0, indexPage=/home, props=[WebsiteProps(id=1241757732924093216, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=articleTextType, value=kx, createTime=1773987714272, updateTime=1773987714272, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732865372957, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=banner, value=null, createTime=1773987714258, updateTime=1773987714258, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732953453347, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=grayFlag, value=0, createTime=1773987714279, updateTime=1773987714279, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732836012828, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=logo, value=https://castjournals.cast.org.cn/joweb/gtlxxb/EN/file/pic?fileId=gh/BtLvApxKS7pGvgd4faA==, createTime=1773987714251, updateTime=1773987714251, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732966036261, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=minRunFlag, value=0, createTime=1773987714282, updateTime=1773987714282, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732911510303, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=picServerUrl, value=https://castjournals.cast.org.cn/joweb/gtlxxb/EN/file/pic, createTime=1773987714269, updateTime=1773987714269, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732961841956, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=silenceFlag, value=0, createTime=1773987714281, updateTime=1773987714281, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732903121694, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=staticResourcePath, value=https://castjournals.cast.org.cn/joweb/cast_kjdb_en_623/, createTime=1773987714267, updateTime=1773987714267, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732936676129, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=themeColor, value=null, createTime=1773987714275, updateTime=1773987714275, creator=18614031015, updator=18614031015), WebsiteProps(id=1241757732945064738, tenantId=1146029695717560320, journalId=null, journalGroupId=null, siteId=1241757301070156588, code=themeStyle, value=null, createTime=1773987714277, updateTime=1773987714277, creator=18614031015, updator=18614031015)])], journalTitle=固体力学学报, weixinUrl=null, journalUrl=http://manu39.magtech.com.cn/Jwk_gtlxxb, iacademicId=null, status=1, seqNo=null, journalTitleEn=Chinese Journal of Solid Mechanics, journalPhotoCn=QijUwme6mcFRwEfHnJkyaw==, journalPhotoEn=3rj3gh183UJiEfa2LeH0yw==, journalFirstLetter=C, journalRecommend=null, journalNew=null, journalCollection=null, jcrJf=null, cjcrJf=null, jcrJfStr=null, cjcrJfStr=null, submissionFirstDecision=null, sciSubjectClassification=null, casSubjectClassification=null, citeScore=null, totalCitationFrequency=null, icpCode=null, psCode=null, advertisingLicenseCode=null, copyrightInformation=null, country=null, option=, provinceCode=null, provinceName=null, collectFlag=false), detailUrlCn=https://castjournals.cast.org.cn/joweb/gtlxxb/CN/10.19636/j.cnki.cjsm42-1250/o3.2023.058, detailUrlEn=https://castjournals.cast.org.cn/joweb/gtlxxb/EN/10.19636/j.cnki.cjsm42-1250/o3.2023.058, pdfUrlCn=https://castjournals.cast.org.cn/joweb/gtlxxb/CN/PDF/10.19636/j.cnki.cjsm42-1250/o3.2023.058, pdfUrlEn=https://castjournals.cast.org.cn/joweb/gtlxxb/EN/PDF/10.19636/j.cnki.cjsm42-1250/o3.2023.058, aliStartDate=null, aliEndDate=null, collectionFlag=false, citedCount=null, citedUrl=null, reference=null)
收藏切换
基于近场动力学算子方法的各向异性板自由振动分析
收藏切换
PDF下载
陆炎洲 , 李志远 , 黄丹 ** , 姚学昊
固体力学学报 | 研究论文 2024,45(3): 341-351
收起
收藏切换
固体力学学报 | 研究论文 2024, 45(3): 341-351
基于近场动力学算子方法的各向异性板自由振动分析
全屏
陆炎洲, 李志远, 黄丹** , 姚学昊
作者信息
  • 河海大学工程力学系，南京，211100

通讯作者:

** E-mail：.
Free Vibration Analysis for Anisotropic Plates Based on Peridynamic Operator Method
Yanzhou Lu, Zhiyuan Li, Dan Huang** , Xuehao Yao
Affiliations
  • Department of Engineering Mechanics, Hohai University, Nanjing, 211100
出版时间: 2024-06-25 doi: 10.19636/j.cnki.cjsm42-1250/o3.2023.058
文章导航
收藏切换
摘要
收起

各向异性材料广泛应用于诸多工程领域，研究其振动特性对结构减振与安全设计具有重要意义. 本文基于一种新的近场动力学算子方法（Peridynamic operator method，PDOM）构建非局部各向异性模型，并应用于各向异性板的自由振动分析. 该模型结合了PDOM将局部微分及其乘积转化为非局部积分的特点，将经典各向异性理论中的应变能密度从局部形式重构为非局部形式. 同时，采用变分原理并引入自由振动方程，构建了适用于各向异性自由振动问题的PDOM求解方案. 通过三个数值算例：各向异性矩形薄板、各向异性矩形含裂纹板、各向异性矩形含孔板的自由振动，并将计算结果与有限元结果比较，说明了模型在计算含缺陷以及不连续的各向异性板自由振动问题时具有收敛性、稳定性以及高计算精度.

自由振动  /  各向异性  /  近场动力学算子方法  /  非局部  /  变分原理

Anisotropic materials find widespread applications across various engineering domains. The investigation on vibrational properties of anisotropic materials holds significance for structural vibration mitigation and safety design. This paper introduces a novel approach, the peridynamic operator method (PDOM), to construct a non-local anisotropic model and applies it to the analysis of free vibrations in anisotropic plates. The model incorporates the unique feature of PDOM, which transforms local differentials and their products into non-local integrals, thereby reformulating the strain energy density from its local form to a non-local form within classical anisotropic theory. Additionally, the paper employs a variational principle and introduces the free vibration equation to develop a PDOM solution for anisotropic free vibration problems. Three numerical examples are provided, including the free vibrations of a thin anisotropic rectangular plate, an anisotropic rectangular plate with cracks, and an anisotropic rectangular plate with holes. The results are compared with finite element results, showcasing the model's convergence, stability, and high computational accuracy in dealing with free vibrations of anisotropic plates with defects and discontinuities.

free vibration  /  anisotropic  /  PDOM  /  non-local  /  variational principle
陆炎洲, 李志远, 黄丹, 姚学昊. 基于近场动力学算子方法的各向异性板自由振动分析. 固体力学学报, 2024 , 45 (3) : 341 -351 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2023.058
Yanzhou Lu, Zhiyuan Li, Dan Huang, Xuehao Yao. Free Vibration Analysis for Anisotropic Plates Based on Peridynamic Operator Method[J]. Chinese Journal of Solid Mechanics, 2024 , 45 (3) : 341 -351 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2023.058
正文
收起
0　引言
收起
各向异性材料广泛应用于航空航天、船舶建造、建筑工程等领域[1,2]. 了解各向异性材料与结构的振动特性，进而采取合理有效的减振措施，具有理论和实践意义. 传统的经典数值方法在处理存在高阶导数和奇异点等情况的各向异性问题时，通常需要额外处理. 近年来，研究者尝试采用辛叠加法[3,4]、伽辽金法[5]、分离变量法[6]、微分求积法[7]和Rayleigh-Ritz法[8,9]等分析各向异性振动问题. 在新兴的数值方法中，近场动力学（Peridynamics，PD）[10,11]方法以其在处理非连续力学问题中的优势，近二十年来被广泛应用于冲击爆炸[12,13]、流固耦合[14,15]、水力劈裂[16,17]和热力耦合[18,19]等问题模拟. 针对振动问题，Diana[20]提出了一种正交各向异性微极PD模型进行含孔板的自由振动模态分析；吴林潮等[21]和Jafari等[22]分别基于PD理论分析了欧拉梁和铁木辛柯梁的自由振动特性；Heo等[23]应用PD方法分析了含裂纹板的自由振动. 在PD理论基础上，研究者近年又提出一些非局部建模和求解方法，典型如近场动力学微分算子[24,25]（Peridynamic differential operator，PDDO）和非局部算子方法[26,27]（Nonlocal operator method，NOM）. 受NOM的启发，Li等[28]进一步提出了键关联的弱形式PDDO，能有效抑制零能模式. 这些非局部建模分析方法近几年被成功应用于非线性热传导[29,30]，功能梯度材料力学行为[31,32]和流体运动[33,34]等问题分析.
结合PDDO和NOM这两种非局部算子方法各自的优势，Li等[35,36]最近提出了近场动力学算子方法（Peridynamic operator method，PDOM），不仅可将局部微分问题直接转化为相应的非局部积分形式，而且扩展适用于微分的乘积. 同时，采用PDOM可以直接重构各种物理问题的非局部模型，并确保消除零能模式的影响. 本文基于PDOM思想推导非局部各向异性模型，将传统各向异性理论从局部形式转化为非局部形式. 同时，利用变分原理并结合自由振动方程，构建了各向异性自由振动的非局部求解方案. 通过对各向异性矩形薄板、含裂缝板和含孔板的自由振动分析，验证了本文所重构模型和求解方法在分析含缺陷以及不连续各向异性自由振动问题方面的适用性和计算精度.
1　PDOM理论简述
收起
考虑二维空间中的向量函数u（x），如图1所示.
由一阶泰勒展开，可得：
其中，Hx表示点x的相互作用域. 将式（1）在Hx上积分，并考虑权函数以及相对位置ξT，得到：
其中，
从式（2）得到的非局部形式：
其中，
若使用二阶泰勒展开，则可得：
其中，
其中，是自定义的微分算子向量，是自定义的微分内积算子，满足性质：
将式（6）在Hx上积分，并考虑权函数以及相对位置矢量，得到：
其中，
则可从式（9）得到的非局部形式：
其中，
2　PDOM各向异性模型
收起
2.1　应变能密度
设二维空间中的各向异性材料，在整体坐标系x1Ox2和材料坐标系1O′2之间存在夹角φ，如图2所示.
在材料坐标系中，应力-应变关系可表示为：
其中，，分别为应力和应变，C为各向异性弹性系数矩阵，表示为：
在整体坐标系中，应力，应变，可分别表示为：
其中，Rm为坐标转换矩阵，可表示为：
将式（15）代入式（13），可得到：
其中，为整体坐标系下的各向异性弹性系数矩阵，可表示为：
应变能密度W可表示为：
应变-位移关系为为位移，L为微分算子矩阵，可表示为：
应变能密度可扩展为：
其中，D为对称微分算子矩阵，其组分可表示为：
其中表示矩阵L的第i列全部元素，是自定义针对微分的张量积算子，则矩阵D的上三角元素可表示为：
将式（22）代入式（21），可得到：
其中θ为体应变，可表示为：
其中
将式（4）代入式（25），可得：
将式（11）代入式（26）、式（27），可得：
其中，
各向异性材料的应变能密度的非局部形式，由式（5）、（12）、（24）、（28）-（30）构成.
2.2　求解方案
将式（28）和式（29）离散为：
其中，k表示Ω中第k个点，ηjk=uj-uk. 将式（31）写成矩阵形式：
式中
其中Nk表示Hk中点的个数，jik中的ji表示Hk中第i个物质点的全局索引. 将式（32）代入式（24），可得：
其中，
对于静力学问题，能量泛函可通过最小二乘原理表示为：
式中，表示边界∂Ωt上的牵引力. 将式（34）代入式（36）的离散形式，并令δΠ=0，可得：
其中，
式中，K表示整体刚度矩阵，Sk表示边界物质点xk的面积，Ntotal表示Ω中总物质点个数. 此处求和符号与有限元方法中的装配运算一致.
不考虑阻尼影响的自由振动方程的特征值形式可表示为：
求解式（39），可确定固有圆频率ω和固有振型φ，M为物质点质量矩阵，表示为：
其中，ρ为材料密度. 式（39）可写为标准特征值形式：
其中，H=M-1K，λ=ω2. 数值算法流程图如图3所示.
3　算例验证
收起
本节应用基于PDOM方法重构的非局部各向异性模型开展自由振动分析. 首先通过求解各向异性矩形薄板的自振频率，验证本文方法的准确性和收敛性. 其次，通过求解各向异性矩形含裂缝板和含孔板在不同各向异性偏角下的各阶自振频率，验证本文方法计算各向异性含缺陷结构自由振动问题的精确性，且通过模态分析，验证本文方法计算结果的连续性与稳定性. 算例中弹性刚度系数均取C11=15.32 GPa，C22=5.11 GPa，C66=4.8 GPa，C12=1.28 GPa，C16=0.16 GPa，C26=0.11 GPa. 材料密度ρ=2500 kg/m3. 自振频率的表达式为：
3.1　各向异性矩形薄板
矩形薄板尺寸为L=0.4 m，W=0.2 m，左端固定. 整体坐标系和材料坐标系之间的夹角为φ=π/2. PDOM数值计算中，将矩形板均匀离散为5000个物质点. 离散间距Δx=4 mm，近场范围尺寸取δ=3Δx. 为进行对比，同时进行有限元计算，矩形板被离散为11486个三角形单元，单元边长为4 mm.
表1中给出了各向异性矩形薄板前8阶自振频率，并与有限元解进行对比. 从表中可以看出，PDOM解与有限元解非常一致，最大相对误差为0.881%.
分别取不同的离散间距Δx=4 mm、6 mm、8 mm、10 mm，图4为前三阶自振频率的相对误差. 从图中可以看出，相对误差随着物质点离散间距的减小而快速减小，说明本方法具有较好的收敛性.
3.2　各向异性矩形含裂缝板
考虑各向异性矩形含裂缝板的自由振动，几何条件如图5所示. L=0.4 m，W=0.2 m，板中心裂缝长度m=0.2 m，宽度n=4 mm，左端固定. PDOM数值计算中，将含裂缝矩形板均匀离散为4900个物质点. 离散间距Δx=4 mm，近场范围尺寸取δ=3Δx. 有限元计算中，含裂缝矩形板被离散为10912个三角形单元，单元边长为4 mm.
表2给出了含裂缝板在偏角φ=0，π/6，π/3，π/2下前3阶自振频率的PDOM和FEM计算结果. 从表中可以看出，前3阶自振频率最大相对误差为1.085%，本文方法所得结果与FEM高度吻合. 图6给出了各向异性偏角φ=π/3时PDOM与FEM前3阶全位移模态. 可以看出，前3阶PDOM与FEM的位移模态结果吻合，模态位移场规则、连续.
3.3　各向异性矩形含孔板
考虑各向异性矩形含孔板的自由振动，几何条件如图7所示. L=0.4 m，W=0.2 m，中心圆孔半径为a=0.04 m，左端固定. r和ϕ分别为相应极坐标系中的极径与极角. PDOM数值计算中，将含孔矩形板均匀离散为4668个物质点. 离散间距Δx=4 mm，近场范围尺寸取δ=3Δx. 有限元计算中，含孔矩形板被离散为10566个三角形单元，单元边长为4 mm.
表3给出了含孔板在偏角φ=0，π/6，π/3，π/2下前3阶自振频率的PDOM和FEM计算结果. 从表中可以看出，前3阶自振频率最大相对误差为0.696%，本文方法所得结果与FEM高度吻合. 图8给出了含孔板的前3阶位移模态在r=0.07 m，0≤ϕ≤π处分布的FEM与PDOM数值结果对比. 图9给出了含孔板在不同偏角下的第3阶位移模态在r=0.07 m，0≤ϕ≤π处分布的FEM与PDOM数值结果对比. 可以看出，在偏角φ=π/2情况下，前3阶径向位移模态ur和环向位移模态uϕ的PDOM与FEM结果基本一致；在偏角φ=0，π/6，π/3，π/2下，第3阶径向位移模态ur和环向位移模态uϕ的PDOM与FEM结果吻合. 图10给出了偏角φ=π/6时PDOM与FEM前3阶全位移模态. 可以看出，前3阶PDOM与FEM的位移模态结果基本一致，且模态位移场规则、连续、稳定，没有出现明显的数值振荡.
4　结论
收起
基于近场动力学算子方法，本文提出了一种新颖的非局部各向异性模型，并应用于各向异性板自由振动问题的研究. 通过结合PDOM的特性，即将局部微分及其乘积转化为非局部积分，本文将经典各向异性理论中关于应变能密度的局部表达重新构建为非局部形式. 同时，借助变分原理并引入自由振动方程，构建了适用于解决各向异性自由振动问题的PDOM数值求解方案. 通过计算各向异性矩形薄板的自由振动问题，证明了该方法具备较好的准确性和收敛性. 通过计算各向异性矩形含裂缝板和各向异性矩形含孔板的自由振动问题，将所提模型的计算结果与有限元分析结果进行了对比. 结果表明，本文提出的模型在处理含缺陷、不连续各向异性板自由振动问题时表现出色，具备了较好的稳定性和连续性，且能够获得高度精确的计算结果.
基金
收起
  • 中央高校基本科研业务费专项资金(B240201144)
  • 国家自然科学基金项目(12071204)
文献
收起
参考文献 引证文献
排序方式：
[1]
Mandal T K, Nguyen V P, Wu J Y. A length scale insensitive anisotropic phase field fracture model for hyperelastic composites[J]. International Journal of Mechanical Sciences, 2020, 188: 105941.
[2]
王久法. 正交各向异性声源膜板的自由振动特性分析[J]. 振动与冲击, 2021, 40(22): 216-220+266.
(Wang J F. Free vibration characteristics analysis of orthotropic sound source plates[J]. Journal of Vibration and Shock, 2021, 40(22): 216-220+266. (in Chinese))
[3]
Su X, Bai E. Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method[J]. Journal of Vibration and Control, 2022, 28(1-2): 3-16.
[4]
Su X, Bai E, Hai G J. Unified solution of some problems of rectangular plates with four free edges based on symplectic superposition method[J]. Engineering Computations, 2023, 40(6): 1330-1350.
[5]
Kumar V, Singh S J, Saran V H, Harsha S P. Vibration response of the exponential functionally graded material plate with variable thickness resting on the orthotropic Pasternak foundation[J]. Mechanics Based Design of Structures and Machines, 2023,
[6]
Hu Z Y, Du J Y, Liu M F, Li Y H, Wang Z X, Zheng X R, Bui T Q, Li R. Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions[J]. Scientific Reports, 2023, 13(1): 2601.
[7]
Hou S X, Li M H, Luo J J, Kiani Y. Numerical modeling of vibration and damping of higher-order magnetorheological elastomer polar orthotropic composite sectorial/annular plates[J]. Thin-walled Structures, 2023, 188: 110825.
[8]
Bai Y, Li H. Vibration characteristics analysis of anisotropic metal rubber medium-thick cylindrical shells[J]. Archive of Applied Mechanics, 2023,
[9]
Strozzi M, Smirnov V V, Pellicano F, Kovaleva M. Nonlocal anisotropic elastic shell model for vibrations of double-walled carbon nanotubes under nonlinear van der Waals interaction forces[J]. International Journal of Non-linear Mechanics, 2022, 146: 104172.
[10]
Silling S A. Reformulation of elasticity theory for discontinuities and long-range forces[J]. Journal of the Mechanics and Physics of Solids, 2000, 48: 175-209.
[11]
黄丹, 章青, 乔丕忠, 沈峰. 近场动力学方法及其应用[J]. 力学进展, 2010, 40(4): 448-459.
(Huang D, Zhang Q, Qiao P Z, Shen F. A review on peridynamics (PD) method and its applications[J]. Advances in Mechanics, 2010, 40(4): 448-459. (in Chinese))
[12]
Wu L W, Wang H, Huang D, Cai X, Guo J B. A reformulated non-ordinary state-based peridynamic method for dynamic failure of ductile materials[J]. Engineering Fracture Mechanics, 2023, 283: 109196.
[13]
Ma Q P, Wu L W, Huang D. An extended peridynamic model for dynamic fracture of laminated glass considering interfacial debonding[J]. Composite Structures, 2022, 290: 115552.
[14]
Yao X H, Huang D. Coupled PD-SPH modeling for fluid-structure interaction problems with large deformation and fracturing[J]. Computers and Structures, 2022, 270: 106847.
[15]
姚学昊, 陈丁, 武立伟, 黄丹. 流固耦合破坏分析的多分辨率PD-SPH方法[J]. 力学学报, 2022, 54(12): 3333-3343.
(Yao X H, Chen D, Wu L W, Huang D. A multi-resolution PD-SPH coupling approach for structural failure under fluid-structure interaction[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3333-3343. (in Chinese))
[16]
张钰彬, 黄丹. 页岩水力压裂过程的态型近场动力学模拟研究[J]. 岩土力学, 2019, 40(7): 2873-2881.
(Zhang Y B, Huang D. State-based peridynamic study on the hydraulic fracture of shale[J]. Rock and Soil Mechanics, 2019, 40(7): 2873-2881. (in Chinese))
[17]
Zhang Y B, Huang D, Cai Z, Xu Y P. An extended ordinary state -based peridynamic approach for modelling hydraulic fracturing[J]. Engineering Fracture Mechanics, 2020, 234: 107086.
[18]
Wang H, Xu Y P, Huang D. A non-ordinary state-based peridynamic formulation for thermo-visco-plastic deformation and impact fracture[J]. International Journal of Mechanics Sciences, 2019, 159: 336-344.
[19]
He D W, Huang D, Wu L W, Xu Y P. Investigation on thermal failure of functionally graded materials using fully coupled thermo-mechanical peridynamics[J]. Composite Structures, 2023, 305: 116454.
[20]
Diana V, Casolo S. A full orthotropic micropolar peridynamic formulation for linearly elastic solids[J]. International Journal of Mechanics Sciences, 2019, 160: 140-155.
[21]
吴林潮, 吴志渊, 张文明. 基于近场动力学的梁结构振动特性分析方法研究[J]. 固体力学学报, 2021, 42(4): 467-475.
(Wu L C, Wu Z Y, Zhang W M. Vibration analysis method of beam structure in peridynamics[J]. Chinese Journal of Solid Mechanics, 2021, 42(4): 467-475. (in Chinese))
[22]
Jafari A, Ezzati M, Atai A A. Static and free vibration analysis of Timoshenko beam based on combined peridynamic-classical theory besides FEM formulation[J]. Computers and Structures, 2019, 213: 72-81.
[23]
Heo J, Yang Z H, Xia W X, Oterkus S, Oterkus E. Free vibration analysis of cracked plates using peridynamics[J]. Ships and Offshore Structures, 2020, 15(1): 220-229.
[24]
Madenci E, Barut A, Futch M. Peridynamic differential operator and its applications[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 408-451.
[25]
Madenci E, Barut A, Dordunce M. Peridynamic differential operator for numerical analysis[M]. Switzerland: Springer Nature Switzerland AG, 2019.
[26]
Ren H L, Zhuang X Y, Rabczuk T. A higher order nonlocal operator method for solving partial differential equations[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 367: 113132.
[27]
Ren H L, Zhuang X Y, Rabczuk T. A nonlocal operator method for solving partial differential equations[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 358: 112621.
[28]
Li Z Y, Huang D, Ren H L, Rabczuk T. Weak form of bond-associated peridynamic differential operator for solving differential equations[J]. Engineering with Computers, 2022,
[29]
Zhou B L, Li Z Y, Xu Y P, Huang D. Analysis of nonlinear heat conduction problems with temperature-dependent conductivity using peridynamic differential operator[J]. International Journal of Applied Mechanics, 2022, 14(5): 2250047.
[30]
周保良, 李志远, 黄丹. 二维瞬态热传导的PDDO分析[J]. 应用数学与力学, 2022, 43(6): 660-668.
(Zhou B L, Li Z Y, Huang D. PDDO analysis of 2D transient heat conduction problems[J]. Applied Mathematics and Mechanics, 2022, 43(6): 660-668. (in Chinese))
[31]
Li Z Y, Huang D, Xu Y P, Yan K H. Nonlocal steady-state thermoelastic analysis of functionally graded materials by using peridynamic differential operator[J]. Applied Mathematical Modelling, 2021, 93: 294-313.
[32]
Li Z Y, Huang D, Yan K H, Xu Y P. Large deformation analysis of functionally graded beam with variable cross-section by using peridynamic differential operator[J]. Composite Structures, 2022, 279: 114788.
[33]
Gao Y, Oterkus S. Multi-phase fluid flow simulation by using peridynamic differential operator[J]. Ocean Engineering, 2020, 216: 108081.
[34]
Nguyen C T, Oterkus S, Oterkus E, Amin I, Ozdemir M, El-Aassar A H, Shawky H. Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator[J]. Ocean Engineering, 2021, 239: 109815.
[35]
李志远, 黄丹, Rabczuk T. 近场动力学算子方法[J]. 力学学报, 2023, 55(07): 1593-1603.
(Li Z Y, Huang D, Rabczuk T. Peridynamic operator method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(07): 1593-1603. (in Chinese))
[36]
Li Z Y, Huang D, Rabczuk T. Peridynamic operator method[J]. Computer Methods in Applied Mechanics and Engineering, 2023, 411: 116047.
2024年第45卷第3期
PDF下载
40
19
引用本文
BibTeX
文章信息
doi: 10.19636/j.cnki.cjsm42-1250/o3.2023.058
  • 接收时间：2023-12-06
  • 首发时间：2026-04-01
  • 出版时间：2024-06-25
补充材料
相关文章
文章信息
作者
出版历史
  • 收稿日期：2023-12-06
基金
中央高校基本科研业务费专项资金(B240201144)
国家自然科学基金项目(12071204)
作者信息
    河海大学工程力学系，南京，211100

通讯作者:

** E-mail：.
参考文献
分享链接
https://castjournals.cast.org.cn/joweb/gtlxxb/CN/10.19636/j.cnki.cjsm42-1250/o3.2023.058
分享至
全文二维码

扫描看全文

引用本文
BibTeX
本文的引用情况
2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
关闭全屏
相关链接
论文
最新文章
热读文章
热点专题
内参
蓝皮书
产业发展报告
传播力报告
期刊分级目录
资讯
学术新闻
行业新闻
学术会议
行业会议
关于
关于我们
联系我们
北京市海淀区学院南路86号
100081
010-62199257
qkjq@cast.org.cn

中国科学技术协会版权所有 京ICP 备10216604号-4 海淀分局备案 1101084647
科技导报社主办 中国科协信息中心技术支持