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Article(id=1320423066698629661, tenantId=1146029695717560320, journalId=1319355204128309394, issueId=1320423027695792874, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1001-4837.2026.02.006, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1759593600000, receivedDateStr=2025-10-05, revisedDate=1767715200000, revisedDateStr=2026-01-07, acceptedDate=null, acceptedDateStr=null, onlineDate=1792742991374, onlineDateStr=2026-10-23, pubDate=1772208000000, pubDateStr=2026-02-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792742991374, onlineIssueDateStr=2026-10-23, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792742991374, creator=13701087609, updateTime=1792742991374, updator=13701087609, issue=Issue{id=1320423027695792874, tenantId=1146029695717560320, journalId=1319355204128309394, year='2026', volume='43', issue='2', pageStart='1', pageEnd='86', issueExtLink='null', onlineDate='null', pubDate='1772208000000', pubDateStr='2026-02-28', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1792742982076, creator='13701087609', updateTime=1792745307038, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1320432779335156588, tenantId=1146029695717560320, journalId=1319355204128309394, issueId=1320423027695792874, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1320432779335156589, tenantId=1146029695717560320, journalId=1319355204128309394, issueId=1320423027695792874, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=61, endPage=70, ext={EN=ArticleExt(id=1320423068573483550, articleId=1320423066698629661, tenantId=1146029695717560320, journalId=1319355204128309394, language=EN, title=Analysis of ultimate pressure‑bearing capacity of cylindrical shells with rectangular tangential nozzles, columnId=1320422992044217077, journalTitle=Pressure Vessel Technology, columnName=Designs & Analyses, runingTitle=null, highlight=null, articleAbstract=

Rectangular tangential nozzles are often used as special process interfaces in petrochemical equipment（such as multiphase flow cyclone separators），but their structural strength design has not been clearly specified in design codes such as GB/T 150.The finite element limit load analysis method was used to calculate the pressure‑bearing capacity of cylindrical shells with rectangular tangential nozzles，and the weakening effects of rectangular tangential nozzles with different dimensionless structural parameters（width‑to‑diameter ratio W/Di，diameter‑to‑thickness ratio Di/T，and thickness ratio t/T） on the strength of the cylindrical shell were investigated.It was found that the cylindrical shell with a square tangential nozzle having a side length ratio of 1 has the maximum pressure‑bearing capacity.Therefore，a limit load reduction factor reflecting the strength reduction of the cylindrical shell due to the provision of a square tangential nozzle was defined.The influences of the three dimensionless structural parameters W/Di，Di/T，and t/T were studied，and regression analysis was performed on the limit load reduction factor based on a large number of numerical calculations.This is helpful for the strength design or safety assessment of cylindrical shells with square tangential nozzles.It was also found that for the same opening area，the pressure‑bearing capacity of the cylindrical shell structure with a square tangential nozzle is significantly lower than that with a circular tangential nozzle.In other words，the strength weakening effect of a square tangential nozzle on the cylindrical shell is significantly greater than that of a circular tangential nozzle.Therefore，from a strength perspective，using a circular tangential nozzle is more reasonable than using a square tangential nozzle.

, authors=Wei CHEN, Hongjie YU, Zhiwei WU, Caifu QIAN, authorsList=Wei CHEN, Hongjie YU, Zhiwei WU, Caifu QIAN, authorCompany=null, correspAuthors=Zhiwei WU, 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, fund=null), CN=ArticleExt(id=1320423071031345723, articleId=1320423066698629661, tenantId=1146029695717560320, journalId=1319355204128309394, language=CN, title=带矩形切向接管圆柱壳极限承压能力分析, columnId=1320422992211989239, journalTitle=压力容器, columnName=设计计算, runingTitle=null, highlight=null, articleAbstract=

矩形切向接管常常作为特殊工艺接口应用于石化设备（如多相流旋风分离器）中，但其结构强度设计在GB/T 150等设计规范中尚无明确规定。采用有限元极限载荷分析方法，计算带矩形切向接管的圆柱壳承压能力，并探讨不同无量纲结构参数（宽径比W/Di、径厚比Di/T、厚度比t/T）的矩形切向接管对圆柱壳强度的削弱作用。结果发现，矩形边长比为1的带正方形切向接管圆柱壳承压能力最大。为此，定义了反映圆柱壳因开设正方形切向接管而导致强度下降的极限载荷折减率，研究了W/Di，Di/T和t/T三个无量纲结构参数的影响，并在大量数值计算基础上，对极限载荷折减率进行了回归分析，这有助于带正方形切向接管圆柱壳强度设计或安全评定。同时还发现，对于相同开孔面积，带正方形切向接管圆柱壳结构承压能力明显小于带圆形切向接管结构承压能力，或者说，正方形切向接管对圆柱壳的强度削弱作用显著大于圆形切向接管，所以从强度角度考虑，开设圆形切向接管比正方形切向接管更合理。

, authors=陈伟, 于洪杰, 吴志伟, 钱才富, authorsList=陈伟, 于洪杰, 吴志伟, 钱才富, authorCompany=null, correspAuthors=吴志伟, authorNote=

陈伟（1993），男，主要研究方向为压力容器有限元分析和计算机辅助工程，通信地址：100029北京市朝阳区北三环东路15号北京化工大学东校区，E-mail：。

, correspAuthorsNote=
吴志伟（1992），男，博士，主要从事压力容器分析设计等工作，通信地址：100029北京市朝阳区北三环东路15号北京化工大学东校区，E-mail：。
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陈伟（1993），男，主要研究方向为压力容器有限元分析和计算机辅助工程，通信地址：100029北京市朝阳区北三环东路15号北京化工大学东校区，E-mail：。

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陈伟（1993），男，主要研究方向为压力容器有限元分析和计算机辅助工程，通信地址：100029北京市朝阳区北三环东路15号北京化工大学东校区，E-mail：。

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pressure vessel with special tangential nozzle, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1320423071341724220, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, xref=null, ext=[AuthorCompanyExt(id=1320423071350112829, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, companyId=1320423071341724220, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=College of Mechanical and Electrical Engineering，Beijing University of Chemical Technology，Beijing 100029，China), AuthorCompanyExt(id=1320423071358501438, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, companyId=1320423071341724220, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=北京化工大学 机电工程学院，北京 100029)])], figs=[ArticleFig(id=1320423074428731996, 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tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=EN, label=Tab.1, caption=

Material parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
材料允许应力/MPa屈服极限/MPa切向模量/MPa泊松比密度/（kg⋅m-3）杨氏模量/GPa
Q345R189283.500.37850197
16Mn181271.500.37850197
), ArticleFig(id=1320423078383960697, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=CN, label=表1, caption=

材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料允许应力/MPa屈服极限/MPa切向模量/MPa泊松比密度/（kg⋅m-3）杨氏模量/GPa
Q345R189283.500.37850197
16Mn181271.500.37850197
), ArticleFig(id=1320423078459458170, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=EN, label=Tab.2, caption=

Range of dimensionless parameters for the finiteelement model

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
W/Di0.14，0.21，0.28，0.35，0.42
t/T0.50，0.75，1.00，1.25，1.50，1.75
Di/T71.43，83.33，100.00，125.00
), ArticleFig(id=1320423078526567035, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=CN, label=表2, caption=

有限元模型无量纲参数取值范围

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
W/Di0.14，0.21，0.28，0.35，0.42
t/T0.50，0.75，1.00，1.25，1.50，1.75
Di/T71.43，83.33，100.00，125.00
), ArticleFig(id=1320423078602064508, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=EN, label=Tab.3, caption=

Limit loads of circular cylinder shells

, figureFileSmall=null, figureFileBig=null, tableContent=
项目筒体厚度/mm
1412108
极限载荷/MPa9.027.756.475.19
Miss计算应力/MPa287.4286.9286.2285.4
), ArticleFig(id=1320423078694339197, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=CN, label=表3, caption=

无接管筒体结构极限载荷

, figureFileSmall=null, figureFileBig=null, tableContent=
项目筒体厚度/mm
1412108
极限载荷/MPa9.027.756.475.19
Miss计算应力/MPa287.4286.9286.2285.4
), ArticleFig(id=1320423078769836670, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=EN, label=Tab.4, caption=

Verification of regression equation

, figureFileSmall=null, figureFileBig=null, tableContent=
W/Dit/TDi/T极限载荷P1/MPaK有限元解/%K公式解/%相对误差/%
0.190.990.913.78046.9149.174.82
0.330.9111.110.88884.6983.401.52
0.261.490.914.34039.0440.363.38
0.361.4111.111.76869.5267.413.04
), ArticleFig(id=1320423078849528447, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=CN, label=表4, caption=

回归方程验证

, figureFileSmall=null, figureFileBig=null, tableContent=
W/Dit/TDi/T极限载荷P1/MPaK有限元解/%K公式解/%相对误差/%
0.190.990.913.78046.9149.174.82
0.330.9111.110.88884.6983.401.52
0.261.490.914.34039.0440.363.38
0.361.4111.111.76869.5267.413.04
), ArticleFig(id=1320423078941803136, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=EN, label=Tab.5, caption=

Limit load and limit load reduction factor of cylindrical shells with different shell diameters di but the same dimensionless numbers

, figureFileSmall=null, figureFileBig=null, tableContent=
W/Dit/TDi/TDi/mmT/mm带切向接管极限载荷P1/MPa圆柱壳极限载荷Po/MPaK有限元解/%K公式解/%相对误差/%
0.141 40.510050051.7526.4772.9271.871.44
0.141 40.51001 000101.7046.4773.6671.872.43
0.141 40.51001 500151.8156.4771.9571.870.11
0.212 00.7510050051.8006.4772.1869.154.20
0.212 00.751001 000101.7806.4772.4969.154.61
0.212 00.751001 500151.8606.4771.2569.152.95
0.282 81.2510050052.8026.4756.6956.680.02
0.282 81.251001 000102.7606.4757.3456.681.15
0.282 81.251001 500152.8086.4756.6056.680.14
0.353 61.510050052.5806.4760.1259.021.83
0.353 61.51001 000102.5406.4760.7459.022.83
0.353 61.51001 500152.5866.4760.0359.021.68
), ArticleFig(id=1320423079050855041, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=CN, label=表5, caption=

相同无量纲数下不同筒体直径Di的圆柱壳极限载荷和极限载荷折减率

, figureFileSmall=null, figureFileBig=null, tableContent=
W/Dit/TDi/TDi/mmT/mm带切向接管极限载荷P1/MPa圆柱壳极限载荷Po/MPaK有限元解/%K公式解/%相对误差/%
0.141 40.510050051.7526.4772.9271.871.44
0.141 40.51001 000101.7046.4773.6671.872.43
0.141 40.51001 500151.8156.4771.9571.870.11
0.212 00.7510050051.8006.4772.1869.154.20
0.212 00.751001 000101.7806.4772.4969.154.61
0.212 00.751001 500151.8606.4771.2569.152.95
0.282 81.2510050052.8026.4756.6956.680.02
0.282 81.251001 000102.7606.4757.3456.681.15
0.282 81.251001 500152.8086.4756.6056.680.14
0.353 61.510050052.5806.4760.1259.021.83
0.353 61.51001 000102.5406.4760.7459.022.83
0.353 61.51001 500152.5866.4760.0359.021.68
), ArticleFig(id=1320423079117963906, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=EN, label=Tab.6, caption=

Values of dimensionless structural parameters in thefinite element model of square tangential nozzle

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
W/Di0.150，0.186，0.221，0.257
t/T0.50，0.75，1.00，1.25，1.50，1.75
Di/T71.43，83.33，100.00，125.00
), ArticleFig(id=1320423079180878467, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=CN, label=表6, caption=

正方形切向接管有限元模型中无量纲结构参数取值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
W/Di0.150，0.186，0.221，0.257
t/T0.50，0.75，1.00，1.25，1.50，1.75
Di/T71.43，83.33，100.00，125.00
), ArticleFig(id=1320423079264764548, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=EN, label=Tab.7, caption=

Values of dimensionless structural parameters in thefinite element model of circular tangential nozzle

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
d0/Di0.17，0.21，0.25，0.29
t/T0.50，0.75，1.00，1.25，1.50，1.75
Di/T71.43，83.33，100.00，125.00
), ArticleFig(id=1320423079331873413, tenantId=1146029695717560320, journalId=1319355204128309394, articleId=1320423066698629661, language=CN, label=表7, caption=

圆形切向接管有限元模型中无量纲结构参数取值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值
d0/Di0.17，0.21，0.25，0.29
t/T0.50，0.75，1.00，1.25，1.50，1.75
Di/T71.43，83.33，100.00，125.00
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带矩形切向接管圆柱壳极限承压能力分析
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陈伟 , 于洪杰 , 吴志伟 , 钱才富
压力容器 | 设计计算 2026,43(2): 61-70
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压力容器 |设计计算 2026 , 43 (2) : 61 -70
带矩形切向接管圆柱壳极限承压能力分析
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陈伟 , 于洪杰, 吴志伟 , 钱才富
作者信息
  • 北京化工大学 机电工程学院，北京 100029
通讯作者:
吴志伟（1992），男，博士，主要从事压力容器分析设计等工作，通信地址：100029北京市朝阳区北三环东路15号北京化工大学东校区，E-mail：。
作者简介:

陈伟（1993），男，主要研究方向为压力容器有限元分析和计算机辅助工程，通信地址：100029北京市朝阳区北三环东路15号北京化工大学东校区，E-mail：。

Analysis of ultimate pressure‑bearing capacity of cylindrical shells with rectangular tangential nozzles
Wei CHEN , Hongjie YU, Zhiwei WU , Caifu QIAN
Affiliations
  • College of Mechanical and Electrical Engineering，Beijing University of Chemical Technology，Beijing 100029，China
出版时间: 2026-02-28 doi: 10.3969/j.issn.1001-4837.2026.02.006
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摘要
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矩形切向接管常常作为特殊工艺接口应用于石化设备（如多相流旋风分离器）中，但其结构强度设计在GB/T 150等设计规范中尚无明确规定。采用有限元极限载荷分析方法，计算带矩形切向接管的圆柱壳承压能力，并探讨不同无量纲结构参数（宽径比W/Di、径厚比Di/T、厚度比t/T）的矩形切向接管对圆柱壳强度的削弱作用。结果发现，矩形边长比为1的带正方形切向接管圆柱壳承压能力最大。为此，定义了反映圆柱壳因开设正方形切向接管而导致强度下降的极限载荷折减率，研究了W/Di，Di/T和t/T三个无量纲结构参数的影响，并在大量数值计算基础上，对极限载荷折减率进行了回归分析，这有助于带正方形切向接管圆柱壳强度设计或安全评定。同时还发现，对于相同开孔面积，带正方形切向接管圆柱壳结构承压能力明显小于带圆形切向接管结构承压能力，或者说，正方形切向接管对圆柱壳的强度削弱作用显著大于圆形切向接管，所以从强度角度考虑，开设圆形切向接管比正方形切向接管更合理。

切向接管  /  圆柱壳  /  极限载荷分析  /  承压能力

Rectangular tangential nozzles are often used as special process interfaces in petrochemical equipment（such as multiphase flow cyclone separators），but their structural strength design has not been clearly specified in design codes such as GB/T 150.The finite element limit load analysis method was used to calculate the pressure‑bearing capacity of cylindrical shells with rectangular tangential nozzles，and the weakening effects of rectangular tangential nozzles with different dimensionless structural parameters（width‑to‑diameter ratio W/Di，diameter‑to‑thickness ratio Di/T，and thickness ratio t/T） on the strength of the cylindrical shell were investigated.It was found that the cylindrical shell with a square tangential nozzle having a side length ratio of 1 has the maximum pressure‑bearing capacity.Therefore，a limit load reduction factor reflecting the strength reduction of the cylindrical shell due to the provision of a square tangential nozzle was defined.The influences of the three dimensionless structural parameters W/Di，Di/T，and t/T were studied，and regression analysis was performed on the limit load reduction factor based on a large number of numerical calculations.This is helpful for the strength design or safety assessment of cylindrical shells with square tangential nozzles.It was also found that for the same opening area，the pressure‑bearing capacity of the cylindrical shell structure with a square tangential nozzle is significantly lower than that with a circular tangential nozzle.In other words，the strength weakening effect of a square tangential nozzle on the cylindrical shell is significantly greater than that of a circular tangential nozzle.Therefore，from a strength perspective，using a circular tangential nozzle is more reasonable than using a square tangential nozzle.

tangential nozzle  /  cylindrical shell  /  limit load analysis  /  pressure‑bearing capacit
陈伟, 于洪杰, 吴志伟, 钱才富. 带矩形切向接管圆柱壳极限承压能力分析. 压力容器, 2026 , 43 (2) : 61 -70 . DOI: 10.3969/j.issn.1001-4837.2026.02.006
Wei CHEN, Hongjie YU, Zhiwei WU, Caifu QIAN. Analysis of ultimate pressure‑bearing capacity of cylindrical shells with rectangular tangential nozzles[J]. Pressure Vessel Technology, 2026 , 43 (2) : 61 -70 . DOI: 10.3969/j.issn.1001-4837.2026.02.006
正文
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0　引言
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压力容器在石油化工、核工业等领域起着重要作用，因特定功能需要，压力容器常需在非轴对称位置上设置异形接管（如矩形切向、椭圆形斜接、带折边偏心接管等）。由于接管与筒体相交区域形成突变曲率界面，会在筒体与接管连接区产生局部高应力，容易使设备发生强度失效，因此，有必要对接管连接部位进行应力分析和强度校核。目前，国内外针对径向接管的应力分析与评定准则已经有完善的分析方法［1-3］，且有成熟的设计标准。但矩形切向接管由于结构特殊，目前缺失相应强度设计规范，也无法按照GB/T 150—2024《压力容器》中的补强方法进行精确设计。
有限元法和基于应力分类的设计方法相结合，为解决切向接管这种特殊结构强度设计和安全评定提供了可靠技术路径。目前，国内外已有不少研究采用极限载荷法对设备接管结构进行应力分析和强度设计。王志亮等［4-5］采用正交试验对径向接管有限元模型进行无量纲分析，拟合回归方程，并采用电阻应变测量技术验证了公式的正确性。段成红等［6］以大直径的径向双开口接管结构为研究对象，研究了3个无量纲数对应力集中系数K的影响，以此为基础对接管壁厚补强进行优化。PRAKASH等［7］利用极限载荷法研究了圆形接管在不同倾角组合下的极限载荷，得出对于所有角度组合，当a=45°和b=90°时，获得的极限载荷值最小，因此这种组合在设计时应避免。XUE等［8］通过对47种几何模型、4种材料（20低碳钢和A672，Q235A，304SS）的3组无量纲参数化研究，提出了相关系数达0.999的爆破压力预测公式，其中，容器径厚比对爆破压力影响最显著。应超［9］采用有限元软件对切向接管进行分析评定，发现接管与筒体的结构相交位置容易破坏，其中以相交的锐角区域应力集中现象最为显著，并指出切向接管因结构不规则和容易形成大开孔（长短径比常大于2），导致常规计算方法（等面积法、压力面积法等）存在局限。古晋斌等［10］以某旋风分离器上的矩形接管为研究对象，对比线弹性应力分析和弹塑性极限载荷法两种分析方法，发现采用弹塑性极限载荷法可以显著降低矩形接管厚度；同时基于极限载荷法研究发现，矩形接管直角边圆角、长宽比及矩形接管布置方式均会对结构极限承载能力产生影响。孙志刚等［11］采用有限元分析平台，对封头切向接管结构采用弹性应力分析与极限载荷计算两种分析方法，研究结果表明，基于传统弹性应力分析法得到的结果有很大安全余量，采用极限载荷分析方法，在保证应力强度分析完整性同时，还可保证分析设计结果的可信度与工程适用性。赵晓凤等［12］针对带圆形切向接管结构的内压圆柱壳，采用极限载荷有限元法对圆形切向接管进行分析，定义并拟合了关于强度削弱系数K=φ（d/D，t/T，D/T）经验关系式，为带圆形切向接管内压圆筒的强度设计校核提供工程参考依据。
鉴于矩形切向接管在工程上有较多应用，特别是用在旋风分离器结构中（见图1）。而目前针对矩形切向接管结构强度设计缺少规范标准。因此，本文以石化行业旋风器为原型，采用极限载荷分析法，研究带矩形切向接管结构的圆柱壳极限承压能力，探讨矩形切向接管对圆柱壳强度的削弱作用，并重点研究正方形接管承压能力及其影响因素，定义极限载荷折减率并拟合回归方程，为带正方形切向接管筒体结构的强度设计和安全评定提供参考依据。
1　有限元模型的建立
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1.1　几何模型
文中所分析的矩形切向接管结构由圆柱形筒体（Q345R）和矩形切向接管（16Mn）组成，其材料参数见表1［13-14］。极限载荷分析的应力-应变模型采用理想弹塑性模型，Q345R和16Mn的应力-应变曲线见图2。考虑到矩形切向接管结构的对称性，选择1/2结构建模分析，鉴于圣维南原理的局部效应，筒体和正方形接管的几何建模长度均远大于2.5RT［15］（R为圆柱壳半径；T为圆柱壳有效厚度）。
文中定义矩形切向接管结构沿圆柱壳轴向方向（Y轴）的边长为L，与之相垂直方向（X轴）的边长为W。有限元几何模型如图3所示。
保持圆柱形筒体直径Di=1 000 mm，定义3个关于切向接管结构无量纲数：矩形切向接管边长与筒体直径宽径比W/Di、矩形切向接管与筒体厚度比t/T、筒体直径和壁厚比Di/T（其中，W为切向接管边长；t为切向接管壁厚；T为筒体厚度）。W/Di，t/T，Di/T取值范围如表2所示。根据参数取值范围，建立120个正方形切向接管分析模型。
1.2　网格模型
考虑到切向接管与筒体相交区域出现突变曲率界面且材料为非线性［12］，选用高阶Solid 186单元，同时在几何不连续区域（应力集中区域）进行局部网格细化，并验证网格无关性，以提高数值模拟精度。图4示出矩形边长比为1的有限元网格划分模型。
1.3　载荷及约束条件
在对称面施加对称边界条件，在几何结构内表面施加压力载荷P，在筒体圆环面施加等效接管应力载荷P2，在矩形切向接管端面施加等效接管应力载荷P3，约束筒体下端面沿轴向位移及绕轴向旋转，如图5所示。
P2和P3计算公式如下［10］：
P2=-PDi2Do2-Di2
P3=-PA0A
式中，P2为圆柱壳上端面施加的等效轴向拉应力载荷，MPa；P为几何模型内表面施加的压力载荷，MPa；Di为圆柱形筒体内径，mm；Do为圆柱形筒体外径，mm；P3为矩形切向接管端部等效接管拉应力载荷，MPa；A0为矩形切向接管内表面围成部分的截面面积，mm²；A为矩形切向接管截面面积，mm²。
2　极限载荷分析及矩形切向接管圆柱壳承压能力计算
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2.1　极限载荷分析法及验证
压力容器分析设计中的极限载荷法能够计算结构在失效前的最大承载能力。极限载荷分析本质属于塑性力学范畴，基于理想弹塑性本构关系，并考虑几何非线性效应。通过逐步增加载荷直至结构发生整体塑性破坏，从而确定其极限载荷［16］。
通过对比无接管筒体极限载荷有限元解和理论解验证本文数值模拟的可信性，同时给出了极限载荷及极限状态下Miss理论应力计算值［17］，如表3所示。可以看出，不同极限载荷下Miss理论应力相对误差均小于1.5%，表明数值模拟和极限分析是准确可信的。
2.2　带矩形切向接管圆柱壳承压能力计算
先计算带不同矩形切向接管圆柱壳结构的极限载荷。为此，保持矩形切向接管的截面面积相同（80 000 mm²），固定结构参数（Di/T=83.33，t/T=1），改变矩形切向接管边长比L/W，分别为0.25（141.5 mm×565.5 mm），0.5（200 mm×400 mm），1（282.8 mm×282.8 mm），2（400 mm×200 mm），3（490 mm×163 mm），4（565.5 mm×141.5 mm），计算不同L/W下结构的极限载荷，结果如图6所示。可以看出，当矩形切向接管边长比为1（即正方形接管）时，结构承压能力最好。因此，若要开设矩形孔，采用正方形结构对圆柱壳的强度削弱最小。图7示出极限载荷作用下带矩形切向接管筒体结构上的von Mises云图。可以看出，大面积屈服出现在接管筒体相交区域，这是因为该区域因结构不连续所产生的应力较大。
由于矩形接管结构和方位变化大，同时正方形承压能力最大，因此，文中重点研究带正方形切向接管圆柱壳结构极限承压能力及其影响因素。
2.3　矩形切向接管折边过渡圆角的影响
接管与壳体连接区域可能为圆角过渡，选取某一结构参数（L/W=2，W/Di=0.2，Di/T=83.33，t/T=1），矩形切向接管折边过渡圆角半径r与切向接管边长W的比值r/W为0，0.05，0.075，0.1，0.125，0.15，0.175和0.2（即r取值范围为0~40 mm），分别研究了不同过渡圆角对矩形切向接管的极限载荷的影响，其结果如图8所示。可以看出，随着矩形切向接管直角边过渡圆角增大，结构不连续性得到改善，矩形切向接管的极限承载能力随着过渡圆角比值r/W近线性增加。
图9示出r/W=0.2时，在极限载荷作用下的von Mises等效应力云图。
极限载荷受矩形切向接管和圆柱形筒体相交部分影响最大，接管和筒体相切部分内侧最先发生屈服。但在本文后续研究中，尤其强度公式拟合中将不引入过渡圆角变量，原因包括：
（1）若引入过渡圆角变量，总的变量由3个变成4个，计算工作量成倍增加，强度公式拟合难度也显著增大；
（2）在实际结构中，由于制造加工缘由，过渡圆角可能达不到设计要求；
（3）忽略过渡圆角的影响，得到的强度公式是偏于保守的。
3　带正方形切向接管圆柱壳承压能力计算
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3.1　极限载荷参数分析
保持圆柱壳内径Di=1 000 mm不变，3个无量纲参数取值见表2，对120个带正方形切向接管圆柱壳有限元模型进行极限载荷分析。图10示出带正方形切向接管筒体结构的承压能力随3个无量纲数的变化。
可以看出，正方形切向接管的边长越长、厚度越小，圆柱壳的承压能力越小。图11示出某一结构参数（W/Di=0.28，t/T=1.5，Di/T=83.33）极限载荷分析过程中，正方形切向接管和圆柱形筒体相交区域的载荷-位移曲线。
3.2　极限载荷折减率定义及其受结构无量纲数的影响
为定量计算正方形切向接管对结构极限载荷的影响，定义极限载荷折减率：
K=P0-P1P0×100%
式中，P0为无接管圆筒极限载荷，MPa；P1为带正方形切向接管圆筒极限载荷，MPa。
从定义可以看出，极限载荷折减率K越小，则正方形切向接管对筒体承压能力折减越小。
图12示出正方形切向接管圆柱壳结构不同W/Di，t/T，Di/T对圆柱壳极限载荷折减率K的影响曲线。可以看出，极限载荷折减率K随W/Di和Di/T增大而增大，随t/T增大而减小。由于正方形切向接管和圆柱形筒体相交区域对极限载荷影响最大，因此，正方形切向接管无量纲数W/Di和t/T对极限载荷影响要大于Di/T。
3.3　正方形切向接管极限载荷折减率回归方程拟合
以圆柱壳极限载荷折减率K为指标，给定L/W=1，r/W=0，以W/Di，t/T，Di/T为变量，拟合K的关联式，为带正方形切向接管的内压圆筒强度设计及安全评定提供参考。
3.3.1　极限载荷折减率回归方程的确定
运用多因素统计方法中的三因素方差，分析无量纲数W/Di，t/T，Di/T对内压筒体极限载荷折减率K的影响关系，可以得到三因素概率值p均小于0.05。分析结果表明，3个无量纲数均有显著性，说明W/Di，t/T，Di/T均会对极限载荷折减率K产生影响。其对K影响由大到小顺序为t/T>W/Di>Di/T，且W/Di和Di/T与K呈现强正相关关系，t/T与K呈现强负相关关系。
基于大量数值计算，运用Origin数据分析软件，采用多种模型对K进行回归分析。经过多次尝试，得到如下回归方程。
当t/T=0.5~1，W/Di=0.14~0.28时：
K=135.476 7-936.793 5W/Di2-0.133 6W/Di2.3×Di/T1.75+93.983 8Di/T0.1t/T4+278.563 2W/Di0.2Di/T0.2-414.442 8×W/Di0.65t/T5+1 923.3W/Di2t/T2-396.992 1Di/T0.1t/T0.25
当t/T=0.5~1，W/Di=0.28~0.42时：
K=99.903 9+32.631 2W/Di-0.1160 1Di/T-32.990 7t/T-84.391 9t/T2+0.684 1×Di/Tt/T-0.986 7W/Dit/TDi/T+178.907 6W/Dit/T2
当t/T=1~1.75，W/Di=0.14~0.28时：
K=-142.058 1+1 212.7W/Di2.1+128.809 1×W/Di1.8Di/T0.3t/T0.1-0.086 4t/T2.5+151.960 3W/Di0.15Di/T0.1+232.399
  ×W/Di2.2t/T2.8-1 468W/Di2t/T  -10.349 8Di/T0.15t/T0.15
当t/T=1~1.75，W/Di=0.28~0.42时：
K=-1.733-91.706 6W/Di2-1 104.2W/Di4.5×Di/T0.25t/T0.1+7.892 6t/T3+37.041W/Di0.1Di/T0.35-2 080.6W/Di2.25×t/T1.25+3 503.2W/Di2.5t/T-53.842 8Di/T0.15t/T0.75
需要强调的是，上述回归方程适用于正方形切向接管，其应用范围为W/Di=0.14~0.42，Di/T=71.43~125.00，t/T=0.5~1.75。
3.3.2　极限载荷折减率回归方程的验证
为验证拟合回归方程式（4）~（7）的准确性和适用性，再建立4组不同结构参数有限元模型进行有限元模拟和公式数值验证，结果见表4。可以看出，回归方程极限载荷折减率公式数值解和有限元解相对误差均在5%以内。
3.3.3　筒体直径的影响
由于采用无量纲数进行参数化分析，拟合得到的极限载荷折减率公式不仅适用于内径1 000 mm的圆筒，还适用于其他内径。表5列出保持W/Di，t/T，Di/T相同，筒体直径分别为500，1 000，1 500 mm时极限载荷和极限载荷折减率的计算结果。
可以看出，保持W/Di，t/T，Di/T相同，圆柱壳极限载荷值不受筒体直径影响，同时极限载荷折减率K回归方程解和有限元模拟解相对误差均在5%以内。因此，对于不同筒体直径的正方形切向接管结构，当W/Di，t/T，Di/T均在本文取值范围内时，公式（4）~（7）仍然有效。
4　不同结构参数正方形和圆形切向接管极限载荷对比
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在工程实际中，切向接管可能是方形的，也可能是圆形的。赵晓凤等［12］对带圆形切向接管的圆柱壳进行了极限载荷分析，定义并拟合得到了强度削弱系数。当矩形边长比为1时，正方形切向接管极限承压能力最好。为了给工程设计提供参考，比较了相同开孔面积下正方形切向接管和圆形切向接管的极限载荷。同样保持圆柱壳内径Di=1 000 mm不变，开孔面积S分别为22 686.5，34 618.5，49 062.5，66 018.5 mm²，正方形切向接管和圆形切向接管具体几何参数分别如表6、表7所示（表7中，d0表示圆形切向接管的内径）。
为了定量比较相同开孔面积下正方形切向接管和圆形切向接管极限载荷，引入强度比例系数（R）：
R=P1P4×100%
式中，P4为圆形切向接管极限载荷。
从定义可以看出，强度比例系数R越大，则说明正方形切向接管极限载荷P1越接近圆形切向接管极限载荷P4。
图13示出相同截面面积条件下，不同结构参数正方形切向接管极限载荷和圆形切向接管极限载荷比值。可以看出，对于相同开孔面积，正方形切向接管圆柱壳极限载荷均小于圆形切向接管极限载荷，或者说，正方形切向接管对圆柱壳的强度削弱作用要大于圆形切向接管，并且开孔面积越大，差值越大。这个结果是合理的，因正方形接管由平板构成，受压时以弯曲应力为主，与圆柱壳连接时变形协调量大，受压时会因变形不协调而产生较大附加应力。因此，从强度角度考虑，开设圆形切向接管比正方形切向接管更合理。另外，t/T越小，正方形切向接管极限载荷和圆形切向接管极限载荷差距越大；当t/T超过一定值时，正方形切向接管和圆形切向接管的极限载荷差值减小，并趋于稳定。
图14示出相同截面面积（80 000 mm²）正方形和圆形切向接管极限载荷应力云图。可以看出，无论是正方形，还是圆形切向接管，影响结构极限承载力的强度薄弱区域都是在切向接管和壳体的连接部位。
5　结论
收起
（1）在带矩形切向接管圆柱壳结构中，边长比为1的正方形切向接管结构承压能力最好，因此，若要开设矩形孔，采用正方形结构对圆柱壳的强度削弱最小。分析发现，对极限载荷起控制作用的大面积屈服出现在接管和筒体连接部位。
（2）定义了反映带正方形切向接管对圆柱壳承载性能影响的极限载荷折减率，并研究了无量纲结构参数对极限载荷折减率的影响。
（3）在数值模拟基础上，拟合得到了带正方形切向接管圆柱壳承压能力极限载荷折减率回归方程，并对回归方程进行了数值验证，证明了回归方程的精确性，可以为带正方形切向接管圆柱壳结构的强度设计和安全评定提供参考。
（4）对于相同开孔面积，带正方形切向接管圆柱壳承压能力小于带圆形切向接管圆柱壳承压能力，或者说，正方形切向接管对圆柱壳的强度削弱作用要大于圆形切向接管，并且开孔面积越大，接管相对壁厚（t/T）越小，差值越大。因此，从强度角度考虑，开设圆形切向接管比正方形切向接管更合理。

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2026年第43卷第2期
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doi: 10.3969/j.issn.1001-4837.2026.02.006
  • 接收时间：2025-10-05
  • 首发时间：2026-10-23
  • 出版时间：2026-02-28
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  • 收稿日期：2025-10-05
  • 修回日期：2026-01-07
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    北京化工大学 机电工程学院，北京 100029

通讯作者:

吴志伟（1992），男，博士，主要从事压力容器分析设计等工作，通信地址：100029北京市朝阳区北三环东路15号北京化工大学东校区，E-mail：。
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