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The stability of thin plates plays an important role in ship design and strength check. To investigate the shear stability of ship's thin plates, a picture frame fixture was designed to conduct an in-plane shear buckling test on square thin plates. In the test, 3D Digital Image Correlation (3D-DIC) was used to obtain mechanical response information such as load-end elongation curve, full-field displacement/strain, etc. The load-end elongation relationship reveals the load-bearing characteristics of the thin plate under in-plane shear condition and determines the critical load for buckling instability. According to the displacement and strain field information of the thin plate at typical moments, it is found that the normal deformation of the thin plate increases with the increase of in-plane shear load. After the instability of the thin plate, there are three half-waves symmetrically distributed along the vertical diagonal, and the internal wave amplitude is greater than the external wave amplitude. The strain waveform and contour plot tend to stabilize during the post-buckling process. By analyzing the response curves of the normal displacement and Mises strain at the key points of the thin plate with time, a new method for identifying the buckling instability of in-plane sheared thin plates was proposed and verified. This study provides a useful reference for experimental research and mechanical behavior analysis of in-plane shear stability for ship’s thin plates.

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板结构的稳定性在船舶设计和强度校核中占据重要地位。为研究船体薄板的剪切稳定性,本文设计画框式夹具对方形薄板进行面内剪切屈曲试验,试验中采用三维数字图像相关法(3 Dimensions Digital Image Correlation,简称3D-DIC),获得了载荷-端部伸长率曲线、全场位移/应变等力学响应信息。载荷-端部伸长率关系揭示了薄板在面内剪切工况下的承载特性,确定了屈曲失稳临界载荷;通过分析薄板在典型时刻的位移场、应变场信息,发现薄板的法向变形会随面内剪切载荷增加而增大。薄板失稳后,沿垂直对角线存在对称分布的三个半波,内部波幅大于外部波幅,应变波形和云图在后屈曲过程中会趋于稳定。通过分析薄板关键点的法向位移和米塞斯应变随时间的响应曲线,提出并验证了一种识别面内受剪薄板屈曲失稳的新方法。本文为船用薄板面内剪切稳定性的试验研究和力学行为分析等提供了有益参考。

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通讯作者,E-mail:
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李晓文(1985-),女,博士,副教授

朱兆一(1987-),男,硕士,实验师,通讯作者,E-mail:

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基于3D-DIC方法的船体薄板剪切稳定性试验研究
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李晓文 1, 2 , 朱兆一 1, 2 , 彭苗娇 1, 2 , 陈清林 1, 2 , 蔡应强 1, 2 , 李妍 1, 2
船舶力学 | 结构力学 2025,29(10): 1608-1617
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船舶力学 | 结构力学 2025, 29(10): 1608-1617
基于3D-DIC方法的船体薄板剪切稳定性试验研究
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李晓文1, 2, 朱兆一1, 2 , 彭苗娇1, 2, 陈清林1, 2, 蔡应强1, 2, 李妍1, 2
作者信息
  • 1.集美大学 轮机工程学院,福建 厦门 361021
  • 2.福建省船舶与海洋工程重点实验室,福建 厦门 361021
  • 李晓文(1985-),女,博士,副教授

    朱兆一(1987-),男,硕士,实验师,通讯作者,E-mail:

通讯作者:

通讯作者,E-mail:
Experimental study on the shear stability of ship's thin plate using 3D-DIC method
Xiao-wen LI1, 2, Zhao-yi ZHU1, 2 , Miao-jiao PENG1, 2, Qing-lin CHEN1, 2, Ying-qiang CAI1, 2, Yan LI1, 2
Affiliations
  • 1.School of Marine Engineering, Jimei University, Xiamen 361021, China
  • 2.Fujian Provincial Key Laboratory for Naval Architecture and Ocean Engineering, Xiamen 361021, China
出版时间: 2025-10-20 doi: 10.3969/j.issn.1007-7294.2025.10.010
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板结构的稳定性在船舶设计和强度校核中占据重要地位。为研究船体薄板的剪切稳定性,本文设计画框式夹具对方形薄板进行面内剪切屈曲试验,试验中采用三维数字图像相关法(3 Dimensions Digital Image Correlation,简称3D-DIC),获得了载荷-端部伸长率曲线、全场位移/应变等力学响应信息。载荷-端部伸长率关系揭示了薄板在面内剪切工况下的承载特性,确定了屈曲失稳临界载荷;通过分析薄板在典型时刻的位移场、应变场信息,发现薄板的法向变形会随面内剪切载荷增加而增大。薄板失稳后,沿垂直对角线存在对称分布的三个半波,内部波幅大于外部波幅,应变波形和云图在后屈曲过程中会趋于稳定。通过分析薄板关键点的法向位移和米塞斯应变随时间的响应曲线,提出并验证了一种识别面内受剪薄板屈曲失稳的新方法。本文为船用薄板面内剪切稳定性的试验研究和力学行为分析等提供了有益参考。

剪切稳定性  /  薄板  /  3D-DIC方法  /  屈曲

The stability of thin plates plays an important role in ship design and strength check. To investigate the shear stability of ship's thin plates, a picture frame fixture was designed to conduct an in-plane shear buckling test on square thin plates. In the test, 3D Digital Image Correlation (3D-DIC) was used to obtain mechanical response information such as load-end elongation curve, full-field displacement/strain, etc. The load-end elongation relationship reveals the load-bearing characteristics of the thin plate under in-plane shear condition and determines the critical load for buckling instability. According to the displacement and strain field information of the thin plate at typical moments, it is found that the normal deformation of the thin plate increases with the increase of in-plane shear load. After the instability of the thin plate, there are three half-waves symmetrically distributed along the vertical diagonal, and the internal wave amplitude is greater than the external wave amplitude. The strain waveform and contour plot tend to stabilize during the post-buckling process. By analyzing the response curves of the normal displacement and Mises strain at the key points of the thin plate with time, a new method for identifying the buckling instability of in-plane sheared thin plates was proposed and verified. This study provides a useful reference for experimental research and mechanical behavior analysis of in-plane shear stability for ship’s thin plates.

shear stability  /  thin plate  /  3D-DIC method  /  buckling
李晓文, 朱兆一, 彭苗娇, 陈清林, 蔡应强, 李妍. 基于3D-DIC方法的船体薄板剪切稳定性试验研究. 船舶力学, 2025 , 29 (10) : 1608 -1617 . DOI: 10.3969/j.issn.1007-7294.2025.10.010
Xiao-wen LI, Zhao-yi ZHU, Miao-jiao PENG, Qing-lin CHEN, Ying-qiang CAI, Yan LI. Experimental study on the shear stability of ship's thin plate using 3D-DIC method[J]. Journal of Ship Mechanics, 2025 , 29 (10) : 1608 -1617 . DOI: 10.3969/j.issn.1007-7294.2025.10.010
在船体结构设计和强度校核中,结构的稳定性至关重要。众多船舶海损事故表明,船体结构的破坏通常不是强度不足引起的,而是因为结构失去了稳定性。当船体发生总纵弯曲或扭转时,船体外板可能承受轴向压缩载荷或剪切载荷,当轴向压应力或剪应力达到一定数值时,船体外板将发生失稳现象[1-2]
一直以来,薄壁结构的稳定性始终都是国内外学者关注的热点[3-4]。以往研究主要侧重加筋板结构的屈曲和后屈曲问题。赵伟等[5]通过约束加筋钢板反对称中心处的转动自由度,限制钢板的刚性转动位移,对加筋钢板剪力墙模型进行了有限元弹性屈曲分析。金阳等[6]通过带斜加强筋矩形板模型模拟楔形腹板的纯剪应力状态,对其弹性屈曲进行数值分析。李晓文等[7]采用ABAQUS软件研究了复合材料船舶加筋板的屈曲、后屈曲行为。史旭东[8]采用有限元软件NASTRAN对复合材料板壳结构的稳定性进行了分析。彭艺琳等[9]基于力学实验和数值模拟,研究剪切载荷下铝锂合金加筋壁板的屈曲与后屈曲行为。在板的稳定性研究方面,Roberts等通过有限元方法研究了开孔板在面内载荷作用下的弹性屈曲问题。朱兆一、李晓文等[10-11]通过力学试验和数值仿真等手段,研究了船舶开孔薄板的面内稳定性问题。冯亮等[12]采用ABAQUS软件分析了船体板格模型在轴压作用下的极限强度。夏劲松等[13]分析了无筋板格在复杂应力状态下的弹性屈曲及后屈曲行为,并与经验公式及ABS规范进行比较研究。孙璐妍[14]将近场动力学应用于金属板的轴压稳定性分析。Renu等[15]运用伽辽金法求解剪应力作用下矩形板的弹塑性屈曲问题。Jaberzadeh等[16]用微分求积法求解剪应力作用下各向异性矩形板的屈曲问题。杨端生等[17]建立了矩形薄板剪切屈曲横向位移函数的微分方程,运用配点法及屈曲变形的反对称特性,简化求解齐次线性代数方程系数矩阵行列式,得到矩形板屈曲临界载荷的解析解。Pham[18]研究了开孔方板的剪切屈曲特性,并给出了关于剪切屈曲系数的近似表达式。
受剪应力作用的局部矩形薄壁板件广泛存在于船舶、建筑等工程结构中,局部板件屈曲失稳已成为工程结构破坏的主要形式之一。以往研究多针对拉、压、弯等载况,关于剪切工况下的薄板失稳问题,学者多用有限元法、解析方法、微分求积法以及伽辽金法等来进行分析。一般来说,解析方法常需要进行编程运算,有限元法[19-20]虽然避免了屈曲分析繁琐的程序编制,但模型大小以及复杂程度、边界条件约束和载荷环境等因素也会对计算精度产生较大影响,因而离不开力学试验进行佐证。
为此,本文针对船体薄板的面内剪切工况,设计制作了画框式夹具,采用对角拉伸方式对方形薄板进行剪切稳定性试验。试验过程中应用3D-DIC方法对受剪区域的全场变形进行测量、分析,重点研究船用薄板在面内剪切载荷工况下的屈曲特性,为船用薄板的面内剪切稳定性研究、薄壁结构优化设计等提供有益参考。
3D-DIC方法即三维数字图像相关方法,其本质是基于光学的全场表面位移和应变的测量方法。简言之,是对涂有随机散斑图案的物体在未变形和变形状态下的两个图像之间的模式匹配。先用立体匹配方法进行左、右图像的相关匹配,再基于时序匹配方法进行物体变形前后图像的相关匹配,通过立体视觉技术进行三维重建,基于三维重建后的结果计算位移和变形。DIC方法的基本原理是在未变形和变形状态下,搜索被测物图像子集之间的最大相关性。如图1所示,基于子集之间的相关性,可以计算分析区域中不同位置的位移场。最简单的图像匹配程序是交叉相关,通过匹配两个图像的不同区域,可以计算出平面内的位移场uxy)和vxy)。相关系数C(uv)如公式(1)所示,用于数字图像上的子区域的相关性计算。
式中,fxy)、gx'y')分别表示参考图像和变形图像的灰度,分别是参考子集和变形子集的平均灰度值。x'y'的表达式为:
式中,u0v0分别是子集中心沿xy方向的平移量,分别是图像子区的位移梯度。
图2所示即试验过程中应用的3D-DIC三维全场变形测量-分析系统。图中,左、右相机为图像采集终端,用于拍摄被测量板,并将图像传输至DIC测量分析系统的控制终端,对采集到的图像进行识别处理。左、右相机与水平面之间的夹角θ均为25°,测量距离d为742.17 mm。系统通过左、右相机实时采集试样表面各个形变阶段的散斑图像。控制终端通过XTDIC-CONST分析软件利用数字图像相关算法实现物体表面变形点的匹配,根据各点的视差数据,重建物面计算点的三维坐标;并通过比较每一变形状态测量区内各点的三维坐标,得到物面的位移场,进一步计算得到物面应变场。如图3所示,DIC方法的具体测量分析过程包括相机标定、图像采集、创建散斑块、构建种子点、求解计算以及后处理等内容。
舷侧列板是船体结构抵抗剪切变形的主要构件,必须满足抗剪稳定性要求。如图4所示,船体板的四周由船体骨材、舱壁等强力构件支撑,当对边的支撑结构(加强筋)发生相对位移时,船体板将受到剪切载荷的作用。由于四周加强筋的刚度远大于船体板,当板失稳后,加强筋沿板边方向的变形很小,此时,可认为板四边受均布剪力作用。研究船体薄板的剪切稳定性时,要充分考虑支撑结构对薄板的约束形式及效果。本文舷侧薄板单元的结构形式与受载工况参见图4
试验过程中,为保证受剪板单元四周承受均布剪应力,需要设计能与画框式夹具匹配的剪切试样,如图5所示。其中,板中有310×310 mm的受剪区,受剪区四周有310×40 mm的加载区,加载区上设有多个螺栓孔,尽量保证均匀受力。鉴于电子万能试验机WDW-100C的载荷承受能力,并参考文献[10-11],试验件的厚度选取1 mm,材料为Q235A冷轧钢板。
3D-DIC系统利用双目立体视觉技术拍摄被测物表面图像,并识别物体表面特征,从而计算出物体表面的应变。测量前,要确保被测物表面图像具有足够的清晰度。为此,必须在被测物表面喷涂白色底漆和黑色散斑。已完成底漆喷涂和散斑处理的试验样品如图6所示。
为研究方形薄板在面内剪切载荷下的屈曲行为,要求板的四边简支并限制扭转,剪应力均匀作用在板四周的边界上。由此可见,薄板剪切屈曲试验的难度较高。为保证方形薄板四周承受均布剪应力,设计对角拉伸式的画框式试验夹具,使试验机的拉力沿夹具的剪力板传递到试验件上。如图7所示,试验件的四边通过56组螺栓固定在四块剪力板上,每对剪力板在端部相互铰接,连成一体。加载时试验机横梁上升并提供拉力P,在剪力板的作用下拉力P沿板边方向分解为Txy,使得方形薄板承受剪切载荷作用。受剪区沿对垂直角线Π受拉,沿水平对角线Ι受压。
试验前将方形薄板与画框式夹具进行组装,通过扭力扳手对56组螺栓均匀施加足够的预紧力,确保在试验过程中夹具与试样之间不发生滑移,然后将画框式夹具两对角端的接头与电子万能试验机相连,并在试验件正前方特定位置布设DIC检测设备。如图8所示,试验中,选用WDW-100C电子万能试验机,最大负荷是100 kN,试验中,设置的加载速度向上为2 mm/min,并应用XTDIC-CONST三维全场应变测量-分析系统实时监测试验件表面位移场和应变场的变化情况,系统每隔500 ms采集1组照片,并实时传输至3D-DIC测量-分析系统的控制终端,进行图像识别处理。
图9所示为船用薄板的载荷(P)-端部伸长率(γ)曲线及其斜率变化曲线。其中,P-γ曲线通过试验机时间-载荷数据与DIC时间-伸长率数据二次匹配获得;P为端部拉伸载荷;γ为对角线伸长率,它表示试样垂直对角线上下对角点的位移伸长量与原始对角线长之比。斜率变化曲线的横轴为端部伸长率,纵轴对应P-γ曲线上各个点的斜率。分析斜率曲线发现,A、B、C、D四点是P-γ曲线上斜率发生突变的点。通过3D-DIC测量-分析系统分别提取与A、B、C、D四点对应的四个时刻的全场法向位移云图,如图10所示。为了便于表征,本文将这四个时刻分别命名为A、B、C、D。其中,位移沿z轴为正,即沿面板法向涂散斑的一侧为正。由图9可见,随着载荷增加,曲线0A段存在明显线性关系,当载荷增加至A点(P=14.6 kN)时,P-γ曲线的斜率开始发生突变,结构刚度随之减小。A点作为P-γ曲线的第一个斜率突变点,通常认为此刻结构产生屈曲失稳并取该点载荷作为结构的屈曲失稳载荷(Pcr)。随着载荷继续增加,P-γ曲线AB段仍近似保持线性关系,直至载荷增加至B点(P=26.0 kN)。对比此刻的位移云图,波形与A时刻相近,法向位移继续增加。随着法向变形增大,P-γ曲线BC段线性关系逐渐消失,当载荷增至C点(P=35.7 kN)时,曲线斜率发生了较大变化,结构刚度明显减小;曲线CD段斜率变化相对和缓,仅在载荷增至D点(P=62.3 kN)时,产生较小的突变,结构刚度又一次减小。
对比图10中法向位移云图发现,船用薄板的法向变形随着外载荷的增加而增大,且薄板失稳后,一直存在沿对角线呈对称分布的半波。为进一步探究薄板的面内剪切屈曲特性,分析薄板试验后的变形特征,将剪切试验后的薄板实物图与图9中E点(P-γ曲线的终点)的法向位移云图进行对比研究。图11为失效后试验板的波形情况,对比试验板的失效波形与E点法向位移,发现二者波形较为一致。如图11(a)所示,在垂直对角线Π上存在一个半波,该波形中心点位移最大,向上下两端逐渐减小,波形沿水平对角线Ι呈对称分布。在水平对角线Ι上存在3个半波,中心点波幅最大,左右两侧波形沿垂直对角线Π呈对称分布,且波幅较小。这一观察结果与图11(a)中所示的试验件实物图相符。
本文基于P-γ曲线,提取了A、B、C、D四个时刻的位移场,进行更深入分析。如图12所示,基于3D-DIC测量-分析系统,分别提取这四点对应的水平对角线Ι和垂直对角线Π的法向位移。从图12(b)可见,在垂直对角线上存在一个波幅不断增加的半波,该波形的中心点位移最大,并向两端逐渐减小,其波形云图沿水平对角线Ι呈对称分布。如图12(a)所示,水平对角线Ι上存在3个半波,中心点波幅最大,左右两侧波形沿垂直对角线Π呈对称分布,且波幅较小。3个波的幅值也随载荷增加而增大。该结果与图10所示的位移场云图一致。
根据图12所示,随着外载荷增加,水平对角线Ι上法向位移变化更为剧烈,为此,基于DIC全场应变测量数据,进一步研究受剪薄板变形场的变化情况。
(1)对角线变形
提取对角线Ι在A、B、C、D这四个时刻的米塞斯应变值及应变场云图,分别如图13图14所示。图13所示随着载荷增加,对角线上的应变波形逐渐趋于稳定。对应时刻A、B,薄板刚发生屈曲失稳时,对角线上存在应变幅值不大的微小波动且波动较频繁,水平对角线中点处存在峰值。对应时刻C、D,应变波形较一致并趋于稳定,仅应变幅值随外载荷增加而明显增大。水平对角线上存在沿垂直对角线对称分布的内大、外小3个较为稳定的峰值,这一结果与图12(a)一致,即法向位移较大处对应存在应变峰值。为确定应变波形稳定的临界时刻,统计图14中A时刻至D时刻内,水平对角线上各节点的平均应变随时间的变化情况,如图15所示。从时刻A至Stage50,该曲线近似呈线性关系;而从Stage50至时刻D,曲线则保持线性关系,且以Stage50处的应变形貌趋于稳定。图15中的应变云图与图14中D时刻较一致。
(2)关键点变形
考虑到试验薄板的几何对称性和受力特点,本文分析了水平对角线Ι上O点和M点的变形特征。其中,O点为对角线中点,M点在对角线1/4处。提取O点和M点的法向位移和米塞斯应变,并绘制其随时间变化的曲线,如图16~17所示。由图可见,两点的位移和应变均在Stage20(A时刻)处发生突变,由P-γ曲线可知,Stage20对应A时刻,此时结构发生屈曲失稳。因此,利用关键点的法向位移和应变信息,可对薄板的剪切失稳进行准确判断。基于DIC检测设备和力学试验机的时间同步信息,我们确定了受剪薄板的临界失稳载荷为14.6 kN,与上文结果一致。
本文基于3D-DIC方法、画框式夹具试验工装,通过对角拉伸方式,对船用薄板进行了面内剪切稳定性试验,试验中,我们研究了方形金属薄板的屈曲、后屈曲行为,并获得了载荷-端部伸长率曲线、临界屈曲载荷等力学响应特征,以及典型时刻和关键位置的全场位移/应变数据,主要结论如下:
(1)通过面内载荷随对角线端部伸长率变化曲线和板面法向位移云图,明确了薄板面内剪切工况下的承载特性,并获得了方形薄板屈曲失稳的临界载荷为14.6 kN;
(2)对比四个典型时刻的全场法向位移,发现方形薄板的法向位移会随面内载荷的增加而增大,且在其失去稳定性后,位移云图的波形较稳定,存在沿垂直对角线对称分布的3个半波;
(3)统计整个受力周期内的应变信息,发现水平对角线上法向位移波动较剧烈,但其应变波形和云图会在某一时刻(即Stage50)后趋于稳定,波形也是内大、外小的3个半波;
(4)研究水平对角线上两个关键点的法向位移及米塞斯应变随时间的变化情况,发现二者的突变时间与薄板发生屈曲失稳的时刻相同,我们通过DIC检测设备和力学试验机的时间同步信息,再次确认了受剪薄板的临界失稳载荷为14.6 kN,由此获得了一种判断受剪薄板临界失稳的新方法。
  • 国家自然科学基金资助项目(51909103; 52301320)
  • 福建省自然科学基金项目(2023J01788; 2021J01841; 2021J01844; 2021J05164)
  • 福建省科技厅对外合作项目(2022I0019)
  • 集美大学国培计划项目(ZP2023008)
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2025年第29卷第10期
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doi: 10.3969/j.issn.1007-7294.2025.10.010
  • 接收时间:2025-04-26
  • 首发时间:2026-03-26
  • 出版时间:2025-10-20
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  • 收稿日期:2025-04-26
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国家自然科学基金资助项目(51909103; 52301320)
福建省自然科学基金项目(2023J01788; 2021J01841; 2021J01844; 2021J05164)
福建省科技厅对外合作项目(2022I0019)
集美大学国培计划项目(ZP2023008)
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    1.集美大学 轮机工程学院,福建 厦门 361021
    2.福建省船舶与海洋工程重点实验室,福建 厦门 361021

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2种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

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
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