加肋对称层合板线性弯曲分析的移动最小二乘无网格法  

Bending analysis of ribbed symmetric laminated plate by the moving-least square meshless method

作　　者：韦冬炎 陈卫 杨健生 彭林欣[1,2,3] WEI Dongyan;CHEN Wei;YANG Jiansheng;PENG Linxin(College of Civil Engineering and Architecture,Guangxi University,530004 Nanning,China;Guangxi Key Laboratory of Disaster Prevention and Reduction and Engineering Safety,Guangxi University,530004 Nanning,China;Key Laboratory of Engineering Disaster Prevention and Structural Safety,Ministry of Education,Guangxi University,530004 Nanning,China)

机构地区：[1]广西大学土木建筑工程学院,南宁530004 [2]广西大学广西防灾减灾与工程安全重点实验室,南宁530004 [3]广西大学工程防灾与结构安全教育部重点实验室,南宁530004

出　　处：《应用力学学报》2025年第2期425-433,共9页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.12162004,11562001);国家重点研发计划(No.2019YFC1511103);广西科技重大专项(桂科No.AA18118029).

摘　　要：基于一阶剪切变形理论,提出了一种求解矩形加肋对称层合板线性弯曲问题的移动最小二乘无网格法。加肋层合板可以视为层合板和肋条组合而成的复合结构。采用移动最小二乘法近似分别建立层合板和肋条的位移场,推导出层合板和肋条的刚度矩阵,再利用板与肋条间的位移协调条件,将肋条的刚度矩阵叠加到层合板的刚度矩阵中,得到整个复合结构的刚度矩阵。由于基于移动最小二乘近似的无网格法,不满足克罗内克条件,故采用完全转换法处理本质边界条件。文末算例分析了不同肋条数量,铺层方式,弹性模量比和宽厚比下的加肋层合板弯曲性能,并将本研究解与ABAQUS解进行对比,验证了本研究方法的有效性及准确性。Based on the first-order shear deformation theory(FSDT),a moving least squares(MLS)meshless method is proposed to solve the linear bending problem of symmetrically laminated plate with ribbed.The stiffened symmetrical laminated plate can be regarded as a composite structure composed of plate and rib.The displacement fields of the laminated plates and ribs are established by the MLS approximation,respectively.Then the stiffness of the laminated plates and ribs are deduced.Lastly,the stiffness matrix of the whole composite structure is obtained by adding the stiffness matrix of the rib to the stiffness matrix of the laminated plates by using the displacement compatibility condition.Since the moving least squares(MLS)meshless method does not satisfy the Kronecker condition,the full transformation method is used to deal with the essential boundary conditions.At the end of this paper,a series of numerical examples are given to analyze the flexural performance of stiffened symmetrical laminated plate with different number of ribs,lamination schemes elastic modulus ratio and width-thickness ratio.The proposed solutions are compared with the ABAQUS solution to verify the effectiveness and accuracy of the proposed method.

关 键 词：加肋对称层合板 线性弯曲 完全转换法 移动最小二乘法 

分 类 号：O241[理学—计算数学] O302[理学—数学]