基于广义变分原理的装配/残余效应下的结构力学特性分析  

Assembly/Residual Effects on Mechanical Behaviors of Structures Based on Generalized Variational Principles

作　　者：谭邹卿[1] 石晓灏 蒋学东[1] 班书昊[1] TAN Zouqing;SHI Xiaohao;JIANG Xuedong;BAN Shuhao(School of Mechanical Engineering and Rail Transit,Changzhou University,Changzhou 213164,China;Institute of Biomedical Engineering and Health Sciences,Changzhou University,Changzhou 213164,China)

机构地区：[1]常州大学机械与轨道交通学院,江苏常州213164 [2]常州大学生物医学工程与健康科学研究院,江苏常州213164

出　　处：《常州大学学报（自然科学版）》2022年第4期43-51,共9页Journal of Changzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11602036);江苏省青蓝工程资助项目(苏教师[2020]10号)。

摘　　要：基于能量法研究了装配/残余效应下结构的力学特性。采用拉格朗日乘数法,构造考虑装配/残余效应的新泛函,求解该新泛函的极值问题,并利用矩阵理论获得了超静定结构支座反力或内力的通解。对比了空腹桁架、曲杆以及层合梁3种实例,验证了该模型的有效性。结果表明该方法对求解装配/残余效应下各种超静定结构力学特性具有良好的通用性。An energy method for assembly/residual effects on mechanical behaviors of structures is presented.A new functional considering assembly/residual effects is given according to Lagrange multiplier method.Solving the extremal problem of the new functional,a matrix form of general solutions for support/internal forces of statically indeterminate structures is obtained by using matrix theory.Compared with three types of structures including the vierendeel truss,the curved bar,and the bilayer cantilever beam,the accuracy of the present model is confirmed.The results show that this method has the good versatility to solve the mechanical behaviors of various statically indeterminate structures considering assembly/residual effects.

关 键 词：广义变分原理 装配效应 残余效应 超静定 拉格朗日乘数法 

分 类 号：O341[理学—固体力学]