平面Cosserat弹性体广义等参元  

Generlized isoparametric finite elements for plane elastic Cosserat bodies

作　　者：卢恩赦 陈明祥[1] LU Enshe;CHEN Mingxiang(School of Civil and Architectural Engineering,Wuhan University,Wuhan 430072,Chin)

机构地区：[1]武汉大学土木建筑工程学院

出　　处：《武汉大学学报（工学版）》2018年第7期601-606,619,共7页Engineering Journal of Wuhan University

摘　　要：将广义等参元理论和Cosserat理论相结合,考虑Cosserat弹性体单元内部不同方向位移间的耦合效应,通过在位移插值形函数中引入耦合附加项,构造了平面Cosserat弹性体4节点广义等参元,并基于自然变分原理,推导了耦合附加项的函数表达式,进而得到广义等参元列式.为了验证单元的适用性,构造了2个不同的分片实验并进行程序实现,结果显示所构造的广义等参元能通过该分片试验.最后分析了悬臂梁弯曲问题和圆孔应力集中问题,结果表明单元数值精度较高.该方法在保证单元协调性和自由度保持不变的情况下,提高了单元的精度;单元基于自然变分原理并且只在传统等参元插值形函数的基础上增加耦合项,程序操作简单且易于实现.A 4-node generalized isoparametric finite element is developed to deal with the problems considering the plane elastic Cosserat bodies.To consider the coupling effect in the different directions of the displacement inside the element;the additional coupling terms are introduced in the shape functions;which can be constructed by variational principle of displacement;and then the element equations are obtained.To verify the applicability of the new element;two different patch tests are described and applied to validate the new element;the results show that the element developed can pass the tests.The cantilever beam under shearing force and the stress concentration around a central circular hole in uniaxial tension are analyzed to check the property of the new element;the results indicate that the new element has high accuracy.The calculation accuracy of the elements are improved;however the degrees of freedom remain the same.The new method just adds the additional coupling terms based on the shape function of the conditional isoparametric finite elements;as a result the new element is convenient for implementation.

关 键 词：COSSERAT理论 广义等参元 形函数 耦合附加项 

分 类 号：O34[理学—固体力学]