平面应力问题新型广义有限元法  

New generalized finite element for plane stress problem

作　　者：杨璞[1] 牛红攀[1] 肖世富[1] 

机构地区：[1]中国工程物理研究院总体工程研究所,四川绵阳621900

出　　处：《计算机辅助工程》2015年第6期23-29,71,共8页Computer Aided Engineering

基　　金：国家自然科学基金(11472256);中国工程物理研究院高性能科学与工程计算战略科技项目(R2014-0203)

摘　　要：结合广义有限元和理性有限元的优势,针对平面应力问题提出一种新型广义四边形单元.该单元考虑泊松效应,以节点位移自由度约束弹性力学平面应力方程的半解析解,构造单元位移模式的附加项,较准确地反映真实位移场,提高单元的计算精度.推导新型广义单元及其等参单元的形函数公式,设计分片试验和数值算例验证单元的精度.数值算例结果表明:在规则网格和非规则网格下新单元的计算精度均优于传统有限元和广义有限元.新单元具有精度高且易于程序实现的特点,可推广应用到实际工程的结构分析中.Considering the advantage of generalized finite element and rational finite element,a new kind of generalized quadrilateral elements is proposed for the plane stress problem. Considering Poisson effect,the additional terms of the displacement mode can be constructed by this kind of element according to the semi-analytical solution of elastic plane stress equation which is constricted by the degrees of freedom of node displacement. The element reflects the real displacement field accurately and the calculation accuracy of the element is improved. The shape functions of the new generalized element and its isoparametric elements are derived,and the patch test and numerical examples are designed to verify the calculation accuracy. The results of the numerical examples indicate that,whether in regular or irregular mesh,the calculation accuracy of the new element is better than that of conventional element and generalized element. The new element is convenient for implementation and has more accuracy,which is suitable for the structure analysis application in practical engineering.

关 键 词：平面四边形单元 等参元 平面应力 广义有限元 形函数 分片试验 

分 类 号：O302[理学—力学]