摘要
Zienkiewicz薄板单元是最早出现的板单元,因节点参数简单,所以在70年代之前曾起过重要作用;但同时它又是非协调的,仅对由三组间距相等的平行直线所形成的网格才能满足分片检验,这限制了这一单元的应用.因此,先后有不少学者对其进行过改进,使其能对任意形状的网格收敛.考虑到数值流形元法(NMM)总是用最佳质量的数学网格来进行逼近,本文尝试用NMM来解决Zienkiewicz单元的网格依赖问题.基于板的最小势能原理,提出了适用于NMM的混合变分提法,然后利用有解析解的椭圆板问题对方法进行了验证.本文所提出的方法,还可被用于其他类型的非协调单元的改造。
Zienkiewicz's thin plate element is the one that was earliest developed in the finite element history.Due to its simplest nodal variables,it had played important roles before 1970 s.As an incompatible element,however,and it can pass the patch test only for triangular meshes created by three sets of equally spaced straight lines,limiting its application.Many researchers ever made efforts to amend this element so that the resulting element passes the patch test in all configurations.Since the numerical manifold method(NMM) always adopts the meshes of highest quality to approximate the field variables,this study aims to solve the mesh-dependency of Zienkiewicz's element by using the NMM.From the minimum potential principle,a mixed primal variational formulation is derived,followed by a numerical test of an elliptic thin plate with the analytic solution.The proposed methodology can be utilized to amend those incompatible elements of other classes as well.
出处
《计算力学学报》
CAS
CSCD
北大核心
2013年第S1期178-182,共5页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(11172313)
国家杰出青年基金(50925933)资助项目
