计算力学学报2016，Vol.33Issue(4)：462-468,7.DOI:10.7511/jslx201604006
基于第二类四边形面积坐标的弹性力学纯弯解及MacNeal局限定理的破解
Analytical solutions in terms of the quadrilateral area coordinates for pure bending state and the finite element model overcoming the limitation of MacNeal’s theorem
摘要
Abstract
In order to improve the performance of finite element models,analytical solutions of problems in theory of elasticity (the general solutions of the homogeneous equations )were often used as the element trial functions.However,the number of the element DOFs usually does not match the number of the complete analytical solutions,and such incomplete trial functions may lead to direction dependence of the finite elements.In this paper,a new local natural coordinate method,i.e.,the second form of the quadrilateral area coordinate method QACM-II (S,T),was employed to formulate the analytical solutions (the linear combination of S3 and T3 )of the Airy stress function for pure bending state along arbitrary directions.And corresponding analytical solutions for stresses,strains or displacements were also derived out.Then,by utilizing above solutions,a new unsymmetric 4-node,8-DOF plane quadrilate-ral element,denoted by USQ4,was successfully created.The new element can pass both the constant strain/stress patch test and the pure bending test,which means that the limitation defined by the MacNeal’s theorem is overcome.关键词
解析解/第二类四边形面积坐标(QACM-II)/纯弯状态/非对称单元/MacNeal定理Key words
analytical solutions/the second form of the quadrilateral area coordinate method (QACM-II)/pure bending state/unsymmetric element/MacNeal’s theorem分类
数理科学引用本文复制引用
岑松,周培蕾..基于第二类四边形面积坐标的弹性力学纯弯解及MacNeal局限定理的破解[J].计算力学学报,2016,33(4):462-468,7.基金项目
国家自然科学基金(11272181) （11272181）
高等学校博士学科点专项科研基金(20120002110080) （20120002110080）
清华大学自主科研计划(2014Z09099)资助项目 （2014Z09099）
