摘要
提出一维有限元法后处理中超收敛解答的一种自然合理的算法,称为单元能量投影法(EEP)。理论分析和数值算例表明,提出的方法简便易行、行之有效、效果显著;此外,还有一些颇合人意的优点,如:任一点的应力和位移的误差与结点位移的误差具有相同的收敛阶(m次单元可达mh2阶)、结点两边单元各自算出的应力自动平衡、自由端点的应力自动为精确值等。
The present paper presents, for one-dimensional FEM at the present stage, a natural and rational approach called Element Energy Projection (EEP) method for super-convergent calculation of both displacements and stresses at any point in an element in post-processing stage. The proposed method is simple, effective and efficient. A large number of numerical examples consistently show that the accuracy of both displacements and stresses so calculated is well comparable to that of the nodal displacements, i.e. being of order mh2 for elements of degree m with sufficiently smooth solutions.
出处
《工程力学》
EI
CSCD
北大核心
2004年第2期1-9,共9页
Engineering Mechanics
基金
国家自然科学基金资助项目(50278046)
关键词
有限元
一维问题
后处理
超收敛
单元能量投影
FEM
one-dimensional problem
post-processing
super-convergence
element energy projection
