Abstract

Based on a modified Hellinger–Reissner mixed variational principle and considering the displacements as known quantity, a simple and straightforward finite element linear system of equations for all transverse stress variables is constructed. Two main advantages are that the system of equations provides the convenience for the introduction of transverse stress boundary conditions and the interface continuity is guaranteed automatically. Comparing with the solutions, the system of equations for transverse stress can not only ensure that the transverse stress components on surface is consistent with prescribed values, but also can provides the high-precision numerical results of all transverse stresses.

摘要

基于改进的 Hellinger-Reissner 混合变分原理，并将位移视为已知量，构建了所有横向应力变量的简单直接的有限元线性方程组。两个主要优点是方程组为引入横向应力边界条件提供了便利，并自动保证了界面连续性。与解相比，横向应力方程组不仅可以保证表面横向应力分量与规定值一致，而且可以提供所有横向应力的高精度数值结果。