一种新的基于余能原理的应力恢复方法

A new method for stress recovery by the complementary energy principle

提出了一种新的基于余能原理的应力恢复方法:首先将单元小片从弹性体中隔离出来,然后构造一个高次的待定平衡应力场,应用余能原理通过解一个最小二次规划问题来确定这个应力场,得到恢复应力。本方法不需要单元中存在超收敛点,直接利用有限元计算结果构造满足平衡条件的应力场,方法简便可靠。最后通过一个经典的线弹性算例验证了方法的有效性。

In this paper, a new stress recovery method is presented. The patch of elements is separated from elastic body, a equilibrated stress field with higher order is constructed, which is decided by the complementary energy principle through resolving a quadratic optimization problem. The method doesn＇t depend on the superconvergent points which don＇t exist in some finite elements, the equilibrated stress field is constructed directly with the results of finite element analysis. A benchmark problem of elasticity is tested to verify the excellent performance of the method.