关键词: 偶应力理论, 非协调元, 能量相容条件, 罚函数

Abstract:

Deduced from the stationary condition of potential function in couple-stress elastic solids, an energy consistency principle for the incompatible element system of couple-stress theory is obtained. Based on its strong patch test form, the well-known Wilson internal parameters for two-dimensional four-node incompatible elements are improved, and a new effective incompatible finite element method for couple-stress problems is put forward. The constraint condition that the microrotations must be equal to the macrorotations is introduced by a penalty function technique. Numerical examples for the influence of couple stresses on the stress concentration around a central circular hole in a uni-axial tension or pure shear field are given. The results show that the present method has high efficiency and good accuracy.The considerably satisfying results can be obtained, even if the characteristic length is very small.

Key words: couple-stress theory, incompat ible elements, energy consistency condition, penalty function