偶应力理论的无网格法

Meshless method for couple-stress theory

根据偶应力理论的基本方程,在能量泛函中引入罚函数来满足偶应力理论的几何约束条件,从而得到偶应力理论的无网格法的控制方程。通过算例,分析了偶应力对带中心圆孔的无限平板在单轴拉伸及纯剪状态下的应力集中的影响,验证了该无网格方法的有效性和可行性。

In accordance with the basic equations of the couple stress theory, the penalty method is introduced into the energy functional to satisfy the geometrical constraint conditions of the couple stress theory. Then the control equation of meshless method for couple-stress theory is obtained. Lastly, numerical examples are given. The problems of the stress concentration around a central circular hole in a field of uniform tension and in a field of pure shear are solved. The results prove good feasibility and high efficiency of the present method.