基面力概念在几何非线性余能有限元中的应用

以基面力为基本未知量描述一个弹性系统的应力状态并表征单元的余能，将大变形的余能分 解为变形余能部分和转动余能部分，采用Lagrange乘子法放松单元的平衡方程，利 用已有的弹性大变形余能原理建立了一种几何非线性显式有限元模型，编制了相应的几何非线 性余能原理有限元程序. 数值算例表明：该方法具有较好的收敛性和计算精度，可进行大 载荷步的大位移、大转动计算.

APPLICATION OF THE BASE FORCES CONCEPT IN GEOMETRICALLY NONLINEAR FINITE ELEMENT METHOD ON COMPLEMENTARY ENERGY

In this paper, a new explicit expression of the geometrically nonlinear finite element method was developed on the complementary energy principle for the large displacement and large rotation problem on the basis of the concept of base forces as fundamental variables. The complementary energy of an element under large deformation case is divided into the deformation part and rotation part. The formulations of the control equations for the base forces finite element method are obtained using the Lagrange multiplier method, and an explicit displacement formulation of nodes is given. The numerical results are compared with those of the theoretical solution and the assumed displacement finite element method based on potential energy principle. It has been demonstrated that the new finite element formulations proposed in this paper is effective, accurate, and capable of simulating the large rotation case under one large load step.