基于基线力概念的平面4节点余能有限元模型

针对二维问题,以基线力为状态变量表征物体的受力状态,以其对偶量位移梯度表征物体的变形状态,提出了一种基于余能原理的平面4节点有限元模型.利用基线力概念构造了单元的余能,通过Lagrange乘子法松弛单元域内的平衡条件,得到一个基线力表达的修正余能原理.在假设平面单元每一个边上的力为均匀分布的条件下,推导出一种平面4节点有限元列式.运用MATLAB语言编制出相应的余能原理有限元分析程序.数值算例结果表明,该类单元精度高,对网格畸变不敏感.

Four-node Plane Element Model on Complementary Energy Based on the Concept of Base Line Forces

Using the base line forces as fundamental variables to describe the stress state for two dimension problems and the displacement gradients that are the conjugate variables of the base line forces,which describe the deformation state of objects,a 4-node plane element model based on complementary energy principle is proposed.In this paper,the complementary energy of an element is constructed by using the base line forces.The equilibrium conditions are released by the Lagrange multiplier method,and a modified complementary energy principle described by the base line forces is obtained.The formulation of the 4-node plane element is derived by assuming that the stress is uniformly distributed on each face of a plane element.A finite element procedure of complementary energy principle is developed using MATLAB language.The numerical results of examples show that this model has high precision and is free from mesh sensitivity.