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.