A 4-Mid-Node Plane Model of Base Force Element Method on Complementary Energy Principle

Abstract EN

Using the base forces as fundamental variables to describe the stress state and the displacement gradients that are the conjugate variables of the base forces to describe the deformation state for the two-dimensional elasticity problems, a 4-mid-node plane model of base force element method (BFEM) based on complementary energy principle is proposed.

In this paper, the complementary energy of an element of the BFEM is constructed by using the base forces.

The equilibrium conditions are released by the Lagrange multiplier method, and a modified complementary energy principle described by the base forces is obtained.

The formulation of the 4-mid-node plane element of the BFEM is derived by assuming that the stress is uniformly distributed on each edge of the plane elements.

A procedure of the BFEM on complementary energy principle is developed using MATLAB language.

The numerical results of examples show that this model of the BFEM has high precision and is free from mesh sensitivity.

This model shows good performances.