Abstract
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.
Highlights
The finite element method based on the assumed displacement field has become a method of choice for the solution of a wide variety of problems in structural mechanics
The equilibrium conditions are released by the Lagrange multiplier method, and a modified complementary energy principle described by the base forces is obtained
A 4-mid-node plane model of base force element method (BFEM) on complementary energy principle is proposed for elasticity problems
Summary
The finite element method based on the assumed displacement field has become a method of choice for the solution of a wide variety of problems in structural mechanics. Based on the complementary energy principle, a hybrid stress-function element method is proposed by Fu et al [8] and Cen et al [9,10,11,12] using the mesh distortion immune technique for developing plane 8-node elements. Using the concept of base forces as state variables, a three-dimensional formulation of base force element method (BFEM) on complementary energy principle was proposed by Peng and Liu [17] for geometrically nonlinear problems. A three-dimensional model of base force element method (BFEM) on complementary energy principle was proposed by Liu and Peng [18] for elasticity problems. A number of elasticity problems are solved using the present formulation, and the results are compared with corresponding analytical solutions
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