Application of the Base Forces Concept to Finite Element Method Based on Complementary Energy Principle

To improve the traditional finite element method based on the complementary energy principle, an element with the center nodes of each side is proposed. The explicit unified expression of element compliance matrix and the explicit formulations for the displacements of element nodes are derived from the concept of base forces. The control equation of the finite element method expressed by the base forces is obtained by using Lagrange multiplier method of the generalized complementary energy principle. A finite element approach program is developed using MATLAB computer language. The researches show that the numerical results are consistent with those of the theoretical solutions.