Research On The3D Base Force Element Based On The Complementary Energy Principle

The3D space field of Base force element——a new finite element proposed byGao Y C was researched in the paper. The3D base force element of six-node and the3D base force program by MATLAB technology were used to solve space problem,and the theory solution, the linear full-integration(Q8) solution and linear reduced-integration(Q8R) solution of the finite element software ABAQUS were compared.Then the calculated performance of3D base force element was analysed anddiscussed. The main research works are as follows:(1) For the space problem, the matrix of spatial element stress tensor and spatialelement compliance expressed by base force was deduced. The control equationexpressed by the3D base force element was obtained by Lagrange multiplier methodof the generalized complementary energy principle, and the displacement formulati-on of spatial nodal point was given.(2) The3D base force element method program of the complementary energyprinciple was developed by MATLAB technology. On pretreatment part, combinedwith the corner node that generated by ABAQUS, the code for making thispolyhedron element that has surface node in unite grid was developed by MATLABtechnology.(3) The applicability of the3D base force element program was studied to solveseveral typical space problems, and the numerical results were compared to thetheoretical solutions.(4) The3D base force element of six-node and the3D base force program byMATLAB technology were used to solve space beam, plate and shell. The influenceof unit width ratio was calculated. The calculated performance of3D base forceelement was analysed and discussed through compare to the Q8solution and theQ8R solution in ABAQUS software.In this paper, the applicability of mathematical model of the3D base forceelement method was demonstrated. And the applicability of the3D base forceelement program and the mesh automatic conversion program were studied. Theapplied researches showed that the numerical results were consistent with those ofthe theoretical solutions. This method was simple and effective. The method was anew idea of finite element method, and it has widely application prospect in space structure.