Study On Multi-scale Analysis Of Structure Based On The Finite Element Mesh Superposition Method

This article proposes a kind of new finite element analysis method– the finite element mesh superposition method. The Linux operating system is used for the software development platform, and C language is applied to develop the code of main process based on the finite element mesh superposition method, and the analysis are conducted by considering the finite element method and the linear elasticity theory based on the fundamental mechanics.In this paper, firstly, basic principle of finite element method is narrated. Secondly, the finite element mesh superposition method theory is introduced in detail, including the constitutive equations of finite element mesh superposition method, and the fundamental discretization of constitutive equations (namely the result of principle formula carries on discretization through the finite element method ) and the solution method of stiffness matrix. Finally, the two examples are applied to carry out the precision test to the program.The stress analyses are carried out to the object by the existing quite mature finite element analysis software ANSYS, and this result assumed as standard. The stress analysis is carried out to the object by the application finite element mesh superposition method. The aim is to contrast this standard analysis result with respect to the finite element mesh superposition method, and evaluate the precision of the program.In this paper, a metal plate with the round hole and the common chair are used to carry out the precision test of program. When the metal plate with round hole is used to numerical analysis based on the finite element mesh superposition method, because of the stress concentration is occur nearby the round hole, so the global model is used in finite element mesh superposition method as a entire block metal plate without the round hole, and the local model should be consider the round hole in the region. It is also divide global model with the different mesh. The different global mesh and the local mesh will be carried out by over lapping of two meshes using the FEM superposition computation, and the effect of different mesh division is analyzed and determined. When the chair is analyzed by application of finite element mesh superposition method, the position that will appear the stress concentration area will be made the local mesh model, and the entire chair will be made the global model. The numerical analyses are carried out by using both local model and global model based on the superposition method. We obtain the stress concentration maximum value and it's the position by using superposition analysis is extremely close to the standard analysis one. The results shown, that the error between the two kinds of method is too small. This is indicated that the finite element mesh superposition method can be applied to large-scale structural analysis and its multi-scale analysis.