Research On 3-D Finite Element Plastic Limit Analysis Method

The basic task of the structure limit analysis is to calculate the structure bearing capacity, which provides the essential, reliable basis for the determination of structure safety tolerance. The anti-load capacity is taped in the plastic limit analysis method without considering the process and rule of the stress redistribution, which provides much convenience for the mathematic disposal. The 3-D finite element lower bound plastic limit analysis method is researched in this paper. The lower bound theorem assumes a rigid plastic material model. Based on the lower bound principles of limit analysis, the mathematical model is established by means of finite element method (FEM), whose object functions are strength accumulation coefficient or over loading coefficient. The lower bound result of the model is obtained by non-linear programming. The paper includes six chapters.In the first chapter, the development and current status of the plastic limit analysis are introduced, and the significance and content of the paper are presented.In the second chapter, the plastic limit analysis theory is described in detail, and the calculation method of the limit load is presented.In the third chapter, the statically admissible stress field is found by finite element method (FEM). The 3-D finite element plastic limit analysis mathematical model is established on the basis of the lower bound principles of limit analysis.In the forth chapter, in order to solve the NLP problem, various optimization methods are compared. According to the characteristic of the plastic limit analysis model, the Sequential Quadratic Programming Method (SQP) should be used to solve the NLP problem. In addition, MATLAB and GAMS are introduced, whose usage and points for attention are explained in detail.In the fifth chapter, the program self-assembled and the interface program connected with fore-treatment and after-treatment are illustrated. Finally, for the example of calculating the bearing capacities of a uniform quality slope, the calculation resultbetween lower bound limit analysis and classical plasticity theory, ANSYS software are compared. The results illustrate the correctness of the model and programs of limit analysis.In the sixth chapter, the work of the paper is summarized, and the feasible approach for further research is pointed out.