关键词: 非连续变形分析, 接触问题, 线性互补理论, 半光滑函数

Abstract: Discontinuous deformation analysis (DDA) is a newly developed discontinuum numerical method for simulating large deformation and displacement of block systems. The core research of this thesis concentrates on improving the method to enforce contact constraints in DDA. The penalty function method and Lagrange multiplier method or its variants are generally utilized to enforce contact constraints in DDA. But it is difficult to set a reasonable penalty parameter. Furthermore, discontinuous change in stiffness matrix due to the open-close iteration frequently causes poor convergence. To avoid troubles in setting artificial penalty parameters and open-close iteration, we reformulate discontinuous deformation analysis method as mixed linear complementarity model (LCDDA). On the basis of these, both advantages of local quadratic convergence rate of the Newton method based on nonsmooth analysis and global linear convergence rate of steepest descent method are integrated to set up the algorithm. According to the above achievement, the complete code for LCDDA is accomplished. Some examples are analyzed to verify the precision and feasibility.

Key words: discontinuous deformation analysis (DDA), contact problem, linear complementarity theory, semismooth function