基于线性互补的非连续变形分析

非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题，合理设定罚参数很困难，此外，因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代，用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上，综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势，提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序，算例计算结果证明了方法的精度及可行性。

Discontinuous deformation analysis based on linear complementarity theory

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.