冲击接触问题的一种双共振投影梯度算法  

Reduced Projection Augmented Lagrange Bi-Conjugate Gradient Method for Contact and Impact Problems

作　　者：李南生[1] 任魁生[1] 沙德松[2] 

机构地区：[1]同济大学土木工程学院,上海200092 [2]大连理工大学工程力学系,大连116023

出　　处：《应用数学和力学》2007年第8期983-990,共8页Applied Mathematics and Mechanics

摘　　要：根据冲击接触计算模型所需满足的基本控制方程和非线性互补条件,应用非线性互补问题与约束优化的等价关系将非线性互补接触问题转变成一个非线性规划问题,系统地推导建立了冲击接触问题的一种双共轭投影梯度计算方法.增广Lagrange乘子法克服了罚函数要求减小迭代步长以达到计算稳定的限制,即使对于冲击接触问题亦可以采用较大迭代步长,在形成的与原互补问题等价的无约束规划模式下,应用双共轭投影梯度算法提高非线性搜索速度和计算效率.算法模型计算结果表明,所建立的双共轭投影梯度计算理论及方法是正确有效的.Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi-conjugate gradient method was proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formnulation of non-linear programming. For contact-impact problems, a larger time-step can be adopted arriving at numerical convergence compared with penalty method. By establishraent of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to improve precision and efficiency of numerical solutions. A numerical example shows that the algorithm suggested is valid and exact.

关 键 词：冲击接触问题 LAGRANGE乘子法 双共轭投影梯度 数值算法 

分 类 号：O343.3[理学—固体力学]