改进的SSOR-PCG迭代法在接触问题研究中应用  

Application of an improved SSOR-PCG iteration method to contact problems

作　　者：李静[1] 陈健云[1] 周晶[1] 

机构地区：[1]大连理工大学土木水利学院,辽宁大连116024

出　　处：《大连理工大学学报》2006年第4期533-537,共5页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(50209002);辽宁省自然科学基金资助项目(20022130)

摘　　要：SSOR-PCG方法对于大型对称正定问题具有很高的求解效率,但采用求解静动力接触问题的L agrange乘子法导致结构刚度矩阵对应L agrange乘子的对角元为零,不满足传统的SSOR-PCG方法的应用条件.为此通过建立联系L agrange乘子的罚函数矩阵,提出了SSOR-PCG罚函数方法,并通过主动自由度和被动自由度的关系,提出了SSOR-PCG变量替换法.数值例题证明SSOR-PCG变量替换法具有良好的精度和效率.SSOR-PCG method is a high efficiency method for solving problems with large symmetric definite matrix. It can not be applied to contact problems which don＇t satisfy the condition as the matrix formulated by Lagrange multiplier method has zero diagonal terms. To solve this problem, the SSOR-PCG penalty method is presented by establishing a penalty matrix which is related to Lagrange multiplier. Furthermore, from the relationship between the active degree-of-freedom and passive degree-of-freedom, the so-called SSOR-PCG variable-substitution method is presented for contact problems with zero diagonal terms. The effectiveness and the precision of SSOR-PCG variable-substitution method are tested and proved by the numerical results.

关 键 词：动接触 LAGRANGE乘子法 水工结构 PCG方法 

分 类 号：TU528.1[建筑科学—建筑技术科学]