求解双层弹性膜单侧接触问题的Uzawa算法  

A Uzawa Algorithm for Solving the Unilateral Contact between Two Elastic Membranes

作　　者：严月月 钟艳丽 郭楠馨 YAN Yue-yue;ZHONG Yan-li;GUO Nan-xin(College of Mathematical Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆工商大学学报（自然科学版）》2018年第6期75-78,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：重庆市科技计划项目(CSTC2017JCYJAX0316)

摘　　要：双层弹性膜问题在力学方面有着很重要的作用,而很难用解析方法直接得到它的解;在变分法和不动点理论的基础上提出了求解问题的Uzawa算法,给出了算法的具体过程;利用双线性形式的一些基本性质和算法特点可证明算法的收敛性;利用算法,在算例中对双层弹性膜问题的数值结果和精确解进行比较,问题数值解及其自由边界与解析解能较好地吻合;理论分析和数值结果都表明了所给算法的有效性。The problem of the unilateral contact between two membranes plays an important role in mechanics,but it is difficult to get its solution directly by analytic method.On the basis of variational method and fixed point theory,the Uzawa algorithm for solving this problem is proposed,and the process of the algorithm is given in detail.The convergence of the algorithm can be proved by using some basic properties of bilinear form and algorithm characteristics.A numerical example is given to compare with the exact solution,and numerical solution of two elastic membranes.The numerical solution and its free boundary are in a good agreement with the analytical solution.Both theoretical analysis and numerical results show the effectiveness of the proposed algorithm.

关 键 词：弹性膜 单侧接触 变分法 不动点 UZAWA算法 

分 类 号：O241.82[理学—计算数学]