求解双层弹性膜单侧接触问题的Uzawa算法
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A Uzawa Algorithm for Solving the Unilateral Contact between Two Elastic Membranes
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    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。

    Abstract:

    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

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严月月, 钟艳丽, 郭楠馨.求解双层弹性膜单侧接触问题的Uzawa算法[J].重庆工商大学学报(自然科学版),2018,35(6):75-78
YAN Yueyue, ZHONG Yanli, GUO Nanxin. A Uzawa Algorithm for Solving the Unilateral Contact between Two Elastic Membranes[J]. Journal of Chongqing Technology and Business University(Natural Science Edition),2018,35(6):75-78

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  • 在线发布日期: 2018-11-19
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