二维弹性力学边界条件反识别TSVD正则化法  

Inverse identification of 2-D elasticity boundary conditions by using TSVD regularization method

作　　者：周焕林[1] 江伟[1] 胡豪[1] 牛忠荣[1] 

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2013年第9期1076-1081,共6页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11072073);教育部留学回国人员科研启动基金资助项目(2009jylh0110);安徽高校省级自然科学研究重点资助项目(KJ2008A041)

摘　　要：针对二维各向同性弹性力学Cauchy问题,文章采用线性单元对边界积分方程进行离散,再引入已知的边界条件,得到包含所有待求边界条件信息的线性病态方程组。采用截断奇异值分解正则化技术求解该病态方程组,并使用L曲线法选择最优正则化参数,即奇异值截断位置,从而得到方程组的解。通过数值算例对求得的边界条件数值解与解析解进行比较,并进行误差分析,以表明截断奇异值分解算法的有效性和稳定性。通过减少已知数据中的随机偏差和增加边界单元密度可提高求解的精确度。The boundary element method（BEM） is developed to analyze the Cauehy boundary condition inverse problems in 2-D isotropic elasticity. The boundary integral equation is diseretized by a set of linear elements, and after the given boundary conditions have been introduced, the ill-posed linear system equations with all the unknown boundary conditions can be given. Truncated singular value decomposition（TSVD） technique is applied to solving the equations. L-curve method is proposed to select the regularization parameter, i.e. the optimal truncation number, and then the solution of the linear system equations can be obtained. Numerical examples are shown to demonstrate the effective- ness and stability of the TSVD algorithm by the comparison of the obtained numerical solution and an- alytical solution. The regularization errors are also analyzed. The accuracy of the solution can be im- proved by reducing the amount of noise added into the known data and refining the mesh size.

关 键 词：边界条件 反问题 边界元法 截断奇异值分解 L曲线法 

分 类 号：O343.1[理学—固体力学]