二维弹性力学边界条件反识别 TSVD 正则化法
周焕林;江伟;胡豪;牛忠荣
【期刊名称】《合肥工业大学学报（自然科学版）》 【年(卷),期】2013(000)009
【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。%T he boundary element method(BEM ) is developed to analyze the Cauchy boundary condition inverse problems in 2-D isotropic elasticity .The boundary integral equation is discretized 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
二维弹性力学边界条件反识别 TSVD 正则化法
