CAJ | 학술논문

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。
침대이유각향동성탄성역학Cauchy문제，문장채용선성단원대변계적분방정진행리산，재인입이지적변계조건，득도포함소유대구변계조건신식적선성병태방정조。채용절단기이치분해정칙화기술구해해병태방정조，병사용L곡선법선택최우정칙화삼수，즉기이치절단위치，종이득도방정조적해。통과수치산례대구득적변계조건수치해여해석해진행비교，병진행오차분석，이표명절단기이치분해산법적유효성화은정성。통과감소이지수거중적수궤편차화증가변계단원밀도가제고구해적정학도。
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 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 know n data and refining the mesh size .