An invariant method of fundamental solutions for two-dimensional isotropic linear elasticity

作者：Sun, Yao^*; Marin, Liviu

来源：International Journal of Solids and Structures, 2017, 117: 191-207.

DOI：10.1016/j.ijsolstr.2017.02.022

• Cauchy-Navier equation
• Boundary value problems
• Regularization
• Morozov's discrepancy principle
• Method of fundamental solutions (MFS)

In this paper, we propose an invariant method of fundamental solutions for solving boundary value problems in two-dimensional isotropic linear elasticity. The invariant method of fundamental solutions keeps a very basic natural property the so-called invariance property under trivial coordinate changes in the problem description, e.g. dilations and/or contractions. The problems are solved by the Tikhonov regularization method in conjunction with Morozov's discrepancy principle. Finally, five examples of boundary value problems are investigated to show the efficiency of this method. The numerical convergence, accuracy, and stability of the proposed method with respect to the number of source points, the distance between the sources and the boundary, and the amount of noise added into the input data, respectively, are also analyzed.

• 出版日期2017-6-15
• 单位中国民航大学