The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity

Abstract

In this paper, the application of the method of fundamental solutions to the Cauchy problem in two-dimensional isotropic linear elasticity is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularised by employing the first-order Tikhonov functional, while the choice of the regularisation parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries, as well as for constant and linear stress states. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are analysed.