Application of the Trefftz method, on the basis of Stroh formalism, to solve the inverse Cauchy problems of anisotropic elasticity in multiply connected domains

In this paper, the Trefftz collocation method is applied to solve the inverse Cauchy problem of anisotropic elasticity, wherein both tractions as well as displacements are prescribed at a small part of the boundary of an arbitrary simply/multiply connected anisotropic elastic domain. The Stroh formalism is used to construct the Trefftz basis functions. Negative and positive power series are used together with conformal mapping to approximate the complex potentials of the Stroh formalism. For inverse problems where noise is present in the measured data, Tikhonov regularization is used together with the L-curve parameter selection method, in order to mitigate the inherent ill-posed nature of inverse problems. By several numerical examples, we show that this simple and elegant method can successfully solve inverse problems of anisotropic elasticity, with noisy measurements, in both simply and multiply connected domains.