A simple multi-source-point trefftz method for solving direct/inverse shm problems of plane elasticity in arbitrary multiplyconnected domains

Abstract: In this paper, a generalized Trefftz method in plane elasticity is devel-oped, for solving problems in an arbitrary multiply connected domain. Firstly, the relations between Trefftz basis functions from different source points are discussed, by using the binomial theorem and the logarithmic binomial theorem. Based on these theorems, we clearly explain the relation between the T-Trefftz and the F-Trefftz methods, and why the traditional T-Trefftz method, which uses only one source point, cannot successfully solve problems in a multiply connected domain with genus larger than 1. Thereafter, a generalized Trefftz method is proposed, which uses logarithmic and negative power series from multiple source points, and positive power series from only one source point, as complex potentials. In addi-tion, a characteristic length for each source point is used to scale the Trefftz basis functions, in order to resolve the ill-posedness of Trefftz methods. For direct prob-lems, no further regularization techniques are used, because the coefficient matrix of the system of linear equations to be solved is already well-conditioned, by using characteristic lengths to scale the Trefftz basis functions. Inverse problems in plan