A Simple Multi-Source-Point Trefftz Method for Solving Direct/Inverse SHM Problems of Plane Elasticity in Arbitrary Multiply-Connected Domains
L. Dong1, S. N. Atluri1
CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 1-44, 2012, DOI:10.3970/cmes.2012.085.001
Abstract In this paper, a generalized Trefftz method in plane elasticity is developed, 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… More >
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