A Trefftz collocation method (TCM) for three-dimensional linear elasticity by using the Papkovich-Neuber solutions with cylindrical harmonics

Guannan Wang, Leiting Dong, Satya N. Atluri

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

A Trefftz collocation method (TCM) is proposed for solving three-dimensional (3D) linear-elastic boundary value problems. By using the Papkovich-Neuber (P-N) general solutions, Trefftz trial functions are expressed in terms of cylindrical harmonics. Both non-singular and singular harmonic functions are included, facilitating the study of interior and exterior problems. To mitigate the problem of ill-conditioned functions, two steps are adopted: the first step is to introduce a characteristic length of the domains of interests into the Laplace equation, and the second step is to scale each column of the coefficient matrix in the established system of linear equations using another multi-scale characteristic length, letting each column have the equal norms. Several examples are presented to validate the proposed 3D Trefftz collocation method. The completeness of the trial functions, the effect of the scaling techniques, and the accuracy of solutions are also discussed.

Original languageEnglish
Pages (from-to)93-103
Number of pages11
JournalEngineering Analysis with Boundary Elements
Volume88
DOIs
StatePublished - Mar 2018

Keywords

  • 3D elasticity
  • Cylindrical harmonics
  • Ill-conditioning
  • Papkovich-Neuber solution
  • Scaling technique
  • Trefftz method

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