Corrective evaluation of multi-valued complex functions for anisotropic elasticity

Chyanbin Hwu, Chung Lei Hsu, Wei Ren Chen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It is well known that the Stroh formalism is an elegant and powerful complex variable method for anisotropic elasticity. Through this formalism, several analytical solutions for the problems of anisotropic elasticity have been presented in the literature. To evaluate the analytical solutions, some problems may occur on the numerical evaluation of multi-valued complex functions and their related singular integrals. In this paper, to get a correct single-valued solution, proper branch cuts are suggested for several different multi-valued complex functions, such as the logarithmic function, inverse trigonometric function, power function, mapping function, Plemelj function, and the logarithmic function with mapped variables. To get the correct numerical integration for weakly and strongly singular integrals with multi-valued complex variables, based upon the concept of finite part integrals, formulae employing the Gaussian quadrature rules of standard, logarithmic, and inverse type are derived. According to the branch cuts selected for different complex functions and the integration formulae for singular integrals, some remarks on the computer programming are provided. Verification of the remarks is then made by typical examples of anisotropic elasticity such as holes, cracks, punches, and singular integrals used in boundary element formulation.

Original languageEnglish
Pages (from-to)2040-2062
Number of pages23
JournalMathematics and Mechanics of Solids
Volume22
Issue number10
DOIs
Publication statusPublished - 2017 Oct 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Materials Science(all)
  • Mechanics of Materials

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