Exact solution of the displacement boundary-value problem of elasticity for a torus

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

This paper presents an exact analytical solution to the displacement boundary-value problem of elasticity for a torus. The introduced form of the general solution of elastostatics equations allows to solve exactly a broad class of boundary-value problems in coordinate systems with incomplete separation of variables in the harmonic equation. The original boundary-value problem for a torus is reduced to infinite systems of linear algebraic equations with tridiagonal matrices. An analytical technique for solving systems of diagonal form is developed. Uniqueness of the solutions of vector boundary-value problems involving the generalized Cauchy-Riemann equations is investigated, and it is shown that the obtained solution for the displacement boundary-value problem for a torus is unique due to the specific properties of the suggested general solution. The analogy between problems of elastostatics and steady Stokes flows is demonstrated, and the developed elastic solution is used to solve the Stokes problem for a torus.

Original languageEnglish (US)
Pages (from-to)345-368
Number of pages24
JournalJournal of Engineering Mathematics
Volume44
Issue number4
DOIs
StatePublished - Dec 1 2002
Externally publishedYes

Keywords

  • Exact solution
  • Multiply-connected regions
  • Stokes flows
  • Toroidal coordinates
  • Torus

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Fingerprint Dive into the research topics of 'Exact solution of the displacement boundary-value problem of elasticity for a torus'. Together they form a unique fingerprint.

  • Cite this