A new fundamental solution for boundary element analysis of thin plates on Winkler foundation

A. El‐Zafrany, S. Fadhil, K. Al‐Hosani

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

This paper introduces an efficient boundary element approach for the analysis of thin plates, with arbitrary shapes and boundary conditions, resting on an elastic Winkler foundation. Boundary integral equations with three degrees‐of‐freedom per node are derived without unknown corner terms. A fundamental solution based upon newly defined modified Kelvin functions is formulated and it leads to a simple solution to the problem of divergent integrals. Reduction of domain loading terms for cases of distributed and concentrated loading is also provided. Case studies, including plates with free‐edge conditions, are demonstrated, and the boundary element results are compared with corresponding analytical solutions. The presented formulations provide a very accurate boundary element solution for plates with different shapes and boundary conditions.

Original languageEnglish
Pages (from-to)887-903
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Volume38
Issue number6
DOIs
Publication statusPublished - Mar 30 1995

Keywords

  • boundary elements
  • boundary integrals
  • foundation
  • plates

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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