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On solution strategies to Saint-Venant problem

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
206
Issue
1
Identifiers
DOI: 10.1016/j.cam.2006.08.008
Keywords
  • Saint-Venant Problem
  • Neumann Boundary-Value Problem
  • Dirichlet Boundary-Value Problem
  • Potential Functions
  • Integral Boundary Equations
Disciplines
  • Computer Science

Abstract

Abstract Different solution strategies to the relaxed Saint-Venant problem are presented and comparatively discussed from a mechanical and computational point of view. Three approaches are considered; namely, the displacement approach, the mixed approach, and the modified potential stress approach. The different solution strategies lead to the formulation of two-dimensional Neumann and Dirichlet boundary-value problems. Several solution strategies are discussed in general, namely, the series approach, the reformulation of the boundary-value problems for the Laplace's equations as integral boundary equations, and the finite-element approach. In particular, the signatures of the finite-element weak solutions—the computational costs, the convergence, the accuracy—are discussed considering elastic cylinders whose cross sections are represented by piece-wise smooth domains.

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