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Vol. 50 (2009) No. 2 August n. 161


Finite Element Analysis for Geometrical Shape Minimization

< Table of Contents for Vol. 50 (2009) No. 2 August n. 161
  • Journal Name: Journal of the International Association for Shell and Spatial Structures (J. IASS)
  • ISSN: (Electronic Version) 1996-9015
  • ISSN: (Print Version) 1028-365X
  • Issue: Vol. 50 (2009) No. 2 August n. 161
  • Pages: 79-86
  • Title: Finite Element Analysis for Geometrical Shape Minimization
  • Author(s): V. F. Arcaro and K. K. Klinka
  • Keywords: Element, Formfinding, Line, Minimization, Nonlinear, Optimization, Tetrahedron, Triangular.
Abstract
This paper presents a mathematical model for minimizing path length, surface area and volume using a line element, a triangle element and a tetrahedron element respectively. The triangle element together with the line element can be used to minimize a surface area with free boundaries through the unifying concept of minimizing shape volume. A quasi-Newton method is used, which avoids the evaluation of the Hessian matrix as required in a Newton method. The source and executable computer codes of the algorithm are available for download from the author’s website.

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