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IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints


IASS Symposium 2014

SESSION: General 9: Computational Tools, Shape Finding and Optimization

Finite element analysis for minimal shape

< Table of Contents for General 9: Computational Tools, Shape Finding and Optimization
  • Proceedings Name: IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints
  • ISSN: (Electronic Version) 2518-6582
  • Session: General 9: Computational Tools, Shape Finding and Optimization
  • Title: Finite element analysis for minimal shape
  • Author(s): Vinicius ARCARO, Katalin KLINKA
  • Keywords: element, line, membrane, minimization, nonlinear, optimization, tetrahedron, triangle.
Abstract
This text describes a novel mathematical model that unifies all geometrical minimal shape problems by defining geometrical finite elements. Three types of elements are defined: line, triangle and tetrahedron. By associating a volume for each element type, the elements can be used together in the discretization of a geometrical shape. For each element type, its corresponding isovolumetric element is also defined. The geometrical minimal shape problem is formulated as an equality constrained minimization problem. The importance of this approach is that apparently distinct problems can be treated by a unified framework. The augmented Lagrangian method is used to solve the associated unconstrained minimization problem. A quasi-Newton method is used, which avoids the evaluation of the Hessian matrix. The source and executable computer codes of the algorithm are available for download from the website of one of the authors.

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