Two-dimensional isostatic meshes in the finite element method

Martínez Marín, Rubén and Samartín, Avelino (2002). Two-dimensional isostatic meshes in the finite element method. In: "International IASS symposium on lightweight structures in civil engineering", 24-28 de Junio, 2002, Varsovia (Polonia). ISBN 83-908867-6-6. pp. 389-395.

Description

Title: Two-dimensional isostatic meshes in the finite element method
Author/s:
  • Martínez Marín, Rubén
  • Samartín, Avelino
Item Type: Presentation at Congress or Conference (Article)
Event Title: International IASS symposium on lightweight structures in civil engineering
Event Dates: 24-28 de Junio, 2002
Event Location: Varsovia (Polonia)
Title of Book: Lightweight structures in civil engineering : Proceedings of the international IASS symposium on lightweight structures in civil engineering
Date: 2002
ISBN: 83-908867-6-6
Subjects:
Freetext Keywords: Remeshing, isostatic mesh, optimal mesh, total potential energy, average quadratic error
Faculty: E.T.S.I. Caminos, Canales y Puertos (UPM)
Department: Ingeniería y Morfología del Terreno
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

More information

Item ID: 41662
DC Identifier: http://oa.upm.es/41662/
OAI Identifier: oai:oa.upm.es:41662
Deposited by: Biblioteca ETSI Caminos
Deposited on: 23 Jun 2016 05:33
Last Modified: 23 Jun 2016 05:33
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