High order sensitivity analysis in shape optimization problems
type: Item
instance of: scholarly article
title: High order sensitivity analysis in shape optimization problems
zbMATH Open document ID: 0665.73072
DOI: 10.1016/0045-7825(89)90029-7
author: F. Navarrina
author: Enrique Bendito
author: M. Casteleiro
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1989-01-01T00:00:00Z
review text: A formulation for high order directional differentiation of functions defined through integration is presented. The formulation has been developed initially for sensitivity analysis in optimal shape design problems by the finite element method. However, its application range is much wider. Explicit analytical expressions are given for sequential directional derivatives. Special emphasis has been made in holding recurrence and simplicity of intermediate operations. The proposed scheme does not depend strongly on any particular form of the state equations, and its numerical implementation in finite elements method programs can be considered easy and efficient. As an example, up to second order sensitivity techniques are applied to the optimization of a concrete roof. Structural analysis has been performed in linear elastic conditions, with quadratic three-dimensional elements for the discretization of the roof.
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 49K40
zbMATH DE Number: 4089092
zbMATH Keywords: high order directional differentiation of functions
zbMATH Keywords: integration
zbMATH Keywords: optimal shape design
zbMATH Keywords: sequential directional derivatives
zbMATH Keywords: optimization of a concrete roof
MaRDI profile type: Publication
full work available at URL: 0045-7825(89)90029-7
OpenAlex ID: W2015972717
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description: scientific article; zbMATH DE number 4089092