A shape optimization approach based on natural design variables and shape functions
type: Item
instance of: scholarly article
title: A shape optimization approach based on natural design variables and shape functions
zbMATH Open document ID: 0616.73080
DOI: 10.1016/0045-7825(88)90061-8
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: The general problem of concern is to find the optimum shape of an elastic body, which requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. The basic approach so far has been to choose a set of geometric design variables that define the shape of the structure. Typically the design variables have been chosen as coefficients of splines and polynomials, coordinates of 'control' nodes, and other geometric parameters. An automatic finite element discretization scheme that uses geometric entities such as lines, arcs, splines, and blending functions, is then used to relate changes in position of interior grid points in the finite element mesh to changes in the design variables. In this paper, a set of natural design variables is chosen as the design variables defining the shape. Specifically, the design variables are the magnitudes of a set of fictitious loads applied on the structure. The displacements produced by these fictitious loads, or natural shape functions, are added onto the initial mesh to obtain the new shape. Consequently, a linear relationship is established between changes in grid point locations and design variables through a finite element analysis. Plane elasticity problems are solved using the new approach. The quality of the finite element meshes produced and other salient features of the shape optimal design problem are discussed.
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 3999441
zbMATH Keywords: initial mesh
zbMATH Keywords: design sensitivity
zbMATH Keywords: natural design variables
zbMATH Keywords: magnitudes of a set of fictitious loads
zbMATH Keywords: displacements
zbMATH Keywords: natural shape functions
zbMATH Keywords: shape optimal design problem
author: Ashok D. Belegundu
author: Subramaniam D. Rajan
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90061-8
OpenAlex ID: W2073660427
cites work: Optimum shape design of rotating disks
cites work: An integrated system for shape optimal design
cites work: Optimum structural design with plate bending elements - A survey
cites work: A domain method for shape design sensitivity analysis of built-up structures
cites work: Q3727511
description: scientific article; zbMATH DE number 3999441