Multimodal optimization of arches under stability constraints with two independent design functions
type: Item
instance of: scholarly article
title: Multimodal optimization of arches under stability constraints with two independent design functions
zbMATH Open document ID: 0669.73070
DOI: 10.1016/0020-7683(89)90104-2
author: Bogdan Bochenek
author: A. Gajewski
published in: International Journal of Solids and Structures
publication date: 1989-01-01T00:00:00Z
review text: An elastic, plane and funicular circular arch loaded by uniformly distributed radial pressure is considered. Fundamental buckling modes corresponding to two lowest critical loads both for out-of-plane and in- plane buckling of the arch are studied. Both depth and width of a rectangular cross-section are treated as independent control functions. The optimization problem determines these cross-sectional dimensions as the functional design variables in order to minimize the total volume of the arch under given external pressure and geometrical constraints. Suitable optimality conditions are derived using the Pontryagin maximum principle. The solution requires a multimodal, even quadrimodal, formulation of the optimization problem to be introduced. Some detailed numerical results are presented and advantages connected with the assumption of two independent design variables are discussed.
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74G60
zbMATH DE Number: 4096901
zbMATH Keywords: optimal design
zbMATH Keywords: elastic, plane and funicular circular arch
zbMATH Keywords: uniformly distributed radial pressure
zbMATH Keywords: Fundamental buckling modes
zbMATH Keywords: lowest critical loads
zbMATH Keywords: out-of-plane
zbMATH Keywords: in-plane buckling
zbMATH Keywords: depth
zbMATH Keywords: width
zbMATH Keywords: rectangular cross- section
zbMATH Keywords: as independent control functions
zbMATH Keywords: minimize the total volume
zbMATH Keywords: external pressure
zbMATH Keywords: geometrical constraints
zbMATH Keywords: Pontryagin maximum principle
zbMATH Keywords: multimodal
zbMATH Keywords: quadrimodal
MaRDI profile type: Publication
full work available at URL: 0020-7683(89)90104-2
OpenAlex ID: W2090324177
description: scientific article; zbMATH DE number 4096901