Optimization of shallow arches against instability using sensitivity derivatives
type: Item
instance of: scholarly article
title: Optimization of shallow arches against instability using sensitivity derivatives
zbMATH Open document ID: 0619.73094
DOI: 10.1016/0168-874X(87)90010-2
author: Manohar P. Kamat
published in: Finite Elements in Analysis and Design
publication date: 1987-01-01T00:00:00Z
review text: In this paper, the problem of optimization of shallow frame structures, which involves coupling of axial and bending responses, is discussed. A shallow arch of given shape and given weight is optimized such that its limit point load is maximized. The cross-sectional area, A(x), and the moment of inertia, I(x), of the arch obey the relationship \(I(x)=p[A(x)]^ n\), where \(n=1,2,3\) and p is a specified constant. Analysis of the arch for its limit point calculation involves a geometric nonlinear analysis which is performed using a co-rotational formulation. The optimization is carried out using a second-order projected Lagrangian algorithm, and the sensitivity derivatives of the critical load parameter with respect to the areas of the finite elements of the arch are calculated using implicit differentiation. Results are presented for an arch of a specified rise to span under two different loadings, and the limitations of the approach for the intermediate rise arches are addressed.
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 4005772
zbMATH Keywords: constrained optimization
zbMATH Keywords: shallow frame structures
zbMATH Keywords: coupling of axial and bending responses
zbMATH Keywords: shallow arch
zbMATH Keywords: second-order projected Lagrangian algorithm
zbMATH Keywords: sensitivity derivatives
zbMATH Keywords: critical load parameter
describes a project that uses: EISPACK
MaRDI profile type: Publication
full work available at URL: 0168-874x(87)90010-2
OpenAlex ID: W2032854560
description: scientific article; zbMATH DE number 4005772