Optimal design of elastic beams under multiple design constraints
type: Item
instance of: scholarly article
title: Optimal design of elastic beams under multiple design constraints
zbMATH Open document ID: 0639.73025
DOI: 10.1016/0020-7683(88)90065-0
author: G. I. N. Rozvany
author: K. M. Yep
author: T. G. Ong
author: Bhushan Lal Karihaloo
published in: International Journal of Solids and Structures
publication date: 1988-01-01T00:00:00Z
review text: This paper discusses the optimization of elastic beams under multiple load conditions and self-weight subject to stress and displacement constraints as well as limits on the cross-sectional area and its rate of spatial change (``Niordson constraint''). The general formulation allows for the effect of both bending moments and shear forces on the stresses and deflections. The proposed method is based on static-kinematic optimality criteria which have been successfully used in optimal plastic design. In the above approach, the Lagrangian of the equilibrium condition is regarded as an ``associated'' (or ``Pragerian'') displacement field. The general theory is then illustrated with the example of a built-in beam subjected to stress and Niordson constraints; the statical redundancy of the beam provides a (zero) displacement constraint. Allowance is also made for the cost of clamping moments. It is found that, in general, some segments of the beams are ``understressed'' and the associated displacement field contains concentrated rotations (``curvature impulses''). Moreover, the solution of this example is found to take on a surprising number of different forms. A beam example with allowance for self-weight will be discussed in Part II of this study.
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 4043382
zbMATH Keywords: deflection constraints
zbMATH Keywords: stress constraints
zbMATH Keywords: constraints on the minimum and maximum cross-sectional area
zbMATH Keywords: elastic beams
zbMATH Keywords: multiple load conditions
zbMATH Keywords: self-weight
zbMATH Keywords: displacement constraints
zbMATH Keywords: Niordson constraint
zbMATH Keywords: bending moments
zbMATH Keywords: shear forces
zbMATH Keywords: static-kinematic optimality criteria
MaRDI profile type: Publication
full work available at URL: 0020-7683(88)90065-0
OpenAlex ID: W2015747637
description: scientific article; zbMATH DE number 4043382