Involutory transformations and variational principles with multi- variables in thin plate bending problems
type: Item
instance of: scholarly article
title: Involutory transformations and variational principles with multi- variables in thin plate bending problems
zbMATH Open document ID: 0615.73069
DOI: 10.1007/BF01895680
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1985-01-01T00:00:00Z
review text: Generalized variational principles of plate bending problems are established from their minimum potential energy principle and minimum complementary energy principle through the elimination of their constraints by means of the method of Lagrange multipliers. The involutory transformations are also introduced in order to reduce the order of differentiations for the variables in the variation. Furthermore, these involutory transformations become in fact the additional constraints in the variation, and additional Lagrange multipliers may be used in order to remove these additional constraints. Thus, various multi-variable variational principles are obtained for the plate bending problems. However, it is observed that, not all the constraints of variation can be removed simply by the ordinary method of linear Lagrange multipliers. In such cases, the method of high-order Lagrange multipliers are used to remove those constraints left over by ordinary linear multiplier method. And consequently, some functionals of more general forms are obtained for the generalized variational principles of plate bending problems.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 49M29
zbMATH DE Number: 3997293
zbMATH Keywords: Generalized variational principles
zbMATH Keywords: plate bending
zbMATH Keywords: minimum potential energy principle
zbMATH Keywords: minimum complementary energy principle
zbMATH Keywords: method of Lagrange multipliers
zbMATH Keywords: involutory transformations
zbMATH Keywords: multi-variable variational principles
author: Wei-zang Chien
MaRDI profile type: Publication
cites work: Q4001895
cites work: Large deflection of circular plate under compound load
full work available at URL: https://doi.org/10.1007/bf01895680
OpenAlex ID: W2013442469
description: scientific article; zbMATH DE number 3997293