A mathematical model of coupled plates and its finite element method
type: Item
instance of: scholarly article
title: A mathematical model of coupled plates and its finite element method
zbMATH Open document ID: 0774.73073
DOI: 10.1016/0045-7825(92)90122-Z
author: Lieheng Wang
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1993-04-01T00:00:00Z
review text: Complex structures are commonly investigated in practice. Although the numerical approaches can easily be applied and in many cases results are satisfactory, the mathematical base has not been sufficiently developed. In the paper the author considers the mathematical modelling of coupled plates and its finite element approximation. The case of two perpendicular rectangular plates is considered for which the total energy of the structure under virtual displacements is determined. Then the mathematical model of the coupled plates is formulated as a variational problem. The existence and uniqueness of the solution are proved. The problem is reduced to the boundary value problem and junction conditions are derived. At the end the finite element approximation is introduced and the approximation error is determined. The paper contains the mathematical consideration of the problem. The concluding formulae give the theoretical view on the convergence of the discrete method and the error estimation. It allows to investigate the properties of some other types of finite elements in the problem mentioned.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 146820
zbMATH Keywords: perpendicular rectangular plates
zbMATH Keywords: total energy
zbMATH Keywords: variational problem
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: boundary value problem
zbMATH Keywords: junction conditions
zbMATH Keywords: convergence
zbMATH Keywords: error estimation
reviewed by: C. I. Bajer
MaRDI profile type: Publication
cites work: Q3906817
cites work: Q3735174
cites work: A new class of variational problems arising in the modeling of elastic multi-structures
cites work: Junctions between three-dimensional and two-dimensional linear elastic structures
cites work: Q5628582
cites work: Q3890207
cites work: The Generalized Patch Test
full work available at URL: 0045-7825(92)90122-z
OpenAlex ID: W1974879940
description: scientific article; zbMATH DE number 146820