On the asymptotic membrane theory of thin hyperelastic plates
type: Item
instance of: scholarly article
title: On the asymptotic membrane theory of thin hyperelastic plates
zbMATH Open document ID: 0917.73033
DOI: 10.1016/S0020-7225(96)00068-7
author: D. Massart
published in: International Journal of Engineering Science
publication date: 1999-08-05T00:00:00Z
review text: Applying the asymptotic expansion technique to the three-dimensional equations of nonlinear elasticity, we derive a nonlinear asymptotic membrane theory considering large deflections and strains for thin hyperelastic plates. To this end, the displacement vector and stress tensor components are scaled via an appropriate thickness parameter, such that the present approximation takes into account larger deflection compared with those of the von Kármán plate theory. Later, for an arbitrary form of the strain energy function, we obtain the hierarchy of the field equations by expanding the displacement vector and the stress tensor in terms of powers of the square root of the thickness parameter. Then the equations belonging to the first three orders of this hierarchy are studied in detail.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 1162162
zbMATH Keywords: hierarchy of field equations
zbMATH Keywords: Föppl membrane theory
zbMATH Keywords: infinitely long strip under uniform load
zbMATH Keywords: large deflections
zbMATH Keywords: thickness parameter
zbMATH Keywords: von Kármán plate theory
zbMATH Keywords: strain energy function
MaRDI profile type: Publication
cites work: A justification of a nonlinear model in plate theory
cites work: A justification of the von Kármán equations
cites work: Q4743856
cites work: Nonlinear plate theory: Dimensional analysis and asymptotic formulation of the large scale problem
cites work: Asymptotic variational methods in large deflection small strain plate theory
cites work: Q5581304
cites work: A Nonlinear Theory for Elastic Plates With Application to Characterizing Paper Properties
cites work: On the foundations of the nonlinear theory of the cylindrical deformation of thin elastic plates
cites work: Dynamical models for plates and membranes. An asymptotic approach
cites work: A justification of nonlinear properly invariant plate theories
cites work: An asymptotic theory of thin hyperelastic plates. I: General theory
cites work: An asymptotic theory of thin hyperelastic plates. II: Incompressible solids and an application of the general theory
cites work: Highly nonlinear deformation of uniformly-loaded circular plates
cites work: Non-linear bending of a circular plate under normal pressure
cites work: Nonlinear Asymptotic Solution of the Reissner Plate Equations
cites work: Q3738668
cites work: Asymptotic expansions for large elastic strain of a circular plate
cites work: On Boundary Layers in a Pressurized Mooney Cylinder
description: scientific article; zbMATH DE number 1162162