Large thermoelastic deflections and stability of simply supported polygonal panels
type: Item
instance of: scholarly article
title: Large thermoelastic deflections and stability of simply supported polygonal panels
zbMATH Open document ID: 0581.73053
DOI: 10.1007/BF01177058
published in: Acta Mechanica
publication date: 1986-01-01T00:00:00Z
review text: A Berger-type approximation for large deflections of thermally loaded initially curved elastic plates is derived. In case of simply supported boundaries and arbitrary polygonal planforms, dimensionless solution is found in terms of Dirichlet's Helmholtz-eigenvalues of the given domain. Stability of this equilibrium solution is exemplarily discussed, showing bifurcation and snapping behaviour in the sense of a cusp catastrophe. Additionally, possibility of mode-jumping is indicated.
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74F05
zbMATH DE Number: 3930466
zbMATH Keywords: post buckling
zbMATH Keywords: imperfection sensitivity
zbMATH Keywords: second order Helmholtz-Klein- Gordon boundary value problem
zbMATH Keywords: homogeneous Dirichlet boundary conditions
zbMATH Keywords: nonlinear algebraic equation for Berger's hydrostatic in-plane force
zbMATH Keywords: Helmholtz eigenvalue problems
zbMATH Keywords: Berger-type approximation
zbMATH Keywords: large deflections
zbMATH Keywords: thermally loaded
zbMATH Keywords: initially curved elastic plates
zbMATH Keywords: simply supported boundaries
zbMATH Keywords: arbitrary polygonal planforms
zbMATH Keywords: dimensionless solution
zbMATH Keywords: Dirichlet's Helmholtz-eigenvalues
zbMATH Keywords: Stability
zbMATH Keywords: equilibrium solution
zbMATH Keywords: bifurcation
zbMATH Keywords: snapping
zbMATH Keywords: cusp catastrophe
zbMATH Keywords: mode-jumping
author: H. Irschik
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3930466