Post-buckling analysis of viscoelastic plates with fractional derivative models

The post-buckling response of thin plates made of linear viscoelastic materials is investigated. The employed viscoelastic material is described with fractional order time derivatives. The governing equations, which are derived by considering the equilibrium of the plate element, are three coupled n...

Full description

Saved in:
Bibliographic Details
Published in:Engineering analysis with boundary elements 2010-12, Vol.34 (12), p.1038-1048
Main Authors: Katsikadelis, J.T., Babouskos, N.G.
Format: Article
Language:English
Subjects:
Analog equation method
Boundary element method
Buckling
Deflection
Derivatives
Differential equations
Exact sciences and technology
Fractional derivatives
Fundamental areas of phenomenology (including applications)
Large deflections
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Physics
Plates
Sciences and techniques of general use
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Viscoelastic materials
Viscoelasticity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The post-buckling response of thin plates made of linear viscoelastic materials is investigated. The employed viscoelastic material is described with fractional order time derivatives. The governing equations, which are derived by considering the equilibrium of the plate element, are three coupled nonlinear fractional partial evolution type differential equations in terms of three displacements. The nonlinearity is due to nonlinear kinematic relations based on the von Kármán assumption. The solution is achieved using the analog equation method (AEM), which transforms the original equations into three uncoupled linear equations, namely a linear plate (biharmonic) equation for the transverse deflection and two linear membrane (Poisson’s) equations for the inplane deformation under fictitious loads. The resulting initial value problem for the fictitious sources is a system of nonlinear fractional ordinary differential equations, which is solved using the numerical method developed recently by Katsikadelis for multi-term nonlinear fractional differential equations. The numerical examples not only demonstrate the efficiency and validate the accuracy of the solution procedure, but also give a better insight into this complicated but very interesting engineering plate problem
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2010.07.003