Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory

• Published in: Applied mathematical modelling Vol. 34; no. 11; pp. 3659 - 3673
• Main Authors: Bodaghi, M., Saidi, A.R.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01-11-2010; Elsevier
• Subjects: Boundary conditions; Buckling; Buckling analysis; Exact sciences and technology; Functionally graded; Functionally gradient materials; Fundamental areas of phenomenology (including applications); Higher-order shear deformation theory; Levy solution; Mathematical analysis; Mathematical models; Physics; Plate theory; Rectangular plates; Shear deformation; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Thick rectangular plate; Thick rectangular plate; Higher-order shear deformation theory; Functionally graded; Levy solution; Buckling analysis; Simple support; Thick plate; Aspect ratio; Equilibrium equation; Modeling; Functionnally graded material; Critical load; Rectangular plate; Non linear effect; Buckling; Boundary layer
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2010.03.016

In this article, an analytical approach for buckling analysis of thick functionally graded rectangular plates is presented. The equilibrium and stability equations are derived according to the higher-order shear deformation plate theory. Introducing an analytical method, the coupled governing stability equations of functionally graded plate are converted into two uncoupled partial differential equations in terms of transverse displacement and a new function, called boundary layer function. Using Levy-type solution these equations are solved for the functionally graded rectangular plate with two opposite edges simply supported under different types of loading conditions. The excellent accuracy of the present analytical solution is confirmed by making some comparisons of the present results with those available in the literature. Furthermore, the effects of power of functionally graded material, plate thickness, aspect ratio, loading types and boundary conditions on the critical buckling load of the functionally graded rectangular plate are studied and discussed in details. The critical buckling loads of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be used as benchmark.