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Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions |
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| Authors: | D.F. Gilhooley R.C. Batra J.R. Xiao M.A. McCarthy J.W. Gillespie Jr. |
| Affiliation: | aCenter for Composite Materials, University of Delaware, Newark, DE 19716, USA bDepartment of Materials Science and Engineering, University of Delaware, Newark, DE 19716, USA cDepartment of Civil and Structural Engineering, University of Delaware, Newark, DE 19716, USA dDepartment of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA eComposites Research Centre, University of Limerick, Ireland fMaterials and Surface Science Institute, University of Limerick, Ireland gDepartment of Mechanical and Aeronautical Engineering, University of Limerick, Ireland |
| Abstract: | Infinitesimal deformations of a functionally graded thick elastic plate are analyzed by using a meshless local Petrov–Galerkin (MLPG) method, and a higher-order shear and normal deformable plate theory (HOSNDPT). Two types of Radial basis functions RBFs, i.e. Multiquadrics and Thin Plate Splines, are employed for constructing the trial solutions, while a fourth-order Spline function is used as the weight/test function over a local subdomain. Effective material moduli of the plate, made of two isotropic constituents with volume contents varying only in the thickness direction, are computed using the Mori–Tanaka homogenization technique. Computed results for a simply supported aluminum/ceramic plate are found to agree well with those obtained analytically. Results for a plate with two opposite edges free and the other two simply supported agree very well with those obtained by analyzing three-dimensional deformations of the plate by the finite element method. The distributions of the deflection and stresses through the plate thickness are also presented for different boundary conditions. It is found that both types of basis functions give accurate values of plate deflection, but the multiquadrics give better values of stresses than the thin plate splines. |
| Keywords: | Higher-order shear and normal deformable plate theory Thick plate Functionally graded materials MLPG method Radial basis function |
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