Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions

• Published in: Composite structures Vol. 80; no. 4; pp. 539 - 552
• Main Authors: Gilhooley, D.F., Batra, R.C., Xiao, J.R., McCarthy, M.A., Gillespie, J.W.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2007; Elsevier Science
• Subjects: Applied sciences; Composites; Computational techniques; Exact sciences and technology; Forms of application and semi-finished materials; Functionally graded materials; Fundamental areas of phenomenology (including applications); Higher-order shear and normal deformable plate theory; Mathematical methods in physics; MLPG method; Physics; Polymer industry, paints, wood; Radial basis function; Solid mechanics; Structural and continuum mechanics; Technology of polymers; Thick plate; Radial basis function; Higher-order shear and normal deformable plate theory; MLPG method; Thick plate; Functionally graded materials; Deformation modulus; Thin plate; Aluminium; Simple support; Metal; Modeling; Spline; Spline approximation; Galerkin-Petrov method; Variable section; Weight function; Functionnally graded material; Meshless method; Homogenization methods; Quadrics; Non linear effect; Effective medium model; Domain decomposition
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/j.compstruct.2006.07.007

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.