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Two-dimensional stress analysis of functionally graded solids using the MLPG method with radial basis functions |
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| Authors: | DF Gilhooley JR Xiao RC Batra MA McCarthy JW Gillespie Jr |
| Affiliation: | aComposites Research Centre, University of Limerick, Ireland bMaterials and Surface Science Institute, University of Limerick, Ireland cDepartment of Mechanical and Aeronautical Engineering, University of Limerick, Ireland dDepartment of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA eCenter for Composite Materials, University of Delaware, Newark, DE 19716, USA fDepartment of Materials Science and Engineering, University of Delaware, Newark, DE 19716, USA gDepartment of Civil and Structural Engineering, University of Delaware, Newark, DE 19716, USA |
| Abstract: | The meshless local Petrov–Galerkin (MLPG) method is used for analysing two-dimensional (2D) static and dynamic deformations of functionally graded materials (FGMs) with material response modelled as either linear elastic or as linear viscoelastic. The multiquadric radial basis function (RBF) is employed to approximate the trial solution. Results are computed with two different choices of test functions, namely a fourth-order spline weight function, and a Heaviside step function, each having a compact support. No background mesh is used to numerically evaluate integrals appearing in the weak formulation of the problem, thus the method is truly meshless. A benefit of using RBFs is that they possess the Kronecker delta property; thus it is easy to satisfy essential boundary conditions. For five problems, the computed results are found to match well with those either from their analytical solutions or numerical solutions of other researchers who employed different algorithms. For a dynamic problem, the Laplace-transform technique is utilised. The numerical examples illustrate that displacements and stress distributions in a structure made of an FGM differ considerably from those at the corresponding points in the same structure made of a homogeneous material. Thus, the inhomogeneity in material properties can be exploited to optimise stress distribution, minimise deflection and reduce the maximum stress. |
| Keywords: | Functionally graded material MLPG method Radial basis functions Static and dynamic problems |
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