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The complex variable meshless local Petrov-Galerkin method for elastodynamic analysis of functionally graded materials. (English) Zbl 1411.74052
Summary: As an improvement of the meshless local Petrov-Galerkin (MLPG), the complex variable meshless local Petrov-Galerkin (CVMLPG) method is extended here to dynamic analysis of functionally graded materials (FGMs). In this method, the complex variable moving least-squares (CVMLS) approximation is used instead of the traditional moving least-squares (MLS) to construct the shape functions. The main advantage of the CVMLS approximation over MLS approximation is that the number of the unknown coefficients in the trial function of the CVMLS approximation is less than that of the MLS approximation, thus higher efficiency and accuracy can be achieved under the same node distributions. In implementation of the present method, the variations of the FGMs properties are computed by using material parameters at Gauss points, so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method (FEM) for the FGMs. Several numerical examinations for dynamic analysis of FGMs are carried out to demonstrate the accuracy and efficiency of the CVMLPG.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74B05 Classical linear elasticity
Software:
Mfree2D
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