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A meshfree approach for transient heat conduction analysis of nonlinear functionally graded materials. (English) Zbl 1404.74202

Summary: In this paper, an alternative meshfree approach is presented for transient heat conduction analysis of nonlinear functionally graded materials (FGMs). The main idea behind the introduced approach is to use collocation in local domains containing of sets of regular or scattered nodes and approximating the solution by B-spline basis functions. It combines the favorable properties of B-spline basis functions in having arbitrary degree for better resolution of solution, partition of unity and the Kronecker delta properties with low computational effort of collocation. The method is called as local B-spline collocation method. It is mathematically simple, efficient to program and truly meshless. The method is applied for analyzing transient heat conduction in a wide range of FGMs with various material gradation models, in both 2D and 3D domains. The results obtained agree well with those computed by analytical solution and other well-known methods, confirming the suitability and efficacy of the presented scheme.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
74A50 Structured surfaces and interfaces, coexistent phases
80A20 Heat and mass transfer, heat flow (MSC2010)
80M22 Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer
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