Analysis of 2D heat conduction in nonlinear functionally graded materials using a local semi-analytical meshless method
Chao Wang,Fajie Wang,Yanpeng Gong,Yanpeng Gong +3 more
- Vol. 6, Iss: 11, pp 12599-12618
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TLDR
In this paper, a local semi-analytical meshless method for simulating heat conduction in nonlinear functionally graded materials is proposed, which uses the non-singular general solution as the basis function and has the merits of simplicity, high accuracy and easy-to-program.Abstract:Â
This paper proposes a local semi-analytical meshless method for simulating heat conduction in nonlinear functionally graded materials. The governing equation of heat conduction problem in nonlinear functionally graded material is first transformed to an anisotropic modified Helmholtz equation by using the Kirchhoff transformation. Then, the local knot method (LKM) is employed to approximate the solution of the transformed equation. After that, the solution of the original nonlinear equation can be obtained by the inverse Kirchhoff transformation. The LKM is a recently proposed meshless approach. As a local semi-analytical meshless approach, it uses the non-singular general solution as the basis function and has the merits of simplicity, high accuracy, and easy-to-program. Compared with the traditional boundary knot method, the present scheme avoids an ill-conditioned system of equations, and is more suitable for large-scale simulations associated with complicated structures. Three benchmark numerical examples are provided to confirm the accuracy and validity of the proposed approach.read more
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References
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The method of fundamental solutions for elliptic boundary value problems
TL;DR: Techniques by which MFS-type methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are outlined.
Posted Content
A meshless, integration-free, and boundary-only RBF technique
Wen Chen,Masataka Tanaka +1 more
TL;DR: Based on the radial basis function (RBF), non-singular general solution and dual reciprocity method (DRM), this article presented an inherently meshless, integration-free, boundary-only RBF collocation techniques for numerical solution of various partial differential equation systems.
Journal ArticleDOI
A meshless, integration-free, and boundary-only RBF technique
Wen Chen,Masataka Tanaka +1 more
TL;DR: The present scheme is named as the boundary knot method (BKM) to differentiate it from the other numerical techniques, and is different from the method of fundamental solution in that the former does not require the artificial boundary and results in the symmetric system equations under certain conditions.
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The simple boundary element method for transient heat conduction in functionally graded materials
TL;DR: In this paper, a boundary element method for transient heat conduction in functionally graded materials is presented, which leads to a boundary-only formulation without any domain discretization, and the results of the test examples are in excellent agreement with analytical solutions and finite element simulation results.
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Singular boundary method for wave propagation analysis in periodic structures
TL;DR: In this article, a strong-form boundary collocation method, the singular boundary method (SBM), is developed for the wave propagation analysis at low and moderate wavenumbers in periodic structures.
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