Abstract
In this article, we propose a novel meshless method for solving two-dimensional stationary heat conduction problems in layered materials. The proposed method is a recently developed boundary-type meshless method which combines the collocation scheme from the method of fundamental solutions (MFS) with the collocation Trefftz method (CTM) to improve the applicability of the method for solving boundary value problems. Particular non-singular basis functions from cylindrical harmonics are adopted in which the numerical approximation is based on the superposition principle using the non-singular basis functions expressed in terms of many source points. For the modeling of multi-layer composite materials, we adopted the domain decomposition method (DDM), which splits the domain into smaller subdomains. The continuity of the flux and the temperature has to be satisfied at the interface of subdomains for the problem. The validity of the proposed method is investigated for several test problems. Numerical applications were also carried out. Comparison of the proposed method with other meshless methods showed that it is highly accurate and computationally efficient for modeling heat conduction problems, especially in heterogeneous multi-layer composite materials.
Highlights
Since the 1940s, the knowledge of using composite laminate materials in industry has improved significantly [1]
The method of fundamental solutions (MFS) is a boundary-type meshless method for solving problems where the solutions are approximated by the fundamental solution which is expressed in terms of source points
For the modeling of multi-layer composite materials, we adopted the domain decomposition method (DDM) [37], which splits the domain into smaller subdomains that are intersected only at the interface between layers
Summary
Since the 1940s, the knowledge of using composite laminate materials in industry has improved significantly [1]. Many heat conduction problems in layered composites have been routinely solved by numerical methods such as the finite difference method [4,5,6], finite element method [7,8], finite volume method [9,10,11] and the boundary element method [12,13]. The CTM [32] is categorized as a boundary-type meshless method for the numerical solution of problems where approximate solutions are expressed as a truncated series of T-complete basis functions automatically satisfying governing equations. The MFS is a boundary-type meshless method for solving problems where the solutions are approximated by the fundamental solution which is expressed in terms of source points. We propose a novel hybrid boundary-type meshless method for solving two-dimensional stationary heat conduction problems in layered composite materials.
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