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Transient 3D heat conduction in functionally graded materials by the method of fundamental solutions

机译:基本解决方法在功能梯度材料中进行3D瞬态热传导

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In this paper, the three-dimensional transient heat conduction problems in functionally graded materials (FGMs) have been solved using the method of fundamental solutions (MFS). To be more specific, we consider the FGMs with thermal conductivity and specific heat vary exponentially in z-direction. In the numerical simulation, we coupled the fundamental solution of diffusion equation with the method of time-space unification which provides a simple and direct approach for solving time-dependent problems. The parameter transformation technique is also utilized to obtain the fundamental solutions which contain the thermal conductivity and the specific heat conditions. The MFS is very attractive in handling problems with irregular domain due to the simplicity of the method. The numerical results are in good agreement comparing with analytical solution and results obtained from the finite element method.
机译:在本文中,已经使用基本解决方案(MFS)解决了功能梯度材料(FGM)中的三维瞬态导热问题。更具体地说,我们认为FGM的热导率和比热在z方向上呈指数变化。在数值模拟中,我们将扩散方程的基本解与时空统一方法相结合,为解决时变问题提供了一种简单直接的方法。参数转换技术还用于获得包含热导率和特定热条件的基本解。由于该方法的简单性,MFS在处理具有不规则域的问题时非常有吸引力。数值结果与解析解和有限元方法得到的结果相吻合。

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