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Boundary element analysis of uncoupled transient thermo-elastic problems with time- and space-dependent heat sources

机译：时空依赖热源的非耦合瞬态热弹性问题的边界元分析

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摘要

A boundary element method (BEM) for the analysis of two- and three-dimensional uncoupled transient thermo-elastic problems involving time- and space-dependent heat sources is presented. The domain integrals are efficiently treated using the Cartesian transformation and the radial integration methods without considering any internal cells. Similar to the dual reciprocity method (DRM), some internal points without any connectivity are considered; however, in contrast to the DRM, any arbitrary mesh-free interpolation method can be used in the present formulation. There is no need to find any particular solutions and the shape functions in the mesh-free interpolation method can be arbitrary and sufficiently complicated. Unlike the DRM, the generated system of equations contains the unknowns only on the boundary. After finding the primary unknowns on the boundary, the temperature, displacement, and stress components at all internal points can directly be found without solving any system of equations. Three examples with different forms of heat sources are presented to demonstrate the efficiency and accuracy of the proposed method. Although the proposed BEM is mathematically more complicated than domain methods, such as the finite element method (FEM), it is more efficient from a modelling viewpoint since only the surface mesh has to be generated in the presented method.
机译：提出了一种边界元方法（BEM），用于分析涉及时间和空间的热源的二维和三维非耦合瞬态热弹性问题。使用笛卡尔变换和径向积分方法可以有效地处理域积分，而无需考虑任何内部单元。与双重互惠方法（DRM）相似，考虑了一些没有任何连通性的内部点。然而，与DRM相反，在本公式中可以使用任何任意的无网格插值方法。无需找到任何特定的解决方案，并且无网格插值方法中的形状函数可以是任意的并且足够复杂。与DRM不同，生成的方程组仅在边界上包含未知数。在找到边界上的主要未知数之后，可以直接找到所有内部点的温度，位移和应力分量，而无需求解任何方程组。给出了三个具有不同形式热源的示例，以证明所提出方法的效率和准确性。尽管所提出的BEM在数学上比领域方法（例如，有限元方法（FEM））更为复杂，但从建模的角度来看，它更为有效，因为在所提出的方法中仅需要生成表面网格。

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