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首页> 外文期刊>Engineering analysis with boundary elements >A new approach to non-homogeneous hyperbolic boundary value problems using hybrid-Trefftz stress finite elements
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A new approach to non-homogeneous hyperbolic boundary value problems using hybrid-Trefftz stress finite elements

机译：混合Trefftz应力有限元的非齐次双曲边值问题的一种新方法

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摘要

A new approach to the solution of non-homogeneous hyperbolic boundary value problems is casted here using the hybrid-Trefftz stress/flux elements. Similarly to the Dual Reciprocity Method, the technique adopted in this paper uses a Trefftz-compliant set of functions to approximate the complementary solution of the problem and an additional trial basis to approximate its particular solution. However, the particular and complementary solutions are obtained here in a single step, and not sequentially, as typical of the Dual Reciprocity Method. The trial functions used for both particular and complementary solutions are merged together in the same basis and offered full flexibility to combine so as to recover the enforced equations in the best possible way. This option enables Trefftz-compliant functions to compensate for deficiencies of the particular solution basis, meaning that accurate total solutions can be obtained with relatively poor particular solution approximations. The formulation preserves the Her-mitian, sparse and localized structure that typifies the matrix of coefficients of hybrid-Trefftz finite elements and avoids the drawbacks of the collocation procedures that arise in the Dual Reciprocity Method. Moreover, all terms of the matrix of coefficients are reduced to boundary integral expressions provided the particular solution trial functions satisfy the static problem obtained after discarding both non-homogeneous and time derivative terms from the governing equation.
机译：本文使用混合Trefftz应力/磁通单元，提出了一种解决非均匀双曲边值问题的新方法。与双重对等方法相似，本文采用的技术使用了符合Trefftz的一组函数来近似解决问题的互补解，并使用了一个额外的试验基础来近似其特定的解。但是，在这里，特定解决方案和补充解决方案是在单一步骤中获得的，而不是双对等方法的典型解决方案。用于特定解决方案和补充解决方案的试验函数在相同的基础上合并在一起，并提供了完全的组合灵活性，以便以最佳方式恢复强制方程。此选项使符合Trefftz的功能可以补偿特定解决方案基础的不足，这意味着可以使用相对较差的特定解决方案近似值来获得准确的总体解决方案。该公式保留了Her-mitian，稀疏和局部化的结构，该结构是Hybrid-Trefftz有限元系数矩阵的代表，并且避免了对偶互易方法中出现的配置程序的缺点。此外，系数矩阵的所有项都简化为边界积分表达式，只要特定的求解试验函数满足从控制方程中丢弃非齐次项和时间导数项之后获得的静态问题。

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