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A scaled boundary finite element formulation over arbitrary faceted star convex polyhedra

机译：任意多面星形凸多面体上的比例边界有限元公式

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摘要

In this paper, a displacement based finite element framework for general three-dimensional convex polyhedra is presented. The method is based on a semi-analytical framework, the scaled boundary finite element method. The method relies on the definition of a scaling center from which the entire boundary is visible. The salient feature of the method is that the discretizations are restricted to the surfaces of the polyhedron, thus reducing the dimensionality of the problem by one. Hence, an explicit form of the shape functions inside the polyhedron is not required. Conforming shape functions defined over arbitrary polygon, such as the Wachpress interpolants are used over each surface of the polyhedron. Analytical integration is employed within the polyhedron. The proposed method passes patch test to machine precision. The convergence and the accuracy properties of the method is discussed by solving few benchmark problems in linear elasticity.
机译：本文提出了一种基于位移的通用三维凸多面体的有限元框架。该方法基于半解析框架，即缩放边界有限元方法。该方法依赖于缩放中心的定义，从该缩放中心可以看到整个边界。该方法的显着特征是离散仅限于多面体的表面，因此将问题的维数减少了一个。因此，不需要多面体内部形状函数的明确形式。在多面体的每个表面上使用在任意多边形上定义的一致形状函数，例如Wachpress插值。多面体内部采用了分析积分。所提出的方法通过了补丁测试，达到了机器精度。通过解决线性弹性中的几个基准问题，讨论了该方法的收敛性和准确性。

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