A scaled boundary finite element formulation over arbitrary faceted star convex polyhedra
- Authors: Natarajan, Sundararajan , Ooi, Ean Tat , Saputra, Albert , Song, Chongmin
- Date: 2017
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 80, no. (2017), p. 218-229
- Full Text: false
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- Description: 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. © 2017 Elsevier Ltd
A dual scaled boundary finite element formulation over arbitrary faceted star convex polyhedra
- Authors: Ooi, Ean Tat , Saputra, Albert , Natarajan, Sundararajan , Ooi, Ean Hin , Song, Chongmin
- Date: 2020
- Type: Text , Journal article
- Relation: Computational Mechanics Vol. 66, no. 1 (2020), p. 27-47
- Full Text: false
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- Description: A novel technique to formulate arbritrary faceted polyhedral elements in three-dimensions is presented. The formulation is applicable for arbitrary faceted polyhedra, provided that a scaling requirement is satisfied and the polyhedron facets are planar. A triangulation process can be applied to non-planar facets to generate an admissible geometry. The formulation adopts two separate scaled boundary coordinate systems with respect to: (i) a scaling centre located within a polyhedron and; (ii) a scaling centre on a polyhedron’s facets. The polyhedron geometry is scaled with respect to both the scaling centres. Polygonal shape functions are derived using the scaled boundary finite element method on the polyhedron facets. The stiffness matrix of a polyhedron is obtained semi-analytically. Numerical integration is required only for the line elements that discretise the polyhedron boundaries. The new formulation passes the patch test. Application of the new formulation in computational solid mechanics is demonstrated using a few numerical benchmarks. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.