A scaled boundary finite element formulation over arbitrary faceted star convex polyhedra. (July 2017)

• Record Type: Journal Article
• Authors: Natarajan, Sundararajan; Ooi, Ean Tat; Saputra, Albert; Song, Chongmin
• Is Part Of: Engineering analysis with boundary elements. Volume 80(2017)
• Page Start: 218
• Page End: 229
• Publication Date: 2017-07
• Subjects: Scaled boundary finite element method -- Polygonal finite element method -- Polyhedra -- Boundary integration -- Wachspress shape functions; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2017.03.007
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: 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.