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http://dx.doi.org/10.7734/COSEIK.2014.27.3.183

A Study on the Development of Shape Functions of Polyhedral Finite Elements  

Kim, Hyun-Gyu (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.27, no.3, 2014 , pp. 183-189 More about this Journal
Abstract
In this paper, a polyhedral element is presented to solve three-dimensional problems by developing shape functions based on Wachspress coordinates and moving least square approximation. A subdivision of polyhedrons into tetrahedral domains is performed for the construction of shape functions of polyhedral elements, and numerical integration of the weak form is carried out consistently over the tetrahedral domains. The weight functions for moving least square approximation are defined by solving Laplace equation with boundary values based on Wachspress coordinates on polyhedral element faces. Polyhedral elements presented in this paper have similar properties to conventional finite element regarding the continuity, the completeness, the node-element connectivity and the inter-element compatibility. Numerical examples show the effectiveness of the present method for solving three-dimensional problems using polyhedral elements.
Keywords
finite elements; polyhedral elements; barycentric coordinates; moving least square approximation;
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