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The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

Sunilkumar, N and Roy, D (2010) The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics. In: Computer Modeling in Engineering and Sciences (CMES), 66 (3). pp. 249-284.

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Official URL: http://www.techscience.com/doi/10.3970/cmes.2010.0...

Abstract

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Tech Science Press.
Keywords: DMS-splines; tetrahedral and triangular prism elements; knotcloud generation; polynomial reproduction; 3D elasticity equations
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Date Deposited: 01 Mar 2011 11:34
Last Modified: 01 Mar 2011 11:34
URI: http://eprints.iisc.ernet.in/id/eprint/35827

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