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Development and Implementation of Discontinuous Galerkin (DG) Finite Element Methods for Topology Optimization

by Kanaglekar, Rohit

Abstract (Summary)
A short design cycle is an important factor in building cost-effective products and staying competitive. In order to meet market demands, structural optimization tools are widely used along with established CAE (Computer Aided Engineering), CAD (Computer Aided Design) and PLM (Product Lifecycle Management) methodologies. Using these tools, the optimal shape of a structure can be predicted at the start of the design process and this can act as an input to the designer in the conceptual design phase and help him design better, stronger and cost-effective structures. The goal of topology optimization is to determine the best distribution of material for a structure such that an objective function such as compliance takes an extremal value, subject to some constraints. After a finite element discretization of the structure, the design variables are normally the "density" of the finite elements. Constraints are placed on these density values and on the volume of the structure to be occupied by the material. In this thesis, we use non-conforming discontinuous Galerkin (DG) methods to overcome some of the numerical problems that occur when the topology optimization problem is solved using conforming finite elements. These numerical problems are the formation of checkerboard type patterns and mesh dependence of the solution. Various non-conforming discontinuous Galerkin formulations are used. The variation of optimal topologies with the penalization parameter present in DG formulations is also studied. The stiffness behavior of checkerboard pattern is also analyzed with both conforming and DG formulations to study the relationship between patch stiffness and occurrence of checkerboards. We find that the non-symmetric interior penalty Galerkin (NIPG) method emerges as a competitive alternative to the standard finite element method and is free from the associated instabilities.
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School:University of Cincinnati

School Location:USA - Ohio

Source Type:Master's Thesis

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Date of Publication:01/01/2005

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