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FINITE ELEMENT ANALYSIS OF PROBLEMS IN TOPOLOGY OPTIMIZATION

by RAKSHIT, ABHIK

Abstract (Summary)
Topology optimization is fast emerging as an integral part of the product development cycle using Computer Aided Engineering tools. The optimal structure and shape of a product can be predicted in the initial stages of a development cycle using topology optimization. The goal of topology optimization is to find the best distribution of material for a structure such that an objective criterion, like global stiffness, takes on an extremum value subject to given constraints. These constraints are typically placed on the volume. In this thesis, some of the numerical issues that occur in the solution of a topology optimization problem are discussed. These numerical issues include the formation of checkerboard patterns in the final topology and sensitivity of the optimal solution to the mesh size used to discretize a domain. A computationally cheaper heuristic filtering scheme to counter these numerical instabilities is studied. The effects of non-conforming or discontinuous Galerkin finite element formulations to solve problems in topology optimization are also studied. Several numerical experiments involving the use of bilinear and biquadratic finite elements for the solution of the topology optimization problem are presented. In addition, an application area referred to as the ``inverse homogenization procedure'' using the topology optimization procedure for the design of materials with prescribed material properties is examined.
Bibliographical Information:

Advisor:

School:University of Cincinnati

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:topology optimization checkerboard patterns

ISBN:

Date of Publication:01/01/2003

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