Date of Award

Spring 1-1-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Kurt K. Mautre

Second Advisor

John A. Evans

Third Advisor

Alireza Doostan

Fourth Advisor

Carlos A. Felippa

Fifth Advisor

Franck Vernerey

Abstract

This thesis is concerned with topology optimization which provides engineers with a systematic approach to optimize the layout and geometry of a structure against various design criteria. Traditional topology optimization uses density-based methods to capture topological changes in geometry. Density-based methods describe a structural layout using artificial elemental densities. To obtain a good resolution of the geometry, fine meshes are required. This however leads to large computational costs in 3D. Using coarser but practical meshes results in blurred structural boundaries and unreliable prediction of physical response along those boundaries. Using immersed boundary methods instead, such as the extended finite element method (XFEM), alleviates these issues. The XFEM provides clear description of the geometry, and approximation of the physical response along boundaries has been shown to converge to the approximation using body-fitted meshes. This thesis focuses on the use of XFEM for topology optimization. Design geometry in this thesis is tracked precisely using the level set method (LSM).

The LSM-XFEM approach is used to solve variety of multiphysics design and optimization problems. However, being a relatively new field of study the LSM-XFEM approach continues to pose many interesting challenges limiting its applicability to topology optimization. The goal of this thesis is to present advances made towards making LSM-XFEM more viable and reliable for design and optimization of multiphysics problems. Specifically, i) The numerical behavior of XFEM-based shape sensitivities has not yet been investigated. This thesis presents a first-of-its kind study on the numerical behavior of shape sensitivities using the XFEM. ii) The matter of overestimation of stresses using the XFEM, a longstanding issue with no concrete resolution available in the literature, is addressed for robust stress-based optimization. iii) LSM-based topology optimization is known to suffer from slow design evolution resulting from localized sensitivities. A recently proposed concept of geometric primitives as design variables alleviates this issue. Literature on this concept has been restricted to single material problems using linear elasticity. Using the XFEM, this thesis extends the concept of geometric primitives as design variables to multiphase multiphysics problems in 3D.

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