Adaptive mesh refinement in topology optimization

Salazar De Troya, Miguel Angel A.

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https://hdl.handle.net/2142/104776 Copy

Description

Title

Adaptive mesh refinement in topology optimization

Author(s)

Salazar De Troya, Miguel Angel A.

Issue Date

2019-04-05

Director of Research (if dissertation) or Advisor (if thesis)

Tortorelli, Daniel A.

Doctoral Committee Chair(s)

Tortorelli, Daniel A.

Committee Member(s)

• Geubelle, Phillipe
• Masud, Arif
• James, Kai

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• topology
• optimization
• adaptive
• mesh
• refinement
• stress
• constrained

Abstract

This dissertation presents developments in stress constrained topology optimization with Adaptive Mesh Refinement (AMR). Regions with stress concentrations dominate the optimized design. As such, we first present an approach to obtain designs with accurately computed stress fields within the context of topology optimization. To achieve this goal, we invoke threshold and AMR operations during the optimization. We do so in an optimal fashion, by applying AMR techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain accurate simulations and greater resolution of the design domain in a computationally efficient manner. We present results in two dimensions to demonstrate the efficacy of our method. The topology optimization community has regularly employed optimization algorithms from the operations research community. However, these algorithms are implemented in the Euclidean space instead of the proper function space where the design, i.e. volume fraction, field resides. In this thesis, we show that, when discretizing the volume fraction field over a non-uniform mesh, algorithms in Euclidean space are mesh dependent. We do so by first explaining the functional analysis tools necessary to understand why convergence is affected by the mesh. Namely, the distinction between derivative and gradient definitions and the role of the mesh dependent inner product. These tools are subsequently used to make the Globally Convergent Method of Moving Asymptotes (GCMMA), a popular optimization algorithm in the topology optimization community, mesh independent. We then benchmark our algorithm with three common problems in topology optimization. High resolution three-dimensional design models optimized for arbitrary cost and constraint functions are absolutely necessary ingredients for the solution of real{world engineering design problems. However, such requirements are non trivial to implement. In this thesis, we address this dilemma by developing a large scale topology optimization framework with AMR. We discuss the need for efficient parallelizable regularization methods that work across different mesh resolutions, iterative solvers and data structures. Furthermore, the optimization algorithm needs to be implemented with the same data structure that is used for the design field. To demonstrate the versatility of our framework, we optimize the designs of a three dimensional stress constrained benchmark L-bracket and a stress-constrained compliant mechanism.

Graduation Semester

2019-05

Type of Resource

text

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http://hdl.handle.net/2142/104776

Copyright and License Information

Copyright 2019 Miguel Angel Salazar De Troya

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