Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 81, Issue 8, Pages 1019-1045Publisher
WILEY
DOI: 10.1002/nme.2724
Keywords
topology optimization; length scale; adaptive mesh refinement; genetic algorithms; projection methods; SIMP
Funding
- National Science Foundation NanoBio IGERT at Johns Hopkins University [0549350]
- Division Of Graduate Education
- Direct For Education and Human Resources [0549350] Funding Source: National Science Foundation
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Topology optimization methodologies typically use the same discretization for the design variable and analysis meshes. Analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense. This paper proposes leveraging properties of the Heaviside projection method (HPM) to separate the design variable field from the analysis mesh in continuum topology optimization. HPM projects independent design variables onto element space over a prescribed length scale. A single design variable therefore influences several elements, creating a redundancy within the design that call be exploited to reduce the number of independent design variables without significantly restricting the design space. The algorithm begins with sparse design variable fields and adapts these fields as the optimization progressed. The technique is demonstrated on minimum compliance (maximum stiffness) problems solved using continuous optimization and genetic algorithms. For the former, the proposed algorithm typically identifies solutions having objective functions within 1% of those found using full design variable fields. Computational savings are minor to moderate for the minimum compliance formulation with a single constraint, and are substantial for formulations having many local constraints. When using genetic algorithms, solutions are consistently obtained on mesh resolutions that were previously considered intractable Copyright (C) 2009 John Wiley & Sons, Ltd.
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