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An Explicit Level-Set Approach for Structural Topology Optimization

[+] Author Affiliations
Karim Hamza

University of Michigan, Ann Arbor, MI

Mohamed Aly

American University in Cairo, Cairo, Egypt

Hesham Hegazi

Cairo University, Giza, Egypt

Paper No. DETC2013-12155, pp. V03AT03A001; 12 pages
doi:10.1115/DETC2013-12155
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3A: 39th Design Automation Conference
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5588-1
  • Copyright © 2013 by ASME

abstract

Level-set approaches are a family of domain classification techniques that rely on defining a scalar level-set function (LSF), then carrying out the classification based on the value of the function relative to one or more thresholds. Most continuum topology optimization formulations are at heart, a classification problem of the design domain into structural materials and void. As such, level-set approaches are gaining acceptance and popularity in structural topology optimization. In conventional level set approaches, finding an optimum LSF involves solution of a Hamilton-Jacobi system of partial differential equations with a large number of degrees of freedom, which in turn, cannot be accomplished without gradients information of the objective being optimized. A new approach is proposed in this paper where design variables are defined as the explicit values of the LSF at knot points, then a Kriging model is used to interpolate the LSF values within the rest of the domain so that classification into material or void can be performed. Perceived advantages of the explicit level-set (ELS) approach include alleviating the need for gradients of objectives and constraints, while maintaining a reasonable number of design variables that is independent from the mesh size. A hybrid genetic algorithm (GA) is then used for solving the optimization problem(s). An example problem of a short cantilever is studied under various settings of the ELS parameters in order to infer the best practice recommendations for tuning the approach. Capabilities of the approach are then further demonstrated by exploring its performance on several test problems.

Copyright © 2013 by ASME

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