Research Papers

A Kriging-Interpolated Level-Set Approach for Structural Topology Optimization

[+] Author and Article Information
Karim Hamza

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2102
e-mail: khamza@umich.edu

Mohamed Aly

Department of Mechanical Engineering,
American University in Cairo,
Cairo 11835, Egypt
e-mail: mfawzyaly@aucegypt.edu

Hesham Hegazi

Mechanical Design and Production Department,
Faculty of Engineering,
Cairo University,
Giza 12316, Egypt
e-mail: hhegazi@aucegypt.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 21, 2013; final manuscript received October 9, 2013; published online November 7, 2013. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 136(1), 011008 (Nov 07, 2013) (12 pages) Paper No: MD-13-1180; doi: 10.1115/1.4025706 History: Received April 21, 2013; Revised October 09, 2013

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 values of the LSF at knot points, then a Kriging model is used sto interpolate the LSF values within the rest of the domain so that classification into material or void can be performed. Perceived advantages of the Kriging-interpolated level-set (KLS) 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 KLS 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.

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Fig. 1

Pareto-plot of compliance verses shape complexity (w/ details of select designs shown) for a short cantilever

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Fig. 2

Illustration of two different level-set functions that correspond to the same structural design

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Fig. 3

Knot points layouts

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Fig. 5

Monte-Carlo simulation of obtainable solution quality verses GA settings and available computational resources

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Fig. 6

Level-set function and its realization with different FE mesh sizes

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Fig. 7

Box plots for various Kriging model tuning and knot points settings with material fraction volume of 0.45

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Fig. 8

Box plots for various Kriging model tuning and knot points settings with material fraction volume of 0.6

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Fig. 4

Box plots for various knot point layouts and optimization algorithm settings

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Fig. 12

Bookshelf problem description and baseline design

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Fig. 13

Bookshelf problem optimization results

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Fig. 9

Short cantilever problem optimization results

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Fig. 10

Bridge problem description and baseline design

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Fig. 11

Bridge problem optimization results

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Fig. 14

Pareto plots for cantilever problem

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Fig. 15

Combining Pareto plots for cantilever problem




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