Topology Optimization of Structures Made of Discrete Geometric Components with Different Materials

[+] Author and Article Information
Hesaneh Kazemi

Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, U-3139, Storrs, Connecticut 06269

Ashkan Vaziri

Department of Mechanical and Industrial Engineering, Northeastern University, 254 Richards Hall, 360 Huntington Ave., Boston, Massachusetts 02115

Julián Norato

Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, U-3139, Storrs, Connecticut, 06269

1Corresponding author.

ASME doi:10.1115/1.4040624 History: Received December 11, 2017; Revised June 18, 2018


We present a new method for the simultaneous topology optimization and material selection of structures made by the union of discrete geometric components, where each component is made of one of multiple available materials. Our approach is based on the geometry projection method, whereby an analytical description of the geometric components is smoothly mapped onto a density field on a fixed analysis grid. In addition to the parameters that dictate the dimensions, position and orientation of the component, a size variable per available material is ascribed to each component. A size variable value of unity indicates the component is made of the corresponding material. Moreover, all size variables can be zero, signifying the component is entirely removed from the design. We penalize intermediate values of the size variables via an aggregate constraint in the optimization. We also introduce a mutual material exclusion constraint that ensures that at most one material has a unity size variable in each geometric component. In addition to these constraints, we propose a novel aggregation scheme to perform the union of geometric components with dissimilar materials. These ingredients facilitate treatment of the multi-material case. We demonstrate our method with several numerical examples.

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