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A Density Gradient Approach to Topology Optimization Under Design-Dependent Boundary Loading

[+] Author Affiliations
Cunfu Wang, Xiaoping Qian

University of Wisconsin - Madison, Madison, WI

Paper No. DETC2018-85960, pp. V02BT03A012; 14 pages
  • ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2B: 44th Design Automation Conference
  • Quebec City, Quebec, Canada, August 26–29, 2018
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5176-0
  • Copyright © 2018 by ASME


The paper proposes a density gradient based approach to topology optimization under design-dependent boundary loading. In the density-based topology optimization method, we impose the design dependent loads through spatial gradient of the density. We transform design-dependent boundary loads into a volume form through volume integral of density gradient. In many applications where loadings only need to be exerted on partial boundary, we introduce an auxiliary loading density to keep track of the loading boundary. During the optimization, the loading density is updated by tracking the changes of the physical density in the vicinity of the loading boundary at previous iteration. The proposed approach is easy to implement and computationally efficient. In addition, by adding more auxiliary density fields, the proposed approach is applicable to multiple design-dependent loads. To prevent the intersection of different loading boundaries, a Heaviside projection based integral constraint is developed. Both heat conduction problems under convection loading and elastic problems under hydrostatic pressure loading are presented to illustrate the effectiveness and efficiency of the method.

Copyright © 2018 by ASME



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