Discrete topology optimization in augmented space: integrated element removal for minimum size and mesh sensitivity control

Abstract

A computational strategy is proposed to circumvent some of the major issues that arise in the classical threshold-based approach to discrete topology optimization. These include the lack of an integrated element removal strategy to prevent the emergence of hair-like elements, the inability to effectively enforce a minimum member size of arbitrary magnitude, and high sensitivity of the final solution to the choice of ground structure. The proposed strategy draws upon the ideas used to arrive at mesh-independent solutions in continuum topology optimization and enables efficient imposition of a minimum size constraint onto the set of non vanishing elements. This is achieved via augmenting the design variables by a set of auxiliary variables, called existence variables, that not only prove very effective in addressing the aforementioned issues but also bring in a set of added benefits such as better convergence and complexity control. 2D and 3D examples from truss-like structures are presented to demonstrate the superiority of the proposed approach over the classical approach to discrete topology optimization.

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Funding

MT received financial support from the National Science Foundation under grants CMMI-1401575 and CMMI-1351742. AA also received support from UMass Dartmouth College of Engineering.

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Correspondence to Alireza Asadpoure.

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Asadpoure, A., Harati, M. & Tootkaboni, M. Discrete topology optimization in augmented space: integrated element removal for minimum size and mesh sensitivity control. Struct Multidisc Optim (2020). https://doi.org/10.1007/s00158-020-02630-3

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Keywords

  • Topology optimization
  • Discrete design
  • Mesh sensitivity
  • Minimum size constraint
  • Hair-like elements
  • Complexity control