Simultaneous material, shape and topology optimization

Felipe Fernandez, Andrew T. Barker, Jun Kudo, James P. Lewicki, Kenneth Swartz, Daniel A. Tortorelli, Seth Watts, Daniel A. White, Jonathan Wong

Research output: Contribution to journalArticlepeer-review


Using three design fields we develop an optimization environment that can simultaneously optimize material, shape and topology. We use the implicit representation of the boundaries with level-set functions that define the shape and topology. Differentiable R-functions allow us to combine these shapes and topology descriptions with Boolean operations. Additionally, we incorporate design dependent-stiffness materials with another design field. Notably, this framework accommodates design dependent loads, has the ability to introduce holes, and ensures the satisfaction of optimality criteria. It builds upon the fictitious domain, ersatz material, material interpolation and level-set methods. It also borrows from parameterized density-based topology optimization methods. Since analytical sensitivities can be computed, we use efficient nonlinear programming algorithms to update the design instead of the Hamilton–Jacobi's scheme of level-set methods. We illustrate the features of our framework by designing a cantilever beam with octet truss microlattice, a dam with design-dependent loads, and a composite clevis plate.

Original languageEnglish (US)
Article number113321
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Nov 1 2020


  • Design dependent loads
  • Material
  • Shape
  • Structural optimization
  • Topology

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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