Topology optimization of multiple deformable bodies in contact with large deformations

Felipe Fernandez, Michael A. Puso, Jerome Solberg, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


Previous works in topology optimization of structures with contact boundary conditions have concentrated on the two-dimensional rigid obstacle problem. This is because the contact analysis of multiple three-dimensional deformable bodies with meshes that are non-matching across the contact interface requires computationally complex contact algorithms beyond the scope of previous optimization investigations. Our research is devoted to addressing topology design problems with multiple deformable three-dimensional components in contact using state-of-the-art contact algorithms. We formulate and resolve the design simulation problem using large deformation continuum mechanics and the finite element method. To account for large sliding that can occur during the design optimization process here, the mortar segment-to-segment approach was used to discretize the contact surface due to its numerical robustness in this regime. Since, mortar integrals provide smooth contact forces as nodes slide on/off the surface, solution convergence is well behaved. Considering the contact problem is computationally expensive to solve, we solve the optimization problem using efficient nonlinear programming algorithms which require the sensitivities of the cost and constraint functions. To this end, we formulate analytical adjoint sensitivity expressions to compute the gradients of general functionals. As expected and corroborated in this work, the adjoint method is computationally efficient. Additionally, we use a B-spline design parameterization to regularize the topology optimization problem. We show that this parameterization reduces the number of design variables compared to usual element-wise parameterizations and provides a precise and smooth description of the design boundary. We present numerical example problems of multiple deformable three-dimensional bodies in contact with large deformations and find optimal topologies that maximize the total contact force, maximize the strain energy, and minimize the compliance.

Original languageEnglish (US)
Article number113288
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Nov 1 2020


  • B-spline
  • Finite elements
  • Large deformation
  • Mortar segment-to-segment
  • Sensitivity analysis

ASJC Scopus subject areas

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


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