Topology optimization of compliant mechanisms considering stress constraints, manufacturing uncertainty and geometric nonlinearity

Gustavo Assis da Silva*, André Teófilo Beck, Ole Sigmund

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


This paper proposes and investigates two formulations to topology optimization of compliant mechanisms considering stress constraints, manufacturing uncertainty and geometric nonlinearity. The first formulation extends the maximum output displacement robust approach with stress constraints to incorporate the effects of geometric nonlinear behavior during the optimization process. The second formulation relies on the concept of path-generating mechanisms, where not only the final configuration is important, but also the load–displacement equilibrium path. A novel path-generating formulation is thus proposed, not only to achieve the prescribed equilibrium path, but also to take stress constraints and manufacturing uncertainty into account during the optimization process. Although both formulations have different goals, the same main techniques are employed: density approach to topology optimization, augmented Lagrangian method to handle the large number of stress constraints, three-field robust approach to handle the manufacturing uncertainty, and the energy interpolation scheme to handle convergence issues due to large deformation in void regions. Several numerical examples are addressed to demonstrate applicability of the proposed approaches. The optimized results are post-processed with body-fitted finite element meshes. Obtained results demonstrate that: (1) the proposed nonlinear analysis based maximum output displacement approach is able to provide solutions with good performance in situations of large displacements, with stress and manufacturing requirements satisfied; (2) the linear analysis based maximum output displacement approach provides optimized topologies that show large stress constraint violations and rapidly varying stress behavior under uniform boundary variation, when these are post-processed with full nonlinear analysis; (3) the proposed path-generating formulation is able to provide solutions that follow the prescribed control points, including stress robustness.
Original languageEnglish
Article number112972
JournalComputer Methods in Applied Mechanics and Engineering
Number of pages31
Publication statusPublished - 2020


  • Topology optimization
  • Robust design
  • Compliant mechanisms
  • Manufacturing uncertainty
  • Stress constraints
  • Geometric nonlinearity

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