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Adaptive mesh refinement in stress-constrained topology optimization

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We present a topology structural optimization framework with adaptive mesh refinement and stress-constraints. Finite element approximation and geometry representation benefit from such refinement by enabling more accurate stress field predictions and greater resolution of the optimal structural boundaries. We combine a volume fraction filter to impose a minimum design feature size, the RAMP penalization to generate “black-and-white designs” and a RAMP-like stress definition to resolve the “stress singularity problem.” Regions with stress concentrations dominate the optimized design. As such, rigorous simulations are required to accurately approximate the stress field. To achieve this goal, we invoke a threshold operation and mesh refinement during the optimization. We do so in an optimal fashion, by applying adaptive mesh refinement techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain more accurate simulations and greater resolution of the design domain. We present results in two dimensions to demonstrate the efficiency of our method.

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    In (48), we have neglected the higher order terms. For details on higher order nonlinear functionals, we refer to Becker and Rannacher (2001).


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This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The author thanks the Livermore Graduate Scholar Program for its support.

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Correspondence to Miguel A. Salazar de Troya.

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Salazar de Troya, M.A., Tortorelli, D.A. Adaptive mesh refinement in stress-constrained topology optimization. Struct Multidisc Optim 58, 2369–2386 (2018).

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  • Topology optimization
  • Stress constrained
  • Adaptive mesh refinement