TY - JOUR
T1 - Local stress constraints in topology optimization of structures subjected to arbitrary dynamic loads
T2 - a stress aggregation-free approach
AU - Giraldo-Londoño, Oliver
AU - Aguiló, Miguel A.
AU - Paulino, Glaucio H.
N1 - Funding Information:
We acknowledge Sandia National Laboratories, a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - We present an augmented Lagrangian-based approach for stress-constrained topology optimization of structures subjected to general dynamic loading. The approach renders structures that satisfy the stress constraints locally at every time step. To solve problems with a large number of stress constraints, we normalize the penalty term of the augmented Lagrangian function with respect to the total number of constraints (i.e., the number of elements in the mesh times the number of time steps). Moreover, we solve the stress-constrained problem effectively by penalizing constraints associated with high stress values more severely than those associated with low stress values. We integrate the equations of motion using the HHT-α method and conduct the sensitivity analysis consistently with this method via the “discretize-then-differentiate” approach. We present several numerical examples that elucidate the effectiveness of the approach to solve dynamic, stress-constrained problems under several loading scenarios including loads that change in magnitude and/or direction and loads that change in position as a function of time.
AB - We present an augmented Lagrangian-based approach for stress-constrained topology optimization of structures subjected to general dynamic loading. The approach renders structures that satisfy the stress constraints locally at every time step. To solve problems with a large number of stress constraints, we normalize the penalty term of the augmented Lagrangian function with respect to the total number of constraints (i.e., the number of elements in the mesh times the number of time steps). Moreover, we solve the stress-constrained problem effectively by penalizing constraints associated with high stress values more severely than those associated with low stress values. We integrate the equations of motion using the HHT-α method and conduct the sensitivity analysis consistently with this method via the “discretize-then-differentiate” approach. We present several numerical examples that elucidate the effectiveness of the approach to solve dynamic, stress-constrained problems under several loading scenarios including loads that change in magnitude and/or direction and loads that change in position as a function of time.
KW - Augmented Lagrangian
KW - Elastodynamics
KW - HHT-α method
KW - Local stress constraints
KW - Newmark-β method
KW - Topology optimization
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U2 - 10.1007/s00158-021-02954-8
DO - 10.1007/s00158-021-02954-8
M3 - Article
AN - SCOPUS:85114913053
SN - 1615-147X
VL - 64
SP - 3287
EP - 3309
JO - Structural and Multidisciplinary Optimization
JF - Structural and Multidisciplinary Optimization
IS - 6
ER -