TY - JOUR
T1 - Stochastic sampling for deterministic structural topology optimization with many load cases
T2 - Density-based and ground structure approaches
AU - Zhang, Xiaojia Shelly
AU - de Sturler, Eric
AU - Paulino, Glaucio H.
N1 - Funding Information:
The authors G.H. Paulino and X.S. Zhang acknowledge the financial support from the US National Science Foundation (NSF) under project #1559594 (formerly #1335160 ). The authors are also grateful for the endowment provided by the Raymond Allen Jones Chair at the Georgia Institute of Technology. The work by E. de Sturler was supported in part by the grant NSF DMS 1217156 . The information provided in this paper is the sole opinion of the authors and does not necessarily reflect the view of the sponsoring agencies. Appendix A
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - We propose an efficient probabilistic method to solve a fully deterministic problem — we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both continuum and truss topology optimization. Practical structural designs by deterministic topology optimization typically involve many load cases, possibly hundreds or more. The optimal design minimizes a, possibly weighted, average of the compliance under each load case (or some other objective). This means that, in each optimization step, a large finite element problem must be solved for each load case, leading to an enormous computational effort. On the contrary, the proposed randomized optimization method with stochastic sampling requires the solution of only a few (e.g., 5 or 6) finite element problems (large linear systems) per optimization step. Based on simulated annealing, we introduce a damping scheme for the randomized approach. Through numerical examples in two and three dimensions, we demonstrate that the randomization algorithm drastically reduces computational cost to obtain similar final topologies and results (e.g., compliance) to those of standard algorithms. The results indicate that the damping scheme is effective and leads to rapid convergence of the proposed algorithm.
AB - We propose an efficient probabilistic method to solve a fully deterministic problem — we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both continuum and truss topology optimization. Practical structural designs by deterministic topology optimization typically involve many load cases, possibly hundreds or more. The optimal design minimizes a, possibly weighted, average of the compliance under each load case (or some other objective). This means that, in each optimization step, a large finite element problem must be solved for each load case, leading to an enormous computational effort. On the contrary, the proposed randomized optimization method with stochastic sampling requires the solution of only a few (e.g., 5 or 6) finite element problems (large linear systems) per optimization step. Based on simulated annealing, we introduce a damping scheme for the randomized approach. Through numerical examples in two and three dimensions, we demonstrate that the randomization algorithm drastically reduces computational cost to obtain similar final topologies and results (e.g., compliance) to those of standard algorithms. The results indicate that the damping scheme is effective and leads to rapid convergence of the proposed algorithm.
KW - Density-based method
KW - Ground structure method
KW - Randomized algorithm
KW - Stochastic sampling
KW - Topology optimization with many load cases
KW - Trace estimator
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U2 - 10.1016/j.cma.2017.06.035
DO - 10.1016/j.cma.2017.06.035
M3 - Article
AN - SCOPUS:85027848253
SN - 0374-2830
VL - 325
SP - 463
EP - 487
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -