Stochastic sampling for deterministic structural topology optimization with many load cases: Density-based and ground structure approaches

Xiaojia Shelly Zhang, Eric de Sturler, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)463-487
Number of pages25
JournalComputer Methods in Applied Mechanics and Engineering
Volume325
DOIs
StatePublished - Oct 1 2017
Externally publishedYes

Keywords

  • Density-based method
  • Ground structure method
  • Randomized algorithm
  • Stochastic sampling
  • Topology optimization with many load cases
  • Trace estimator

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'Stochastic sampling for deterministic structural topology optimization with many load cases: Density-based and ground structure approaches'. Together they form a unique fingerprint.

Cite this