4.6 Article

Multilevel Monte Carlo method for topology optimization of flexoelectric composites with uncertain material properties

期刊

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
卷 134, 期 -, 页码 412-418

出版社

ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2021.10.008

关键词

Uncertainty quantification; Multilevel Monte Carlo; Flexoelectric; Topology optimization

资金

  1. ERC Grant COTOFLEXI [802205]
  2. Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [492535144]
  3. European Research Council (ERC) [802205] Funding Source: European Research Council (ERC)

向作者/读者索取更多资源

An efficient MLMC method for topology optimization of flexoelectric structures is proposed in this study, utilizing NURBS-based IGA to solve governing equations and GA for integer-valued optimization. Material properties and volume fraction uncertainties are taken into account, resulting in the determination of minimum number of simulations required under different error tolerances.
We present an efficient multilevel Monte Carlo (MLMC) method for the topology optimization of flexoelectric structures. A flexoelectric composite consisting of flexoelectric and purely elastic building blocks is investigated. The governing equations are solved by Non-Uniform Rational B-spline (NURBS)-based isogeometric analysis (IGA) exploiting its higher order continuity. Genetic algorithms (GA) based integer-valued optimization is used to obtain the optimal topological design. The uncertainties in the material properties and the volume fraction of the constituents are considered to quantify the uncertainty in the electromechanical coupling effect. Then, a multilevel hierarchy of computational meshes is obtained by a uniform refinement according to a geometric sequence. We estimate the growth rate of the simulation cost, in addition to the rates of decay in the expectation and the variance of the differences between the approximations over the hierarchy. Finally, we determine the minimum number of simulations required on each level to achieve the desired accuracy at different prescribed error tolerances. The results show that the proposed method reduces the computational cost in the numerical experiments without loss of the accuracy. The overall computation saving was in the range 2.0-3.5.

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