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

authored by: Khader Hamdia, H Ghasemi, XY Zhuang, T Rabczuk
Abstract: 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.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Arak University of Technology
Ton Duc Thang University
Type: Article
Journal: Engineering Analysis with Boundary Elements
Volume: 134
Pages: 412-418
No. of pages: 7
ISSN: 0955-7997
Publication date: 01.01.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Engineering, Computational Mathematics, Analysis, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.enganabound.2021.10.008 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{a140e5257aaf499e93a215731bf7ada5,
title = "Multilevel Monte Carlo method for topology optimization of flexoelectric composites with uncertain material properties",
abstract = "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.",
keywords = "Uncertainty quantification, Multilevel Monte Carlo, Flexoelectric, Topology optimization, DESIGN",
author = "Khader Hamdia and H Ghasemi and XY Zhuang and T Rabczuk",
note = "Funding Information: X. Zhuang would like to acknowledge the support of ERC Grant COTOFLEXI (802205). Khader M. Hamdia thanks the support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -Projektnummer 492535144 .",
year = "2022",
month = jan,
day = "1",
doi = "10.1016/j.enganabound.2021.10.008",
language = "English",
volume = "134",
pages = "412--418",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Ltd.",
}