Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

Chen, L.L., Lian, H., Liu, Z. , Chen, H.B., Atroshchenko, E. and Bordas, S.P.A. (2019) Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods. Computer Methods in Applied Mechanics and Engineering, 355, pp. 926-951. (doi: 10.1016/j.cma.2019.06.012)

Abstract

The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to special techniques to truncate infinite domains. The isogeometric boundary element method (IGABEM) is a recent progress in the category of boundary element approaches, which is inspired by the concept of isogeometric analysis (IGA) and employs the spline functions of CAD as basis functions to discretize unknown physical fields. As a boundary representation approach, IGABEM is naturally compatible with CAD and thus can directly perform numerical analysis on CAD models, avoiding the cumbersome meshing procedure in conventional FEM/BEM and eliminating the difficulty of volume parameterization in isogeometric finite element methods. The advantage of tight integration of CAD and numerical analysis in IGABEM renders it particularly attractive in the application of structural shape optimization because (1) the geometry and the analysis can be interacted, (2) remeshing with shape morphing can be avoided, and (3) an optimized solution returns a CAD geometry directly without postprocessing steps. In the present paper, we apply the IGABEM to structural shape optimization of three dimensional exterior acoustic problems, fully exploiting the strength of IGABEM in addressing infinite domain problems and integrating CAD and numerical analysis. We employ the Burton–Miller formulation to overcome fictitious frequency problems, in which hyper-singular integrals are evaluated explicitly. The gradient-based optimizer is adopted and shape sensitivity analysis is conducted with implicit differentiation methods. The design variables are set to be the positions of control points which directly determine the shape of structures. Finally, numerical examples are provided to verify the algorithm.

• Item Type: Articles
• Additional Information: Financial supports from the National Natural Science Foundation of China (NSFC) under Grant No. 11702238, the Henan Provincial Department of Science and Technology Research, China under Grant no. 172102210453, Key Scientific Research Project of Henan University, China under Grant no. 17A560009, and Nanhu Scholars Program for Young Scholars of XYNU, China are acknowledged. Stéphane Bordas thanks the financial support of the European Research Council Starting Independent Research Grant (ERC Stg grant agreement no. 279578) entitled “Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery” and the support of the Fonds National de la Recherche Luxembourg INTER/FNRS/15/11019432/EnLightenIt/Bordas. Haibo Chen appreciates the support of the National Natural Science Foundation of China (NSFC) under Grant No. 11772322.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Liu, Dr Zhaowei
• Authors: Chen, L.L., Lian, H., Liu, Z., Chen, H.B., Atroshchenko, E., and Bordas, S.P.A.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computer Methods in Applied Mechanics and Engineering
• Publisher: Elsevier
• ISSN: 0045-7825
• ISSN (Online): 1879-2138
• Published Online: 16 July 2019
• Copyright Holders: Copyright © 2019 Elsevier B.V.
• First Published: First published in Computer Methods in Applied Mechanics and Engineering 355: 926-951
• Publisher Policy: Reproduced in accordance with the publisher copyright policy