Eulerian shape design sensitivity analysis and optimization with a fixed grid |
| |
| Affiliation: | 1. Strand 7, Sydney 2000, Australia;2. National Technical University of Athens, Institute of Structural Analysis & Seismic Research, 9 Iroon Polytechneio, Zografou Campus, 157 80 Athens, Greece;1. Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720, USA;2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510, Ciudad de México, Mexico;1. The University of Birmingham, Department of Mechanical Engineering, School of Engineering, Birmingham, UK;2. The University of Baghdad, Mech. Eng. Dept., Iraq;1. Institute of Mathematical Sciences, CIT Campus, Tharamani, Chennai 600113, India;2. Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India;1. University of Tunis El Manar, National Engineering School of Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia;2. Aix-Marseille Université, CNRS, CPT UMR 7332, 13288 Marseille, France;3. Université de Toulon, CNRS, CPT UMR 7332, 83957 La Garde, France;1. Dipartimento di Matematica ‘F. Casorati’, Università di Pavia, Via Ferrata 1, I-27100 Pavia, Italy;2. Institut für Mathematik, Universität Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland |
| |
| Abstract: | Conventional shape optimization based on the finite element method uses Lagrangian representation in which the finite element mesh moves according to shape change, while modern topology optimization uses Eulerian representation. In this paper, an approach to shape optimization using Eulerian representation such that the mesh distortion problem in the conventional approach can be resolved is proposed. A continuum geometric model is defined on the fixed grid of finite elements. An active set of finite elements that defines the discrete domain is determined using a procedure similar to topology optimization, in which each element has a unique shape density. The shape design parameter that is defined on the geometric model is transformed into the corresponding shape density variation of the boundary elements. Using this transformation, it has been shown that the shape design problem can be treated as a parameter design problem, which is a much easier method than the former. A detailed derivation of how the shape design velocity field can be converted into the shape density variation is presented along with sensitivity calculation. Very efficient sensitivity coefficients are calculated by integrating only those elements that belong to the structural boundary. The accuracy of the sensitivity information is compared with that derived by the finite difference method with excellent agreement. Two design optimization problems are presented to show the feasibility of the proposed design approach. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
