On structural shape optimization using an embedding domain discretization technique

Riehl, S. and Steinmann, P. (2017) On structural shape optimization using an embedding domain discretization technique. International Journal for Numerical Methods in Engineering, 109(9), pp. 1315-1343. (doi: 10.1002/nme.5326)

Abstract

This contribution presents a novel approach to structural shape optimization that relies on an embedding domain discretization technique. The evolving shape design is embedded within a uniform finite element background mesh which is then used for the solution of the physical state problem throughout the course of the optimization. We consider a boundary tracking procedure based on adaptive mesh refinement to separate between interior elements, exterior elements, and elements intersected by the physical domain boundary. A selective domain integration procedure is employed to account for the geometric mismatch between the uniform embedding domain discretization and the evolving structural component. Thereby, we avoid the need to provide a finite element mesh that conforms to the structural component for every design iteration, as it is the case for a standard Lagrangian approach to structural shape optimization. Still, we adopt an explicit shape parametrization that allows for a direct manipulation of boundary vertices for the design evolution process. In order to avoid irregular and impracticable design updates, we consider a geometric regularization technique to render feasible descent directions for the course of the optimization.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul
• Authors: Riehl, S., and Steinmann, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal for Numerical Methods in Engineering
• Publisher: Wiley
• ISSN: 0029-5981
• ISSN (Online): 1097-0207
• Published Online: 27 June 2016
• Copyright Holders: Copyright © 2016 John Wiley & Sons, Ltd.
• First Published: First published in International Journal for Numerical Methods in Engineering 109(9):1315-1343
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher