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Aspects of sensitivity analysis using the level‐set method in structural optimization
Author(s) -
Rotthaus Monika,
Barthold FranzJoseph
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700793
Subject(s) - heaviside step function , level set method , topology optimization , material derivative , mathematics , level set (data structures) , shape optimization , sensitivity (control systems) , mathematical optimization , signed distance function , cartesian coordinate system , minification , algorithm , computer science , mathematical analysis , finite element method , geometry , physics , segmentation , artificial intelligence , electronic engineering , engineering , image segmentation , thermodynamics
The level‐set method is very common for modelling structural optimization problems, e.g. multi‐material structures. Essentially two different approaches are known. The first method describes the shape by an implicit function formulation. The weak form is expressed as a Heaviside function of this implicit function and the optimization problem is solved by an iterative procedure. This method is applied to topology optimization by e.g. Belytschko et al. [1]. The second approach is based on the combination of the shape derivative and the level‐set method for front propagation, which has been devised by Osher and Sethian [2]. Allaire et. al. [3] use the shape derivative for the minimization problem to compute the advection velocity in the Hamilton‐Jacobi equation. The Hamilton‐Jacobi equation can be solved numerically by an explicit first order upwind scheme on a Cartesian grid. We propose a new numerical method for shape optimization of multi‐material structures. This approach is based on the level‐set method combined with the variational sensitivity analysis, see Barthold [4]. The aim of the present contribution is to point out the essential aspects of this combination and to compare it with the two methods mentioned above. Furthermore the sensitivity of multi‐material structures in terms of various design parameters is discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)