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Shape optimisation analysing the inner structure of sensitivity matrices
Author(s) -
Gerzen Nikolai,
Barthold FranzJoseph
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110345
Subject(s) - hessian matrix , sensitivity (control systems) , singular value decomposition , eigenvalues and eigenvectors , matrix (chemical analysis) , decomposition , mathematical optimization , mathematics , algorithm , computer science , topology (electrical circuits) , engineering , combinatorics , physics , chemistry , organic chemistry , quantum mechanics , chromatography , electronic engineering
Abstract This contribution deals with sensitivity analysis in nodal based shape optimisation. Sensitivity analysis is one of the most important parts of a structural optimisation algorithm. The efficiency of the algorithm mainly depends on the obtained sensitivity information. The pseudo load and sensitivity matrices which appear in sensitivity analysis are commonly used to derive and to calculate the gradients and the Hessian matrices of objective functions and of constraints. The aim of this contribution is to show that these matrices contain additional useful information which is not used in structural optimisation until now. We demonstrate the opportunities and capabilities of the new information which are obtained by singular value decomposition (SVD) of the pseudo load and sensitivity matrices and by eigenvalue decomposition of the Hessian matrix. Furthermore, we avoid jagged boundaries in shape optimisation by applying a density filtering technique well‐known in topology optimisation. Numerical examples illustrate the advocated theoretical concept. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)