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On curvature control in node–based shape optimization
Author(s) -
Schmitt Oliver,
Steinmann Paul
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510279
Subject(s) - curvature , boundary (topology) , constraint (computer aided design) , domain (mathematical analysis) , node (physics) , shape optimization , mathematics , computer science , mathematical optimization , topology (electrical circuits) , mathematical analysis , geometry , physics , combinatorics , finite element method , quantum mechanics , thermodynamics
We present and compare three approaches to control of the curvature of the domain boundary in two–dimensional shape optimization. Since the coordinates of the FE–nodes are used as design variables, objective and constraint functions have to be formulated in terms of the nodal coordinates. Therefore we investigate various formulations for the curvature of the domain boundary in terms of the coordinates of the boundary nodes. In addition, the sensitivities of these expressions with respect to the design nodes are required for the application of gradient–based optimization algorithms. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)