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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 212
A New Algorithm for Three-Dimensional Topology Optimisation in Structural Mechanics Using a Level-Set Method H. Andrä1, S. Amstutz2, I. Matei1 and E. Teichmann1
1Fraunhofer Institut für Techno- und Wirtschaftsmathematik, ITWM, Kaiserslautern, Germany
Full Bibliographic Reference for this paper
, "A New Algorithm for Three-Dimensional Topology Optimisation in Structural Mechanics Using a Level-Set Method", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 212, 2006. doi:10.4203/ccp.83.212
Keywords: topology optimisation, level-set, topological sensitivity.
Summary
In this paper, we present a new algorithm for 3D topology
optimisation in structural mechanics which combines the concept of
topological gradient and the representation of the domain by a
level-set function. Unlike other algorithms which have been
developed in this area, we use the level-set function only as a
boundary description tool and not for propagating the boundary by
a Hamilton-Jacobi equation as in the classical level-set method.
The way we use the level-set function makes topology changes of
all kind, including nucleation of holes, very easy and natural.
After the presentation of a model optimisation problem having the equations of linear isotropic elasticity as constraints, a short review of the topological gradient and the level-set function approach is given. The main part consists of a detailed description of the algorithm and the new features it provides. Two examples from the context of structural mechanics show the performance of the algorithm.
The iterative scheme presented is based on two main components:
The boundary of the structure is represented by a level-set
function As the topology optimisation problem is well-known to be ill-posed, some regularisation has to be applied. The level-set function and, or the topological gradient are smoothed by convolution with a nonlinear filter kernel. The quality of the surface triangulation is improved by application of a Laplace-Beltrami type operator.
The crucial point in this optimisation loop is the update of the
level-set function In addition to the efficient level-set update, the algorithm provides several other desirable features:
The last item is of special interest to the authors since consideration of the effects of the casting process such as residual stresses and eigenstrains on the optimisation is part of the project "MIDPAG - Innovative Methods for Integrated Dimensioning and Process Design for Cast Parts". This is to be presented in a forthcoming paper. References
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