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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 211
Numerical Methods to Avoid Topological Singularities V. Pomezanski
Computational Structural Mechanics Research Group, Hungarian Academy of Sciences and Budapest University of Technology and Economics, Hungary Full Bibliographic Reference for this paper
V. Pomezanski, "Numerical Methods to Avoid Topological Singularities", 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 211, 2006. doi:10.4203/ccp.83.211
Keywords: topology, optimization, corner node, corner contact, checkerboard patterns, diagonal chains, numerical method.
Summary
One of the most severe computational difficulties in finite element (FE) based topology optimization
is caused by solid (or "black") ground elements connected only through a corner
node. This configuration may appear in checkerboard patterns, diagonal element
chains or as isolated hinges. Corner contacts in nominally optimal topologies are
caused by discretization errors associated with simple (e.g. four-node) elements (e.g.
Sigmund and Petersson [1]), which grossly overestimate the stiffness of corner
regions with stress concentrations. In fact, it was shown by Gaspar et al. [2] that both
checkerboard patterns and diagonal element chains may give an infinite compliance,
if the latter is calculated by an exact analytical method. This makes them the worst
possible solution, if an exact analysis is used in compliance minimization.
Corner contacts may be suppressed by
The approach (d) seems to be the most rational, because it rectifies the discretization errors, which lower incorrectly the value of the objective function (e.g. compliance). The proposed method is particularly effective in combination with the SIMP method, since the latter is a penalization method in its original form, and requires only a minor modification for corner contact control (CO-SIMP). An early corner contact function was suggested by Bendsoe et al. [8]. Defining and employing new CCFs, continuous functions which have a high value for corner contacts and a low value for any other configuration around a node, as an objective a new mathematical programming process CO-SIMP was developed [9]. The CO-SIMP method for the case of Michell's cantilever generates a similar result as the exact solution. The development of the CCFs properties, the numerical method, the modified SIMP algorithm and extensive numerical examples are included in the paper. References
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