IJPAM: Volume 66, No. 3 (2011)

KKT CONDITIONS SATISFIED USING
ADAPTIVE NEIGHBORING IN HYBRID CELLULAR
AUTOMATA FOR TOPOLOGY OPTIMIZATION

Charles L. Penninger$^1$, Andrés Tovar$^2$, Layne T. Watson$^3$, John E. Renaud$^4$
$^{1,2,4}$Department of Aerospace and Mechanical Engineering
University of Notre Dame
365, Fitzpatrick Hall, Notre Dame, Indiana, 46556, USA
$^1$e-mail: cpenning@nd.edu
$^2$e-mail: atovar@nd.edu
$^4$e-mail: jrenaud@nd.edu
$^3$Department of Computer Science and Mathematics
Virginia Polytechnic Institute and State University
Mail Code 0106, Blacksburg, Virginia, 24061, USA
e-mail: ltw@cs.vt.edu


Abstract.The hybrid cellular automaton (HCA) method is a biologically inspired algorithm capable of topology synthesis. Karush-Kuhn-Tucker (KKT) optimality conditions have been derived to determine the expression for the local evolutionary rules that guide synthesis process. While averaging techniques have been used to mitigate numerical instabilities such as checkerboard patterns and mesh dependency, some questions have been raised whether KKT conditions are fully satisfied in the final topologies. Furthermore, the averaging procedure might result in cancellation or attenuation of the error between the field variable and its target. The objective of this work is to develop an adaptive neighboring scheme to guarantee the satisfaction of the KKT conditions while minimizing numerical instabilities. This approach is demonstrated in the topology optimization of a classic Mitchell-type structure using the HCA method.

Received: November 4, 2010

AMS Subject Classification: 90C90

Key Words and Phrases: structural optimization, filtering, checkerboarding, optimality conditions, mathematical programming

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 3