||John E. Renaud
Aerospace and Mechanical Engineering
• Research Areas
|Click images for full size graphics.
||Hybrid Cellular Automata: a biologically-inspired
structural optimization technique
Structural adaptation models of living organisms can be used to
solve topology optimization problems in engineering applications.
This work presents a new approach for obtaining optimal topologies
in continuum structures. The approach is referred to as the hybrid
cellular automaton (HCA) method. The development of the HCA methodology
has been inspired by the biological process of bone remodeling. The
HCA method divides the design domain into a lattice of cellular automata
(CAs). Locally, each CA is able to modify a continuum structural
design variable based on the strain energy level in its neighborhood.
A global structural analysis, using the finite element method, is
used to obtain the strain energy information during each iteration.
The local change in the design variable (i.e., density) is determined
by a local design rule. The design rule drives the strain energy
level towards a target point using a closed-loop control strategy.
The controllers developed in this work include two-position, proportional,
derivative and integral control.
In more recent efforts, the hybrid
cellular automaton (HCA) method for structural synthesis has been
extended to facilitate simultaneous topology and shape optimization.
The HCA methodology has been developed for application to continuum
structures. In bone remodeling, only those elements located on the
surface of the mineralized structure can be modified. In the HCA
methodology implemented in this research only surface elements are
allowed to change density during the structural synthesis process.
Closed-loop control is used to modify the mass distribution on the
internal and external surfaces of the design domain to find an optimum
structure. The local control maintains a balance between mass and
rigidity. The new methodology effectively combines elements of topology
optimization and shape optimization into a single tool.
||Tovar, A., Patel, N., Niebur, G.L.,
Sen, M., Renaud, J.E., "Topology Optimization Using a Hybrid
Cellular Automaton Method With Local Control Rules", ASME
Journal of Mechanical Design. (in press)
Tovar, A, Gano, S.E., Mason, J.J.,
Renaud, J.E., 2005, "Optimum
Design of an Interbody Implant for Lumbar Spine Fixation",
Advances in Engineering Software, Volume 36, Issue 9, pp.
634-642, September, Published by Elsevier Science, The Netherlands.
Li, C., Renaud, J.E., Mason, J.J., 2005, "Improvement
of Mechanical Properties of Bone Cement by Shape Optimization of
Short Fibers", Engineering Optimization, Volume 37
(2), March , pp. 121-134, Published by Taylor & Francis.
Tovar, A., Patel,
N., Letona, G., Kaushik, A., Sanders, B., Renaud, J.E., 2004, "Hybrid
Cellular Automata: A Biological Inspired Structural Optimization
Technique", AIAA-2004-4558, Proceedings
of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization
Conference, Albany, NY, August 30-September
Tovar, A., Niebur, G.L.,
Sen, M., Sanders, B., Renaud, J.E., 2004, "Bone
Structure Adaptation as a Cellular Automaton Optimization Process",
AIAA 2004-1914, pp. 1-14, Proceedings of the
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and
Materials Conference, Palm Springs,
CA, April 19-22.