Title: Hybrid Cellular Automata: a biologically-inspired structural optimization technique

Speaker: John E. Renaud, Aerospace and Mechanical Engineering, University of Notre Dame

Date/Time: Thursday, November 2, 2006, 9:30-10:30am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: 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. Recent extensions of the HCA methodology for compliant mechanism design, crashworthiness design and for simulating the bone remodeling process will also be presented.