Topological Design of Structures Using a CellularAutomata Method

Topological design of continuum structures usually involves numerical instabilities, such as checkerboards and mesh-dependency, which degenerate the manufacturability, the efficiency and the robustness of the optimal design. This paper will propose a new topology optimization method to suppress numerical instabilities occurred in the topology optimization of continua, according to the principle of error amplifier and feedback control in the control system. The design variables associated with topological design are updated based on the Cellular Automata (CA) theory. A couple of typical numerical examples are used to demonstrate the effectiveness of the proposed method in effectively suppressing numerical instabilities occurred in the numerical procedure of topology optimization.

[1]  C. S. Jog,et al.  Stability of finite element models for distributed-parameter optimization and topology design , 1996 .

[2]  W. Gao,et al.  Topology optimization of structures using meshless density variable approximants , 2013 .

[3]  Z. Luo,et al.  Topological Optimization of Structures Using a Multilevel Nodal Density-Based Approximant , 2012 .

[4]  C. S. Jog,et al.  A new approach to variable-topology shape design using a constraint on perimeter , 1996 .

[5]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[6]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[7]  Layne T. Watson,et al.  Structural Design Using Cellular Automata , 2001 .

[8]  John E. Renaud,et al.  Bone Structure Adaptation as a Cellular Automaton Optimization Process , 2004 .

[9]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[10]  Satya N. Atluri,et al.  The MLPG Mixed Collocation Method for Material Orientation and Topology Optimization of Anisotropic Solids and Structures , 2008 .

[11]  Z. Kang,et al.  Structural topology optimization based on non-local Shepard interpolation of density field , 2011 .

[12]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[13]  K. Matsui,et al.  Continuous approximation of material distribution for topology optimization , 2004 .

[14]  Yixian Du,et al.  Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods , 2012 .

[15]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[16]  Z. Kang,et al.  Integrated Optimization of Material Layout and Control Voltage for Piezoelectric Laminated Plates , 2008 .

[17]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[18]  J. Petersson,et al.  Slope constrained topology optimization , 1998 .

[19]  K. Tai,et al.  Structural topology design optimization using Genetic Algorithms with a bit-array representation , 2005 .

[20]  Nong Zhang,et al.  A Multi-Criteria Topology Optimization for Systematic Design of Compliant Mechanisms , 2012 .

[21]  Liyong Tong,et al.  Shape morphing of laminated composite structures with photostrictive actuators via topology optimization , 2011 .

[22]  John E. Renaud,et al.  Topology Optimization Using a Hybrid Cellular Automaton Method With Local Control Rules , 2006 .

[23]  M. Jakiela,et al.  Continuum structural topology design with genetic algorithms , 2000 .

[24]  Mohammad Hadi Afshar,et al.  Application of cellular automata to size and topology optimization of truss structures , 2012 .

[25]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[26]  Thomas A. Poulsen.  A new scheme for imposing a minimum length scale in topology optimization , 2003 .

[27]  M. Wang,et al.  Design of distributed compliant micromechanisms with an implicit free boundary representation , 2008 .

[28]  Hichem Smaoui,et al.  Multigrid Implementation of Cellular Automata for Topology Optimization of Continuum Structures , 2009 .

[29]  O. Sigmund,et al.  Checkerboard patterns in layout optimization , 1995 .

[30]  Satya N. Atluri,et al.  Topology-optimization of Structures Based on the MLPG Mixed Collocation Method , 2008 .

[31]  M. Bruggi.  On the solution of the checkerboard problem in mixed-FEM topology optimization , 2008 .

[32]  Michael Yu Wang,et al.  Design of piezoelectric actuators using a multiphase level set method of piecewise constants , 2009, J. Comput. Phys..