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Structural Synthesis with a Hybrid Cellular Automata Technique

Structural Synthesis with a Hybrid Cellular Automata Technique. Andrés Tovar Design Automation Laboratory University of Notre Dame Presentation at University of Notre Dame, Indiana March 22, 2004. Content. Biological Structural Optimization Cellular Automata (CA)

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Structural Synthesis with a Hybrid Cellular Automata Technique

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  1. Structural Synthesis with aHybrid Cellular Automata Technique Andrés Tovar Design Automation Laboratory University of Notre Dame Presentation at University of Notre Dame, Indiana March 22, 2004

  2. Content • Biological Structural Optimization • Cellular Automata (CA) • Hybrid Cellular Automata (HCA) • HCA local control rules • Other applications • Final remarks

  3. Biological Structural Optimization Hypothesis: Via Remodeling, bones adapt their structure to mechanical stimuli.

  4. Biological Structural Optimization Remodeling Reshaping of the bone by coupled action of osteblasts and osteoclasts 250mm 1mm [American Society for Bone and Mineral Research]

  5. 10 mm 20-100 mm Osteocytes 100 mm

  6. Cellular Automata Created by von Neumann (1940s) to simulate the human brain. Machine able to build and heal by itself. Local rule Neighborhoods No neighborhood N = 0 Neumann N = 4 Moore N = 8 Expanded Moore N = 24 Margolus

  7. Cellular Automata R=2 IF c(k)=0 & (sum=1 | sum=R) THEN c(k+1)=1; ELSE c(k+1)=0;

  8. Cellular Automata R=2 IF c(k)=0 & (sum=1 | sum=R) THEN c(k+1)=1; ELSE c(k+1)=0;

  9. Cellular Automata IF c(k)=0 & (sum=1 | sum=R) THEN c(k+1)=1; ELSE c(k+1)=0; R = 2 R = 3

  10. Applications Hour glassProbabilistic CA model with Margolus Neighborhood Non-stationary flowLattice Boltzmann FCHP (face-centered-hyper-cubic) model [Chopard and Droz, 1998] [Humieres, Lallemand and Frisch, 1986] Crack PropagationLattice Boltzmann Probabilistic CA model Topology OptimizationCellular Automata and Finite Element Method (HCA) [Chopard and Droz, 1998] [Renaud, Tovar, 2003]

  11. Why Cellular Automata? Are suitable to solve complex problems Inherent parallelism makes them suitable to simulate very large scale models. Applications in structural synthesis e.g. Hajela, Gurdal, Tovar. Can be used to simulate non-deterministic phenomena e.g., fire forest models, lattice gas. CA perspectives CA can be combined with “learning” strategies (e.g., GAs) Offer a frame work for complex problems in Engineering.

  12. Hybrid Cellular Automaton Algorithm Initial design Structural Analysis (FEM) U(r) New material distribution (HCA rule) r no Converged? yes Stop

  13. FEM HCA Global Control Loop Structural Analysis (FEM) U* r U(r) . . .

  14. ri = ri(ei) Ui* ei ri FEM HCA Local Control FEM

  15. Local Control No neighborhood N = 0 Neumann N = 4 Moore N = 8 Expanded Moore N = 24

  16. Control strategies 1) Two-position control 2) Proportional control 3) Integral control 4) Derivative control

  17. Two-position control

  18. Proportional control

  19. Integral control

  20. Proportional-Integral control

  21. Proportional-Derivative control

  22. Proportional-Integral-Derivative control

  23. Effect of the Neighborhood

  24. Global strain U and global V vs. target U*

  25. Isotropic Iterative Approximation

  26. Anisotropic solution

  27. Isotropic element Anisotropic element Isotropic vs. Anisotropic structure

  28. A self organizing structure(no target U*) Still under study

  29. Do we have time for more?

  30. ux uy uy ux ux ux uy uy HCAs in Morphing Aircraft Structures Structure Actuators Supports r u k [Hajela, Gurdal, Tovar] [Buhl, 2002] Simultaneous Structure, Actuator, and Support Design Optimization in MAS Active Rib Design

  31. Location of Supports in Continuum Structures min C=uTKu ,z s.t. viTi=V* 0  i  1 ziTsi=S* 0  zi  1 Progress • Developed stiffness based support location optimization for noncompliant structures using the SIMP approach [Buhl, 2002] • Linear finite element analysis • Optimization using Optimality Criteria OC [Sigmund 2001] • Provides framework for HCA modifications

  32. Location of Actuators in Continuum Structures SIMP Support Location - 10 Support Location - 4

  33. Location of Supports in Compliance Mechanisms max uout ,z s.t. viTi=V* 0  i  1 ziTsi=S* 0  zi  1 ? uin uout

  34. ux uy uy ux ux ux uy uy Location of Actuators in Compliance Mechanisms max uout ,z s.t. viTi=V* 0  i  1 ziTfi=F* 0  zi  1 ? uin uout

  35. Final Remarks • HCAs models are suitable to solve unconstrained topology optimization problems. • HCAs can be applied to constrained topology optimization using global analysis. • HCAs can be combined with other optimization techniques, including heuristic or gradient based methods.

  36. Thanks

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