Crashworthiness Design Using Topology Optimization

1. Crashworthiness Design Using Topology Optimization Andrés Tovar & John E. Renaud Design Automation Laboratory Department of Aerospace and Mechanical Engineering University of Notre Dame, IN Symposium for Design Optimization and Simulation-Based Design New Advancements, Technology and Future Northwestern University, Evanston, IL November 11, 2008

2. The Design Automation Laboratory Instrumentation Crashworthiness Morphing Blast Bone Biological Simulation Topology Shape Optimization Design Automation Decision-basedCollaborative Optimization Structures Optimization Methods Uncertainty Modeling and Propagation in MDO Comp Mech Reliability-Robust Design Optimization Variable Fidelity Optimization Multi-scale Material Simulation

3. Vehicle crashworthiness design Introduction • Multi-body models subject to contact and dynamic loading. • Nonlinear material model and nonlinear analysis: large deformation and plastic behavior. • Simulations of designs typically take hours to days to execute. • In the United States, these tests follow the regulations of the National Highway Traffic Safety Administration (NHTSA), particularly Standard No. 208 - Occupant Crash Protection. http://www.nhtsa.dot.gov/cars/rules/import/fmvss/index.html#SN208

4. Vehicle crashworthiness design Objective Design structural components to absorb the crash energy while retaining stiffness Knee bolster Bumper Door beams

5. Design for Crashworthiness MethodologyThe Hybrid Cellular Automata (HCA) Cell FEM Load LocalCA rule Tissue Organ

6. The Hybrid Cellular Automata (HCA) Characteristics • Gradient-free topology synthesis methodology. • Material modeling using the density approach. • Mass control to control material cost • Manufacturing constraints of constant cross section topologies to generate extrusion-based designs.

7. The Hybrid Cellular Automata (HCA) Previous applicationsNon-compliant structures (NCS) and compliant mechanisms (CM) NCS min wSED+(1-w)M CM min -wMPE+(1-w)SED

8. The Hybrid Cellular Automata (HCA) Previous applicationsBone remodeling simulations

9. Design for CrashworthinessCrasHCA Y Eh  E  Implementation • Inclusion of nonlinear transient finite-element analysis • Material modeling accounting for plastic deformation • Manufacturing constraints of constant cross section topologies to generate extrusion-based designs • Performance constraints to tailor force-displacement behavior Elastic-plastic behavior Dynamic analysis

10. Design for CrashworthinessCrasHCA Analysis Problem Formulation Design Process Performance analysis using Altair HyperView Objective: Maximum energy absorption Define: Design Domain Loads Boundary Conditions Material properties Mass constraint Design Iterations using Matlab Initial design Crash analysis t(k+1) U(x(k)) Update thickness distribution using HCA rule Δx = f(U,U*) Modeling Finite element modeling using Altair HyperMesh t(k+1) = t(k)+Δt Validation Convergence test no Industrial Collaboration • Build prototype • Perform real time crash test and evaluate • Mass production yes Final design Design Phases

11. Design for CrashworthinessCrasHCA Current design S*(0)(x(k)) x(k), S*(j+1) Apply HCA material update rules x(k+1) Convergence test no Update global setpoint S*(j) yes New design Mass control Design ProcessUniform Internal Energy Density Distribution Initial design Crash analysis x(k+1) U(x(k)) Update material distribution using HCA rule Δx = f(U,U*) x(k+1) = x(k)+Δx Convergence test no yes Final design

12. Design for CrashworthinessCrasHCA: short beam * Mf =0.2 y z x Problem Formulation and ModelingDesign domain composed of 80x20x20 elements 80 mm 20 mm v0 40 mm 20 mm v0=40 m/s Altair HyperMesh

13. Design for CrashworthinessCrasHCA: short beam * Mf =0.2 z y x Results of the Design ProcessEffects of model simplifications Linear-static Nonlinear-static Nonlinear-dynamic

14. Design for CrashworthinessCrasHCA: short beam AnalysisForce-displacement behavior Fr (N) d (mm)

15. Design for CrashworthinessCrasHCA ManufacturabilityDesign for extrusion • Most topologies require complex manufacturing techniques • Cast manufacturing • Secondary machining • Added costs • Extrusion is a relatively inexpensive manufacturing technique • Material is forced through a die • Constant cross section

16. Design for CrashworthinessCrasHCA ManufacturabilityDesign for extrusion • Generate constant cross section topologies • Design domain is 2-D and material enforced along direction • The integration of the IED along the extrusion rows represents the information that is operated on

17. Design for CrashworthinessShort beam: extrusion results Extruded topology z y x dmax= 47.6 mm z y v0=40 m/s * Mf =0.2 Conventional topology (no extrusion) dmax= 40.1 mm

18. Design for CrashworthinessCrasHCA: bumper Final topology Simulation Design domain

19. Design for CrashworthinessCrasHCA: knee-bolster Design domain Optimization Simulation Final topology Analysis

20. Design for CrashworthinessCrasHCA: knee-bolster AnalysisForce-displacement behavior Fr (N) d(mm)

21. Design for CrashworthinessCrasHCA: door beam Design domain Analysis Final topology AltairHyperView

22. Blast Simulation & Optimization (BSO) Integrated Rupture Modeling Mechanisms OptimizeStructure Simulate Blast Loading Altair HyperView

23. Blast Simulation & Optimization (BSO) Altair HyperView

24. Final comments • Phases in Crashworthiness Design Using Topology Optimization: • Problem formulation • Modeling using Altair HyperMesh • Topology optimization using crasHCA (Matlab and FEA) • Performance analysis using Altair HyperView • Validation • Applications of crasHCA include: • Bumber structures • Knee-bolster • Door beam • Current research include: • Force-displacement constraints • Design for blast impacts • Altair HyperWorks is also used as an academic tool in Finite Element Analysis, Introduction to Optimum Design, and Topology Optimization.

25. Thank you Andrés Tovar atovar@nd.edu