Particle Dynamics with MBD and FEA Using CUDA

What is MFBD Used For?• Design– Motion prediction– Durability– Optimization– Safety factor– Control systems• Performance analysis– Failure analysis• Key reasons for MFBD:– When motion & system levelanalysis are important– High-speed, complex contact,complex boundary conditionsc 2012 FunctionBay, Inc.

The MFBD Environment• Strong coupling of system variables– Nonlinear systems• Rotation, nonlinear constraints• Nonlinear deformation, materials• Implicit differential-algebraicequation (DAE) solvers– Alpha-family of steppers• Newmark, generalized-alpha– Requires heavy use of Newton-Raphson nonlinear system solvers• Sparse direct multi-frontal linearsystem solver• Small systems of equations– 1,000’s ~ 1,000,000’s of variables• Long simulation times– 1,000’s ~ 1,000,000’s of time stepseeFee T Fer T Φee0 Φreqq eeeq qq F eeΦ e 0 0 0 0 ee ee q λ Φ F F q F r r rr rT rrT T erT 0 B Φe r zB Φzrr rr q q λ Φrr0 0 Φer err 0 0 qλ ΦererΦ e 0 Φ r 0 0 qq c 2012 FunctionBay, Inc.

MFBD + GPU Computing• Goal:– Add value to MFBDthrough thecomputational power ofthe GPU.• First application:– Particle dynamicsc 2012 FunctionBay, Inc.

Particle Dynamics for MFBD• Particles:– High value for MFBD code• Solve more complex problems• Earthmovers, lubrication, wheel-soil interaction, tank sloshing, toner systems …Vehicle model courtesy of Jacob Hustadc 2012 FunctionBay, Inc.

Particle Dynamics for MFBD• Particles:– Expensive on the CPU• More particles = more useful• Huge number of particles & variables• Loose coupling of equations• Particles interact through forces (not joints)– Excellent fit for GPU computing– Implementation cost relatively low• Particle formulations:– Granular solids: DEM (Discrete element method)• Dirt, sand, rocks, toner– Fluids: SPH (Smoothed particle hydrodynamics)• Lubrication, flows, slosh, splashc 2012 FunctionBay, Inc.

Co-Simulation of Particles and MFBD• Key Issue: Time stepping– MFBD• CPU• Implicit integrator• Large steps• Variable time step size 10 -2 ~ 10 -4 sec– Particles• GPU• Explicit integrator• Small steps• Fixed time step size 10 -5 ~ 10 -7 secMFBDPositionForcesParticlec 2012 FunctionBay, Inc.

Co-SimulationPositionMFBD (CPU Side)MFBDForcesParticleParticle (GPU Side)c 2012 FunctionBay, Inc.

Co-Simulation Stepping AlgorithmPositionMFBDParticleForces1.Solve MFBD motion from t i to t i+1 .Particle contact forces considered constant.3.Solve particle motion between t i and t i+1 .Linearly interpolate MFBD contact surfaces from t i to t i+1 .MFBD StepParticle Steps2.Transfer MFBD surfacepositions to particle solver(on GPU).t i t i+1 t i t i+14.Transfer particle-to-surface forces at t i+1 to MFBD solverc 2012 FunctionBay, Inc.

Particle Stepper• Per step (all on GPU):– Identify contacts– Compute contact forces– Compute positions at next time step• Explicit stepperc 2012 FunctionBay, Inc.

Contact Algorithm Details• Particle-to-MFBD-surface contact algorithm:– Particle shape: spherical– MFBD body surface: triangles– Contact search: sphere-to-triangle– Force: penalty-basedPenetration depthc 2012 FunctionBay, Inc.

Particle-to-MFBD-Surface Contact• Linear interpolation of body position from t i to t i+1– Rigid bodies:• Interpolate center point and orientation– Flexible bodies:• Interpolate nodal positionsc 2012 FunctionBay, Inc.

Examples• Particle computational performance– Test hardware:• GPU: Tesla C2050• CPU: Intel i5 760 (Quad-core, 2.8GHz)• RAM: 8GB– Test problem:• Particle step size: 10 -6 sec• Simulation t end : 1 sec• # time steps: 1,000,000# Spheres ComputationTime (Hours)1,000 0.452,000 0.505,000 0.6710,000 0.9020,000 1.8350,000 4.67100,000 9.12200,000 22.00500,000 46.83c 2012 FunctionBay, Inc.

ExamplesHardware:GPU:CPU:RAM:Tesla C2050Intel i5 760 (Quad-core, 2.8GHz)8GBParticles In Box Waterfall WashingmachineTanker truck Camera Camera Gears# Spheres 9900 52000 25100 53000 8640 10296Radius of Spheres (mm) 6.25 10 6.5 22.5 1 0.15Simulation t end (sec) 0.3 2 2 5 3 1MBD Step Size (sec) 10 -3 10 -3 10 -3 10 -3 10 -3 10 -3Particle Step Size (sec) 6.67x10 -6 2.89x10 -6 2.35x10 -6 8.54x10 -6 6.67x10 -6 5.82x10 -9Comp. Time (hours) 0.27 5.85 4.5 4.4 3.67 24.0c 2012 FunctionBay, Inc.

Implementation Status, Future Direction• Current Status:– DEM + MBD (rigid only)– Single GPU only• Next Targets:– MFBD (add flexible body interaction)– SPH– Multi-GPU supportc 2012 FunctionBay, Inc.

Conclusion• Particle Dynamics:– Adds high value to MFBD– Excellent match for GPU computing– Low implementation cost– Co-simulation to combine MFBD solver and particle solverc 2012 FunctionBay, Inc.

Thank Youc 2012 FunctionBay, Inc.