Particle Dynamics with MBD and FEA Using CUDA

Transcription

1 Particle Dynamics with MBD and FEA Using CUDA Graham Sanborn, PhD Senior Research Engineer Solver 2 (MFBD) Team FunctionBay, Inc., S. Korea

2 Overview MFBD: Multi-Flexible-Body Dynamics Rigid & flexible body motion simulation tool Adding Particles Dynamics to MFBD via the GPU Adds high value to MFBD Excellent match for GPU computing Low implementation cost Issues and examples of the particle dynamics with MFBD Vehicle model courtesy of Jacob Hustad

3 What is MFBD? MFBD: Multi-Flexible-Body Dynamics = MBD + FEA MBD = Multi-body dynamics FEA = Finite element analysis Compute Motion Forces, stresses, strains For systems of bodies Both rigid and flexible Interactions through Joints Contact

4 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 level analysis are important High-speed, complex contact, complex boundary conditions

5 The MFBD Environment Strong coupling of system variables Nonlinear systems Rotation, nonlinear constraints Nonlinear deformation, materials Implicit differential-algebraic equation (DAE) solvers Alpha-family of steppers Newmark, generalized-alpha Requires heavy use of Newton- Raphson nonlinear system solvers Sparse direct multi-frontal linear system 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 steps e e F ee T F er T Φ e e 0 Φ r e q q ee e q q q F ee Φ e ee ee q λ Φ F F q F r r rr r T rrt T ert 0 B Φ e r z B Φz rr rr q q λ Φ rr 0 0 Φ er er r 0 0 q λ Φ er er Φ e 0 Φ r 0 0 q q

6 MFBD + GPU Computing Goal: Add value to MFBD through the computational power of the GPU. First application: Particle dynamics

7 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 Hustad

8 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, splash

9 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 sec MFBD Position Forces Particle

10 Co-Simulation Position MFBD (CPU Side) MFBD Forces Particle Particle (GPU Side)

11 Co-Simulation Stepping Algorithm Position MFBD Particle Forces 1. 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 Step Particle Steps 2. Transfer MFBD surface positions to particle solver (on GPU). t i t i+1 t i t i+1 4. Transfer particle-to-surface forces at t i+1 to MFBD solver

12 Particle Stepper Per step (all on GPU): Identify contacts Compute contact forces Compute positions at next time step Explicit stepper

13 Contact Algorithm Details Particle-to-MFBD-surface contact algorithm: Particle shape: spherical MFBD body surface: triangles Contact search: sphere-to-triangle Force: penalty-based Penetration depth

14 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 positions

15 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 Computation Time (Hours) 1, , , , , , , , ,

16 Examples Hardware: GPU: CPU: RAM: Tesla C2050 Intel i5 760 (Quad-core, 2.8GHz) 8GB Particles In Box Waterfall Washing machine Tanker truck Camera Camera Gears # Spheres Radius of Spheres (mm) Simulation t end (sec) MBD Step Size (sec) Particle Step Size (sec) 6.67x x x x x x10-9 Comp. Time (hours)

17 Implementation Status, Future Direction Current Status: DEM + MBD (rigid only) Single GPU only Next Targets: MFBD (add flexible body interaction) SPH Multi-GPU support

18 Conclusion Particle Dynamics: Adds high value to MFBD Excellent match for GPU computing Low implementation cost Co-simulation to combine MFBD solver and particle solver

19 Thank You