Additive Manufacturing Simulation on the GPU

Krishnan Suresh

ProfessorMechanical Engineering

Overview

2

1.AM: What & Why?

2.AM Simulation

3.Computational Bottlenecks

4. Ideas for Fast Simulation

Manufacturing

3

Traditional (Subtractive) Additive Manuf. (AM)

(3D printing)

AM Methods

4

Why AM?

5

Design Freedom!

Cool designs Fewer parts CustomizationBetter designs

AM Market

6

Where is the catch?

Additive manufacturing (AM) is an art!

The Real Truth

8

CAD Model (torture test)Our attempt

Vendor Print

AM Issues

[Ref: Cheng 2014]

[ma3jic, OSU]

Warping

Micro-defects

DelaminationBurning

[Ref: Mertens 2014]

Surface Finish

[Ref: NASA techbrief]

Voids

[Apriso]

[Ref: UMTech 2012]

AM Price Tag

10

Material cost:$ per gram!

Can’t afford playing around

Unless you are GE

> $500K

GE Success Story

11

Additive manufacturing is an art

AM Simulation

13

AM Simulation

14

Identify relevant physics

Discretization

Numerical solution

Results

Experiments

Errors

Relevant Physics?

15

• Thermal analysis• Elasticity/plasticity analysis

• Thermal analysis• Viscous/flow modeling

[Ref: Thomson 2015]

• Particle dynamics• Laser absorption• Melt pool formation• Thermal transfers• Macro-structural loads• Micro-structural evolution• …

Mathematical Model

( ) ( )( )i i

i i p i i

u h u Hh k E HQ

t x x x t xc

Energy Equation

Transient Term

Flow Term

Conductivity Term

Latent Heat Terms

Internal Energy Source

Double Ellipsoidal Volumetric Heat Source

http://www.ams.org.cn/EN/10.11900/0412.1961.2013.00832

AM Simulation

17

Identify relevant physics

Discretization

Numerical methods

Simulation Results

Experiments

Errors

Discretization

18

Discretization(Mesh)

Printing resolution ~ 20 microns

Hand-sized part ~ 125 billion elements!

AM Issues

[Ref: Cheng 2014]

[ma3jic, OSU]

Warping

Micro-defects

DelaminationBurning

[Ref: Mertens 2014]

Surface Finish

[Ref: NASA techbrief]

Voids

[Apriso]

[Ref: UMTech 2012]

Resolution Map for AM

201 element ~ 3 degrees of freedom

4 20 50 150 500

#ELEMENTS (MILLION)

#Elements for 10x10x10 cm

Discretization & Solver

21

Discretization(Mesh)

Kd = fPhysics

AM Simulation Bottleneck

22

Kd f

AM Simulation

23

Identify relevant physics

Discretization

Numerical methods

Simulation Results

Experiments

Errors

24

Kd = f (GTC Topics)

Fine-grained Parallel Preconditioners

CULA

MAGMA

Accelerating Iterative Linear Solvers

Efficient AMG on Hybrid GPU Clusters

Preconditioning for Large-Scale Linear Solvers

…

AM Simulation: Highly Nonlinear

Transient

Phase change

Radiation non-linearity

Material non-linearity

Typical Discretization

[ANSYS]

Distinctly shaped elements

AM Discretization

Voxelization: Identical elements~ microns to mm

‘Identical’ element stiffness Ke

Implication: SpMV

28

1

Classic: N

ei

Kd K d

: Sparse Matrix-Vector Multiplication (SpMV)

Critical operation in ALL iterative solvers

Kd

1

Assembly-free: N

e ei

Kd K d

Store a single Ke (4 kB)

Assembly-Free SpMV

29

Million Elements

0

200

400

600

800

1000

Assembled AF-CPU AF-GPU

SpMV; Kd (msec)

770

37

CPU

Assembly-free Kd

Classic Kd

Challenge

How to construct pre-conditioner for K, without assembling K?

Assembly-free deflation

(Agglomeration + rigid body)

Yadav, P., Suresh, K., “Large Scale Finite Element Analysis via Assembly Free Deflated Conjugate Gradient,” Journal of Computing and Information Science in Engineering, Volume 14, Number 4, December 2012

Example

31

3.15 million DOF

Multi-core/GPU Friendly

AM Simulation

32

Identify relevant physics

Discretization

Numerical methods

Simulation Results

Experiments

Errors

Preliminary Results

CPU:

– Xeon E5-2620, 2.2 GHz, 8 core

– 32 GB

– C/C++ Code (OpenMP)

GPU:

– GP 100

– 16 GB

– CUDA

Double-precision

Timings include CPU-GPU transfer

33

0

200

400

600

800

1000

0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000

Tim

e(s)

Number of Elements

ANSYS 14.5 Direct

ANSYS 14.5 CGiterative

PareTO FSW

Transient Thermo-Elastic Simulation

34

Friction Stir Welding (only CPU)

35

Friction Stir Welding: Accuracy

35

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

0 10 20 30 40 50

Str

ess

(Pa)

Distance from center line

ANSYS 14.5

PareTO FSW

0

100

200

300

400

500

600

0 10 20 30 40 50

Tem

per

atu

re (

Deg

C)

Distance from center line

ANSYS 14.5

PareTO FSW

Temperature Stress

GPU Speed-up

36

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Tim

e in

Min

ute

s

Millions of elements

Clock time in minutes

Xeon E5-2620

Nvidia GP100

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60

Sp

eed

-up

Millions of elements

GP100 Speed-up

Deflated Assembly-free Kd = f

1 million elements ~ 3 million degrees of freedom

Resolution Map for AM

371 element ~ 3 degrees of freedom

4 20 50 150 500

#ELEMENTS (MILLION)

#Elements for 10x10x10 cm

Single-GPU limit

FDM: Thermal + Phase Change

AM Simulation

39

Identify relevant physics

Discretization

Numerical methods

Simulation Results

Experiments

Errors

40

Friction Stir Welding: Accuracy

[Fehrenbacher, 2014]

ParametersExperimental Parameters used:Force = 3500 NFriction coeff = 0.4

525

530

535

540

545

550

555

50 52 54 56 58 60 62

Experimental Numerical

AM:Verification

LENS (Metal) Process

Technology Transfer

www.sciartsoft.com

AM simulation on the desktop!

Conclusions

1. Strong need for AM simulation

2. Complexity of AM Simulation

3. Assembly-free methods on GPU

4. Current focus on Multi-GPU

Acknowledgements

Praveen Yadav Shiguang Deng Amir M. Mirzendehdel Chaman Singh Alireza Taheri Bian Xiang

Anirudh Krishnakumar Anirban Niyogi Victor Cavalcanti Cameron Gilanshah Yibo Hu Alex Buehler

Funding NSF Air-force Luvata Autodesk Sandia National Lab NVidia

ksuresh@wisc.edu