Skip to main content

Advertisement

Log in

Acceleration strategies for explicit finite element analysis of metal powder-based additive manufacturing processes using graphical processing units

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

Metal powder-based Additive Manufacturing (AM) processes are increasingly used in industry and science due to their unique capability of building complex geometries. However, the immense computational cost associated with AM predictive models hinders the further industrial adoption of these technologies for time-sensitive applications, process design with uncertainties or real-time process control. In this work, a novel approach to accelerate the explicit finite element analysis of the transient heat transfer of AM processes is proposed using Graphical Processing Units. The challenges associated with this approach are enumerated and multiple strategies to overcome each challenge are discussed. The performance of the proposed algorithms is evaluated on multiple test cases. Speed-ups of about 100 ×–150 × compared to an optimized single CPU core implementation for the best strategy were achieved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Yang L, Harrysson O, West H, Cormier D (2012) Compressive properties of Ti–6Al–4V auxetic mesh structures made by electron beam melting. Acta Mater 60(8):3370–3379

    Article  Google Scholar 

  2. Guo C, Ge W, Lin F (2015) Dual-material electron beam selective melting: hardware development and validation studies. Engineering 1(1):124–130

    Article  Google Scholar 

  3. Wenjun G, Chao G, Feng L (2015) Microstructures of components synthesized via electron beam selective melting using blended pre-alloyed powders of Ti6Al4V and Ti45Al7Nb. Rare Metal Mater Eng 44(11):2623–2627

    Article  Google Scholar 

  4. Tan X, Kok Y, Tan YJ, Descoins M, Mangelinck D, Tor SB, Leong KF, Chua CK (2015) Graded microstructure and mechanical properties of additive manufactured Ti–6Al–4V via electron beam melting. Acta Mater 97:1–16

    Article  Google Scholar 

  5. Dehoff R, Kirka M, Sames W, Bilheux H, Tremsin A, Lowe L, Babu S (2015) Site specific control of crystallographic grain orientation through electron beam additive manufacturing. Mater Sci Technol 31(8):931–938

    Article  Google Scholar 

  6. Gibson I, Rosen DW, Stucker B (2010) Sheet lamination processes. In: Additive manufacturing technologies. Springer, pp 223–252

  7. Gu D, Meiners W, Wissenbach K, Poprawe R (2012) Laser additive manufacturing of metallic components: materials, processes and mechanisms. Int Mater Rev 57(3):133–164

    Article  Google Scholar 

  8. King W, Anderson A, Ferencz R, Hodge N, Kamath C, Khairallah S, Rubenchik A (2015) Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges. Appl Phys Rev 2(4):041304

    Article  Google Scholar 

  9. Parry L, Ashcroft I, Wildman RD (2016) Understanding the effect of laser scan strategy on residual stress in selective laser melting through thermo-mechanical simulation. Addit Manuf 12:1–15

    Article  Google Scholar 

  10. Schoinochoritis B, Chantzis D, Salonitis K (2017) Simulation of metallic powder bed additive manufacturing processes with the finite element method: a critical review. Proc Inst Mech Eng Part B: J Eng Manuf 231(1):96–117

    Article  Google Scholar 

  11. Khairallah SA, Anderson AT, Rubenchik A, King WE (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 108:36–45

    Article  Google Scholar 

  12. Rai A, Markl M, Körner C (2016) A coupled cellular automaton-lattice Boltzmann model for grain structure simulation during additive manufacturing. Comput Mater Sci 124:37–48

    Article  Google Scholar 

  13. Yan W, Lin S, Kafka OL, Lian Y, Yu C, Liu Z, Yan J, Wolff S, Wu H, Ndip-Agbor E (2018) Data-driven multi-scale multi-physics models to derive process–structure–property relationships for additive manufacturing. Comput Mech 61:1–21

    Article  MathSciNet  MATH  Google Scholar 

  14. Wolff SJ, Lin S, Faierson EJ, Liu WK, Wagner GJ, Cao J (2017) A framework to link localized cooling and properties of directed energy deposition (DED)-processed Ti–6Al–4V. Acta Mater 132:106–117

    Article  Google Scholar 

  15. Francois MM, Sun A, King WE, Henson NJ, Tourret D, Bronkhorst CA, Carlson NN, Newman CK, Haut T, Bakosi J (2017) Modeling of additive manufacturing processes for metals: challenges and opportunities. Curr Opin Solid State Materials Sci 21(LA-UR-16-24513)

  16. NVIDIA (2016) NVIDIA GPU accelerated applications catalog

  17. Tajdari M, Tai BL (2016) Modeling of brittle and ductile materials drilling using smoothed-particle hydrodynamics. In: ASME 2016 11th international manufacturing science and engineering conference, 2016. American Society of Mechanical Engineers

  18. Bell N, Hoberock J (2011) Thrust: a productivity-oriented library for CUDA. In: GPU computing gems Jade edition. Elsevier, pp 359–371

  19. Bolz J, Farmer I, Grinspun E, Schröoder P (2003) Sparse matrix solvers on the GPU: conjugate gradients and multigrid. In: ACM transactions on graphics (TOG). ACM

  20. Nvidia C (2014) Cusparse library. NVIDIA Corporation, Santa Clara

    Google Scholar 

  21. Price AD (2013) Multi-GPU Computing with Abaqus: benchmarking and scaling for multiphysics applications in mechatronics

  22. Lukarski D (2015) Paralution-library for iterative sparse methods

  23. Pichler F, Haase G (2019) Finite element method completely implemented for graphic processor units using parallel algorithm libraries. Int J High Perf Comput Appl 33(1):53–66

    Article  Google Scholar 

  24. Cecka C, Lew AJ, Darve E (2011) Assembly of finite element methods on graphics processors. Int J Numer Meth Eng 85(5):640–669

    Article  MATH  Google Scholar 

  25. Markall G, Slemmer A, Ham D, Kelly P, Cantwell C, Sherwin S (2013) Finite element assembly strategies on multi-core and many-core architectures. Int J Numer Meth Fluids 71(1):80–97

    Article  MathSciNet  Google Scholar 

  26. Markall GR, Ham DA, Kelly PH (2010) Towards generating optimised finite element solvers for GPUs from high-level specifications. Proc Comput Sci 1(1):1815–1823

    Article  Google Scholar 

  27. Dziekonski A, Lamecki A, Mrozowski M (2011) A memory efficient and fast sparse matrix vector product on a GPU. Prog Electromagn Res 116:49–63

    Article  Google Scholar 

  28. Dziekonski A, Lamecki A, Mrozowski M (2016) GPU-accelerated finite element method. In: 2016 IEEE MTT-S international conference on numerical electromagnetic and multiphysics modeling and optimization (NEMO). IEEE

  29. Dziekonski A, Sypek P, Lamecki A, Mrozowski M (2012) Finite element matrix generation on a GPU. Prog Electromagn Res 128:249–265

    Article  MATH  Google Scholar 

  30. Saad Y (2003) Iterative methods for sparse linear systems, vol 82. SIAM

  31. Knepley MG, Rupp K, Terrel AR (2016) Finite element integration with quadrature on the GPU. arXiv preprint arXiv:1607.04245

  32. Knepley MG, Terrel AR (2013) Finite element integration on GPUs. ACM Trans Math Softw (TOMS) 39(2):10

    Article  MathSciNet  MATH  Google Scholar 

  33. Georgescu S, Chow P, Okuda H (2013) GPU acceleration for FEM-based structural analysis. Arch Comput Methods Eng 20(2):111–121

    Article  MathSciNet  MATH  Google Scholar 

  34. Van Belle L, Vansteenkiste G, Boyer JC (2012) Comparisons of numerical modelling of the selective laser melting. In: Key engineering materials. Trans Tech Publ

  35. Zaeh MF, Branner G (2010) Investigations on residual stresses and deformations in selective laser melting. Prod Eng Res Dev 4(1):35–45

    Article  Google Scholar 

  36. Wang Z, Beese AM (2017) Effect of chemistry on martensitic phase transformation kinetics and resulting properties of additively manufactured stainless steel. Acta Mater 131:410–422

    Article  Google Scholar 

  37. Belytschko T, Liu WK, Moran B, Elkhodary K (2013) Nonlinear finite elements for continua and structures. Wiley, Hoboken

    MATH  Google Scholar 

  38. Fish J, Belytschko T (2007) A first course in finite elements. Wiley, Hoboken

    Book  MATH  Google Scholar 

  39. Smith J, Xiong W, Cao J, Liu WK (2016) Thermodynamically consistent microstructure prediction of additively manufactured materials. Comput Mech 57(3):359–370

    Article  MATH  Google Scholar 

  40. Golub GH, Welsch JH (1969) Calculation of Gauss quadrature rules. Math Comput 23(106):221–230

    Article  MathSciNet  MATH  Google Scholar 

  41. Zhu J (2013) The finite element method: its basis and fundamentals. Elsevier, Amsterdam

    MATH  Google Scholar 

  42. Yan W, Lin S, Kafka OL, Lian Y, Yu C, Liu Z, Yan J, Wolff S, Wu H, Ndip-Agbor EJCM (2018) Data-driven multi-scale multi-physics models to derive process–structure–property relationships for additive manufacturing. Comput Mech 61(5):521–541

    Article  MATH  Google Scholar 

  43. Mozaffar M, Paul A, Al-Bahrani R, Wolff S, Choudhary A, Agrawal A, Ehmann K, Cao JJMI (2018) Data-driven prediction of the high-dimensional thermal history in directed energy deposition processes via recurrent neural networks. Manuf Lett 18:35–39

    Article  Google Scholar 

  44. Cheng J, Grossman M, McKercher T (2014) Professional Cuda C programming. Wiley, Hoboken

    Google Scholar 

  45. NVIDIA (2008) NVIDIA CUDA C programming guide, pp. 1–261

  46. Lee C-C, Lee D-T (1985) A simple on-line bin-packing algorithm. J ACM (JACM) 32(3):562–572

    Article  MathSciNet  MATH  Google Scholar 

  47. Graham RL (1969) Bounds on multiprocessing timing anomalies. SIAM J Appl Math 17(2):416–429

    Article  MathSciNet  MATH  Google Scholar 

  48. NVIDIA (2018) Features and technical specifications. https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html#compute-capabilities

  49. Meng H-T, Nie B-L, Wong S, Macon C, Jin J-MJIA, Magazine P (2014) GPU accelerated finite-element computation for electromagnetic analysis. IEEE Antennas Propag Mag 56(2):39–62

    Article  Google Scholar 

  50. Wang H, Zeng Y, Li E, Huang G, Gao G, Li GJCMIAM (2016) “Seen Is Solution” a CAD/CAE integrated parallel reanalysis design system. Comput Methods Appl Mech Eng 299:187–214

    Article  MathSciNet  MATH  Google Scholar 

  51. Zhang R, Wen L, Naboulsi S, Eason T, Vasudevan VK, Qian DJCM (2016) Accelerated multiscale space–time finite element simulation and application to high cycle fatigue life prediction. Comput Mech 58(2):329–349

    Article  MathSciNet  Google Scholar 

  52. Yamaguchi T, Fujita K, Ichimura T, Hori T, Hori M, Wijerathne LJPCS (2017) Fast finite element analysis method using multiple gpus for crustal deformation and its application to stochastic inversion analysis with geometry uncertainty. Proc Comput Sci 108:765–775

    Article  Google Scholar 

  53. Bennett JL, Wolff SJ, Hyatt G, Ehmann K, Cao J (2017) Thermal effect on clad dimension for laser deposited Inconel 718. J Manuf Process 28:550–557

    Article  Google Scholar 

  54. Commons W (2015) File: selective laser melting system schematic.jpg—Wikimedia Commons{,} the free media repository. https://commons.wikimedia.org/w/index.php?title=File:Selective_laser_melting_system_schematic.jpg&oldid=154088078. Accessed 15 Oct 2018

Download references

Acknowledgements

The authors acknowledge the support by the National Institute of Standards and Technology (NIST)—Center for Hierarchical Materials Design (CHiMaD) under Grant No. 70NANB14H012, and the National Science Foundation (NSF)—Cyber-Physical Systems (CPS) under Grant No. CPS/CMMI-1646592. Stephen Lin is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1324585.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jian Cao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mozaffar, M., Ndip-Agbor, E., Lin, S. et al. Acceleration strategies for explicit finite element analysis of metal powder-based additive manufacturing processes using graphical processing units. Comput Mech 64, 879–894 (2019). https://doi.org/10.1007/s00466-019-01685-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-019-01685-4

Keywords

Navigation