한국항공우주학회지 (Journal of the Korean Society for Aeronautical & Space Sciences)

  • 제48권10호
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  • Pages.773-782
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  • 2020
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  • 1225-1348(pISSN)
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  • 2287-6871(eISSN)
한국항공우주학회 (The Korean Society for Aeronautical and Space Sciences)
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하이브리드 유한요소해석을 위한 인공지능 조인트 모델 개발

Development of Artificial Intelligence Joint Model for Hybrid Finite Element Analysis

  • Jang, Kyung Suk (Department of Aerospace Engineering, Seoul National University) ;
  • Lim, Hyoung Jun (Department of Aerospace Engineering, Seoul National University) ;
  • Hwang, Ji Hye (LSMtron Tractor Design Validation Team) ;
  • Shin, Jaeyoon (LSMtron Tractor Design Validation Team) ;
  • Yun, Gun Jin (Department of Aerospace Engineering, Seoul National University)
  • 투고 : 2020.07.23
  • 심사 : 2020.09.14
  • 발행 : 2020.10.01
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초록

심층신경망 기반 하이브리드 유한요소해석을 위한 조인트 모델 방법 구축을 소개한다. 트렉터의 앞차축에서 다양한 체결 조건에 의해 유발되는 복잡한 거동 상태를 가지는 볼트와 베어링의 재료 모델을 심층신경망으로 대체했다. 볼트는 6자유도를 갖는 1차원 티모센코 빔 요소를 이용했고, 베어링은 3차원 솔리드 요소를 이용했다. 다양한 하중 조건을 바탕으로 유한요소해석을 한 뒤, 모든 요소에서 응력-변형률 데이터를 추출하고 텐서플로를 이용하여 학습시켰다. 신경망 기반 유한요소해석을 할 때 추출된 데이터를 바탕으로 학습된 심층신경망은 ABAQUS 서브루틴 안에 포함되어 현재 해석 증분의 응력을 예측하고 접선강도행렬을 계산할 수 있게 했다. 학습된 심층신경망 조인트 모델의 일반화 성능은 훈련에 사용되지 않은 새로운 하중 조건에서 해석하여 검증하였다. 최종적으로 이 방법을 이용하여 심층신경망 기반 앞차축 해석을 진행하고 응력장 분포를 검증했다. 또한, 실제 트렉터의 3점 굽힘 실험 결과와 비교하여 심층신경망 기반 해석의 타당성을 검토했다.

The development of joint FE models for deep learning neural network (DLNN)-based hybrid FEA is presented. Material models of bolts and bearings in the front axle of tractor, showing complex behavior induced by various tightening conditions, were replaced with DLNN models. Bolts are modeled as one-dimensional Timoshenko beam elements with six degrees of freedom, and bearings as three-dimensional solid elements. Stress-strain data were extracted from all elements after finite element analysis subjected to various load conditions, and DLNN for bolts and bearing were trained with Tensorflow. The DLNN-based joint models were implemented in the ABAQUS user subroutines where stresses from the next increment are updated and the algorithmic tangent stiffness matrix is calculated. Generalization of the trained DLNN in the FE model was verified by subjecting it to a new loading condition. Finally, the DLNN-based FEA for the front axle of the tractor was conducted and the feasibility was verified by comparing with results of a static structural experiment of the actual tractor.

키워드

참고문헌

  1. Alkatan, F., Stephan, P., Daidie, A. and Guillot, J., "Equivalent axial stiffness of various components in bolted joints subjected to axial loading," Journal of Finite Elements in Analysis Design, Vol. 43, No. 8, 2007, pp. 589-598. https://doi.org/10.1016/j.finel.2006.12.013
  2. Williams, J., Anley, R., Nash, D. and Gray, T., "Analysis of externally loaded bolted joints: Analytical, computational and experimental study," International Journal of Pressure Vessels Piping, Vol. 86, No. 7, 2009, pp. 420-427. https://doi.org/10.1016/j.ijpvp.2009.01.006
  3. Guo, M. and Ali, S., "Study on simplified finite element simulation approaches of fastened joints," Society of Automotive Engineers International, Vol. 115, No. 6, 2006, p. 10.
  4. Oldfield, M., Ouyang, H. and Mottershead J. E., "Simplified models of bolted joints under harmonic loading," Computers and Structures, Vol. 84, No. 1-2, 2005, pp. 25-33. https://doi.org/10.1016/j.compstruc.2005.09.007
  5. Oishi, A. and Yagawa, G., "Computational mechanics enhanced by deep learning," Journal of Computer Methods in Applied Mechanics Engineering, Vol. 327, No. 1, 2017, pp. 327-351. https://doi.org/10.1016/j.cma.2017.08.040
  6. Ghaboussi, J. and Sidarta, D., "A new nested adaptive neural network for modeling of constitutive behavior of materials," International Journal of Computer and Geotechnics, Vol. 22, No. 1, 1998, pp. 29-51. https://doi.org/10.1016/S0266-352X(97)00034-7
  7. Ghaboussi, J., Garrett Jr., J. H. and Wu, X., "Knowledge-based modeling of material behavior with neural networks," Journal of engineering mechanics, Vol. 117, No. 1, 1991, pp. 132-153. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:1(132)
  8. Ghaboussi, J., Pecknold, D. A., Zhang, M. and Haj‐Ali, R. M., "Autoprogressive training of neural network constitutive models," International Journal for Numerical Methods in Engineering, Vol. 42, No. 1, 1998, pp. 105-126. https://doi.org/10.1002/(SICI)1097-0207(19980515)42:1<105::AID-NME356>3.0.CO;2-V
  9. Settgast, C., Hutter, G., Kuna, M. and Abendroth, M., "A hybrid approach to simulate the homogenized irreversible elastic-plastic deformations and damage of foams by neural networks," International Journal of Plasticity, Vol. 126, 2020, pp. 102-624.
  10. Bessa, M. A., Bostanabad, R., Liu, Z., Hu, A., Apley, D. W., Brinson, C., Chen, W. and Liu, W. K., "A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality," Computer Methods in Applied Mechanics Engineering, Vol. 320, 2017, pp. 633-667. https://doi.org/10.1016/j.cma.2017.03.037
  11. Le, B., Yvonnet, J. and He, Q. C., "Computational homogenization of nonlinear elastic materials using neural networks," International Journal for Numerical Methods in Engineering, Vol. 104, No. 12, 2015, pp. 1061-1084. https://doi.org/10.1002/nme.4953
  12. Eggersmann, R., Kirchdoerfer, T., Reese, S., Stainier, L. and Ortiz, M., "Model-Free Data-Driven inelasticity," Computer Methods in Applied Mechanics and Engineering, Vol. 350, 2019, pp. 81-99. https://doi.org/10.1016/j.cma.2019.02.016
  13. Kirchdoerfer, T. and Ortiz, M., "Data-driven computing in dynamics," International Journal for Numerical Methods in Engineering, Vol. 113, No. 11, 2018, pp. 1697-1710. https://doi.org/10.1002/nme.5716
  14. Kirchdoerfer, T. and Ortiz, M., "Data-driven computational mechanics," Computer Methods in Applied Mechanics and Engineering, Vol. 304, 2016, pp. 81-101. https://doi.org/10.1016/j.cma.2016.02.001
  15. Kirchdoerfer, T. and Ortiz, M., "Data Driven Computing with noisy material data sets," Computer Methods in Applied Mechanics and Engineering, Vol. 326, 2017, pp. 622-641. https://doi.org/10.1016/j.cma.2017.07.039
  16. Raissi, M., Perdikaris, P. and Karniadakis, G. E., "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations," Journal of Computational Physics, Vol. 378, 2019, pp. 686-707. https://doi.org/10.1016/j.jcp.2018.10.045
  17. Raissi, M., Perdikaris, P. and Karniadakis, G. E., "Inferring solutions of differential equations using noisy multi-fidelity data," Journal of Computational Physics, Vol. 335, 2017, pp. 736-746. https://doi.org/10.1016/j.jcp.2017.01.060
  18. Raissi, M. and Karniadakis, G. E., "Hidden physics models: Machine learning of nonlinear partial differential equations," Journal of Computational Physics, Vol. 357, 2018, pp. 125-141. https://doi.org/10.1016/j.jcp.2017.11.039
  19. Raissi, M., "Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations," Journal of Machine Learning Research, Vol. 19, 2018, pp. 1-24.
  20. Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G. S., Davis, A., Dean, J. and Devin, M., "Tensorflow: Large-scale machine learning on heterogeneous distributed systems," arXiv preprint arXiv:04467. 2016
  21. Geron, A., Book Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems. 1st ed. O'Reilly Media, 2017.
  22. Yun, G. J., Ghaboussi, J. and Elnashai, A. S., "A new neural network‐based model for hysteretic behavior of materials," International Journal for Numerical Methods in Engineering, Vol. 73, No. 4, 2008, pp. 447-469. https://doi.org/10.1002/nme.2082
  23. Maas, A. L., Hannun, A. Y. and Ng, A. Y., "Rectifier nonlinearities improve neural network acoustic models," Proceeding of icmll, 2013.
  24. Kingma, D. P. and Ba, J., "Adam: A method for stochastic optimization," arXiv1412:6980, 2014.