Advances in Computational Design

  • 제9권3호
  • /
  • Pages.213-227
  • /
  • 2024
  • /
  • 2383-8477(pISSN)
  • /
  • 2466-0523(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Developing a framework to integrate convolution quadrature time-domain boundary element method and image-based finite element method for 2-D elastodynamics

  • Takahiro Saitoh (Department of Civil and Environmental Engineering, Gunma University) ;
  • Satoshi Toyoda (Department of Civil and Environmental Engineering, Gunma University)
  • 투고 : 2024.03.13
  • 심사 : 2024.09.11
  • 발행 : 2024.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, a framework for coupling of the convolution quadrature time-domain boundary element method (CQBEM) and image-based finite element method (IMFEM) is presented for 2-D elastic wave propagation. This coupling method has three advantages: 1) the finite element modeling for heterogeneous areas can be performed without difficulties by using digital data for the analysis model, 2) wave propagation in an infinite domain can be calculated with high accuracy by using the CQBEM, and 3) a small time-step size can be used. In general, a small time-step size cannot be used in the classical time-domain boundary element method. However, the CQBEM used in this analysis can address a small time-step size. This makes it possible to couple the CQBEM and image-based FEM which require a small-time step size. In this study, the formulation and validation of the pro-posed method are described and confirmed by solving fundamental elastic wave scattering problems. As a numerical example, elastic wave scattering in inhomogeneous media is demonstrated using the proposed coupling method.

키워드

과제정보

This study was supported by JSPS KAKENHI (21K0423100, 24K00966), Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures, and High-Performance Computing Infrastructure in Japan (Project IDs: jh230036, jh240035). Support was also provided by the SECOM Science and Technology Foundation.

참고문헌

  1. Abreu, A.I., Carrer, J.A.M. and Mansur, W.J. (2003), "Scalar wave propagation in 2D: A BEM formulation based on the operational quadrature method", Eng. Anal. Bound. Elem., 27, 101-105. https://doi.org/10.1016/S0955-7997(02)00087-5
  2. Aour, B., Rahmani, O. and Nait-Abdelaziz, M. (2006), "A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics", Int. J. Solids Struct., 44, 2523-2539.
  3. Azqandi, M.S., Hassanzadeh, M. and Arjmand, M. (2019), "Sensitivity analysis based on complex variables in FEM for linear structures", Adv. Comput. Des., 4(1), 15-32. https://doi.org/10.12989/acd.2019.4.1.015
  4. Bebendorf, M. (2008), Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems, Springer-Verlag.
  5. Beskos, D. (1987), Boundary Element Methods in Mechanics, North Holland.
  6. Chung, S.Y., Han, T.S. and Kim S.Y. (2015) "Reconstruction and evaluation of the air permeability of a cement paste specimen with a void distribution gradient using CT images and numerical methods", Constr. Build. Mater., 87(15), 45-53. https://doi.org/10.1016/j.conbuildmat.2015.03.103
  7. Eringen, A.C. and Suhubi, E.S. (1975), Elastodynamics: Vol.1 and 2, Academic Press Inc.
  8. Fellinger, P., Marklein, R., Langenberg, K. J. and Klaholz, S. (1995), "Numerical modeling of elastic wave propagation and scattering with EFIT -elastodynamic finite integration technique", Wave Motion, 21(1), 47-66. https://doi.org/10.1016/0165-2125(94)00040-C
  9. Fukui. T, and Ishida, Y. (1987), "Time marching BE-FE method in wave problem", Proceedings of the 1st Japan-China Symposium Boundary Element Methods, 95-106.
  10. Givoli, D. (2004), "High-order local non-reflecting boundary conditions: a review", Wave Motion, 39, 319-326. https://doi.org/10.1016/j.wavemoti.2003.12.004
  11. Greengard, L. and Rokhlin, V. (1987), "A fast algorithm for particle simulations", J. Comput. Phys., 73, 325-348.
  12. Hughes, T.J.R. (1987), The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Publications, New York, N.Y., U.S.A.
  13. Logan, D.L. (2016), A First Course in the Finite Element Method: SI Edition, Cl-Engineering.
  14. Lubich, C. (1998), "Convolution quadrature and discretized operational calculus I", Numerische Mathematik, 52, 129-145. https://doi.org/10.1007/BF01398686
  15. Lubich, C. (1998), "Convolution quadrature and discretized operational calculus II", Numerische Mathematik, 52, 413-425. https://doi.org/10.1007/BF01462237
  16. Mansur, W.J. and Brebbia, C.A. (1983), "Transient elastodynamics using a time-stepping technique", Bound. Elem., 677-698.
  17. Nakahata, K, Hirose, S., Schbert, F. and Kohler, B. (2009), "Image based EFIT simulation for nondestructive ultrasonic testing of austenitic steel", J. Solid Mech. Mater. Eng., 3(12), 1256-1262. https://doi.org/10.1299/jmmp.3.1256
  18. Niwa, Y., Fukui, T., Kato, S. and Fujiki, K. (1980), "An application of the integral equation method to two-dimensional elastodynamics", Theor. Appl. Mech., 28, 281-290.
  19. Rokhlin, V. (1985), "Rapid solution of integral equations of classical potential theory", J. Comput. Phys., 60, 187-207.
  20. Rose J.L. (1999), Ultrasonic Waves in Solid Media, Cambridge University Press, Cambridge, Cambridgeshire, U.K.
  21. Saitoh, T. (2024), "Convolution quadrature time-domain boundary element method for antiplane anisotropic viscoelastic wave propagation", Eng. Anal. Bound. Elem., 164, 105753. https://doi.org/10.1016/j.enganabound.2024.105753
  22. Saitoh, T., Chikazawa, F. and Hirose, S. (2014), "Convolution quadrature time-domain boundary element method for 2-D fluid-saturated porous media", Appl. Math. Modell., 38, 3724-3740. https://doi.org/10.1016/j.apm.2014.02.009
  23. Saitoh, T., Ichikawa, R. and Inagaki, Y. (2016), "Development of coupling method of convolution quadrature BEM and image-based FEM for 2-D wave propagation in time-domain", J. Japan Soc. Comput. Meth. Eng., 16, 1-6 (in Japanese).
  24. Saitoh, T. and Takeda, H. (2021), "Convolution quadrature time-domain boundary element method for viscoelastic wave scattering by many cavities in 3-D infinite space", Int. J. Comput. Methods, 2141020. https://doi.org/10.1142/S0219876221410206
  25. Schanz, M. and Antes, H. (1997), "Application of operational quadrature methods in time domain boundary element method", Meccanica., 32, 179-186. http://doi.org/10.1023/A:1004258205435
  26. Schanz, M. (2001), Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach, Springer.
  27. Shaw, I.D. and Andrawes, B. (2017), "Finite element analysis of CFRP laminate repairs on damaged end regions of prestressed concrete bridge girders", Adv. Comput. Des., 2(2), 147-168. https://doi.org/10.12989/acd.2017.2.2.147
  28. Terada, K., Miura, T. and Kikuchi, N. (1997), "Digital image-based modeling applied to the homogenization analysis of composite materials", Comput. Mech., 20(4), 331-346. https://doi.org/10.1007/s004660050255
  29. Von, E.O. and Prabucki, M.J. (1990), "Dynamic response in the time domain by coupled boundary and finite elements", Comput. Mech., 6, 35-46.
  30. Xinzhong, G. and Shunming, L. (2018), "Convolution quadrature time-domain boundary element method for two-dimensional aeroacoustic noise prediction", Acoust. Phys, 64, 731-741.
  31. Yu, W., Yang, X., Liu, Y., Mittra, R. and Muto, A. (2011), Advanced FDTD Method: Parallelization, Acceleration, and Engineering Applications, Artech House.