A modified scaled boundary method to analyze structural elements

Document Type : Research

Authors

1 Department of Civil Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

2 Robotics & Soft Technologies Research Centre, Tabriz Branch, Islamic Azad University, Tabriz, Iran,

Abstract

It is possible to resolve numerical issues by utilizing a method known as the conventional scaled boundary finite element method (also known as SBFEM), which is a dimension reduction technique. This method can be utilized in conjunction with mesh-free technologies to enhance the numerical characteristics of the conventional SBFEM. Within the scope of this investigation, a novel interpretation of the SBM is presented that makes use of the advantages offered by the meshless local Petrov Galerkin method. Using the moving Kriging interpolation (MKI) method, one can create shape functions that conform to the requirements of the Kronecker delta function property. The interpolating scaled boundary local Petrov Galerkin method that was proposed then can implement essential boundary conditions (ISBLPGM) directly. This new method offers a number of benefits in comparison to scaled boundary approaches that have been presented in the past. It is optional to have a mesh that has been predefined, and the boundary conditions can be determined with very little additional effort. It has been demonstrated that the numerical approach that is being presented yields results that are in very good agreement with analytical and other numerical approaches. Solving the benchmark numerical problems allows for an evaluation of the effectiveness of the proposed method as well as its precision

Keywords

Main Subjects

References

[1] Liu, G. R. (2002). Mesh-free methods, moving beyond the finite element method. CRC press
https://doi.org/10.1201/9781420040586
 
[2] Vafaei Pousorkhabi, R. (2020). Investigating the Effect of Flow and Sediment Particles Characteristics on Sandy Sediments Transport in Circular Sections using Data Driven Methods. Water and Soil Science, 30(4), 75-87. doi: 10.22034/ws.2020.11649
 
[3] Hajialilue-Bonab, M., & Razavi, S. K. (2015). A study of soil-nailed wall behavior at limit states. Proceedings of the Institution of Civil Engineers-Ground Improvement, 169(1), 64-76. 
https://doi.org/10.1680/jgrim.14.00021
 
[4] Khalili‑Maleki, M., Vafaei Pousorkhabi, R., Nadiri, A.A., & Dabiri, R. (2022). Prediction of hydraulic conductivity based on the soil grain size using supervised committee machine artificial intelligence. Earth Science Informatics, 15, 2571-2583. 
https://doi.org/10.1007/s12145-022-00848-x
 
[5] Zienkiewicz, O. C., Owen, D. R. J., & Lee, K. N. (1974) Least square‐finite element for elasto‐static problems. Use of 'reduced integration. International Journal for Numerical Methods in Engineering, 8(2), 341-358. 
https://doi.org/10.1002/nme.1620080212
 
[6] Farajniya, R., Poursorkhabi, R. V., Zarean, A., & Dabiri, R. (2022). Investigation of the arching in rock-fill dam ten years after the end of construction using Numerical analysis and monitoring. Ferdowsi Civil Engineering, 35(1), 59-74. https://doi.org/ 10.22067/JFCEI.2022.73934.1098
 
[7] Belytschko, T., Lu, Y. Y., Gu, L. (1994) Element‐free Galerkin methods. International Journal for Numerical Methods in Engineering, 37(2), 229-256. 
https://doi.org/10.1002/nme.1620370205
 
[8] Liu, W. K., Jun, S., & Zhang, Y. F. (1995). Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids, 20(8‐9), 1081-1106. 
https://doi.org/10.1002/fld.1650200824
 
[9] Atluri, S. N., & Zhu, T. (1998). A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 22(2), 117-127. 
https://doi.org/10.1007/s004660050346
 
[10] Liu, G. R., Zhang, G. Y., Gu, Y., & Wang, Y. Y. (2005). A mesh-free radial point interpolation method (RPIM) for three-dimensional solids. Computational Mechanics, 36(6), 421-430. 
https://doi.org/10.1007/s00466-005-0657-6
 
[11] Rafiezadeh, K., Ataie-Ashtiani, B. (2014). Transient free-surface seepage in three-dimensional general anisotropic media by BEM, Engineering Analysis with Boundary Elements, 46, 51-66. 
https://doi.org/10.1016/j.enganabound.2014.04.025
 
[12] Rafiezadeh, K., Ataie-Ashtiani, B. (2016) Three-dimensional flow in anisotropic zoned porous media using boundary element method, Engineering Analysis with Boundary Elements, 36, 812-824. 
https://doi.org/10.1016/j.enganabound.2011.12.002
 
[13] Mendonça, A. V., De Paiva, J. B. (2000). A boundary element method for the static analysis of raft foundations on piles. Engineering Analysis with Boundary Elements, 24(3), 237-247. 
https://doi.org/10.1016/S0955-7997(00)00002-3
 
[14] Tanaka, M., Bercin, A. N. (1998). Static bending analysis of stiffened plates using the boundary element method. Engineering Analysis with Boundary Elements, 21(2), 147-154. 
https://doi.org/10.1016/S0955-7997(98)00002-2
 
[15] Li, Z. H., Ribe, N. M. (2012). Dynamics of free subduction from 3‐D boundary element modeling. Journal of Geophysical Research: Solid Earth, 117(B6). 
https://doi.org/10.1029/2012JB009165
 
[16] Brebbia, C. A., Nardini, D. (1983). Dynamic analysis in solid mechanics by an alternative boundary element procedure. Soil Dynamics and Earthquake Engineering, 2(4), 228-233. 
https://doi.org/10.1016/S0955-7997(00)00031-X
 
[17] Brebbia, C. A., Telles, J. C. F., Wrobel, L. C. (2012). Boundary element techniques: theory and applications in engineering. Springer Science & Business Media.
https://doi.org/10.1115/1.3169016
 
[18] Song, C., Wolf, J. P. (1997). The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method for elastodynamics. Computer Methods in Applied Mechanics and Engineering, 147(3-4), 329-355. 
https://doi.org/10.1016/S0045-7825(97)00021-2
 
[19] Deeks, A. J., Wolf, J. P. (2002). A virtual work derivation of the scaled boundary finite-element method for elastostatics. Computational Mechanics, 28(6), 489-504.
https://doi.org/10.1007/s00466-002-0314-2
 
[20] Bazyar, M. H., Talebi, A. (2015). Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method. International Journal for Numerical and Analytical Methods in Geomechanics, 39(1), 1-22. 
https://doi.org/10.1002/nag.2291
 
[21] Fengzhi, L. I. (2009). Scaled boundary finite-element method for seepage-free surfaces analysis. Chinese Journal of Computational Physics, 5, 004.
 
[22] Song, C., Wolf, J. P. (2000). The scaled boundary finite-element method-a primer: solution procedures. Computers & Structures, 78(1-3), 211-225. 
https://doi.org/10.1016/S0045-7949(00)00100-0
 
[23] Song, C., Wolf, J. P. (1999). Body loads in scaled boundary finite-element method. Computer Methods in Applied Mechanics and Engineering., 180(1-2), 117-135. 
https://doi.org/10.1016/S0045-7825(99)00052-3
 
[24] Tohidvand, H. R., Hajialilue-Bonab, M. (2014). Seismic soil-structure interaction analysis using an effective scaled boundary spectral element approach, Asian Journal of Civil Engineering, 15, 501-516.
 
[25] Hajialilue-Bonab, M., Tohidvand, H. R. (2015). A modified scaled boundary approach in the frequency domain with diagonal coefficient matrices. Engineering Analysis with Boundary Elements, 50, 8-18. 
https://doi.org/10.1016/j.enganabound.2014.07.001
 
[26] Mukherjee, Y. X., Mukherjee, S., (1997). Boundary node method for potential problems, International Journal for Numerical Methods in Engineering, 40, 797-815. 
https://doi.org/10.1002/(SICI)1097-0207(19970315)40:5<797::AID-NME89>3.0.CO;2-#
 
[27] Zhu, T. & Atluri, S., N. (1998). A modified collocation and a penalty formulation for enforcing the essential boundary conditions in the element-free Galerkin method, Computational Mechanics, 21: 211-222. 
https://doi.org/10.1007/s004660050296
 
[28] Liu, G. R., Gu, Y., T. (2000) Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation, Computational Mechanics, 26(2): 166-173. 
https://doi.org/10.1007/s004660000164
 
[29] Deeks, A. J., Augarde, C. E. (2005). A meshless local Petrov-Galerkin scaled boundary method, Computational Mechanics, 36, 159-170. 
https://doi.org/10.1007/s00466-004-0649-y
 
[30] He, Y., Yang, H., Deeks, A. J. (2012). An Element free Galerkin (EFG) scaled boundary method, Finite Elements in Analysis and Design, 62, 28-35. 
https://doi.org/10.1016/j.finel.2012.07.001
 
[31] Chen, S. S., Wang, J., Li, Q. H. (2016). Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method, Chinese Physics, 25(4): 1-8.
https://doi.org/10.1088/1674-1056/25/4/040203
 
[32] Chen, S. S., Li, Q. H., Liu, Y. H. (2012) Scaled boundary node method applied to two-dimensional crack problems, Chinese Physics, 21(11): 1-9. 
https://doi.org/10.1088/1674-1056/21/11/110207
 
[33] Hajiazizi, M., & Graili, A. (2017). A scaled boundary radial point interpolation method for 2‐D elasticity problems. International Journal for Numerical Methods in Engineering, 112(7), 832-851. https://doi.org/10.1002/nme.5534
https://doi.org/10.1002/nme.5534
 
[34] Hassanzadeh, M., Tohidvand, H.R., Hajialilue-Bonab, M., Javadi, A.A. (2018). Scaled boundary point interpolation method for seismic soil-tunnel interaction analysis, Computers and Geotechnics, 101, 208-216. 
https://doi.org/10.1016/j.compgeo.2018.05.007
 
[35] Gu, L. (2003). Moving kriging interpolation and element‐free Galerkin method. International Journal for Numerical Methods in Engineering, 56(1), 1-11. 
https://doi.org/10.1002/nme.553
 
[36] Wolf, J.P., Song, C. (1996). Finite-element modeling of unbounded media, Chichester. Wiley.
 
[37] Zang, Q., Bordas, S. P., Liu, J., & Natarajan, S. (2023). NURBS-Enhanced polygonal scaled boundary finite element method for heat diffusion in anisotropic media with internal heat sources. Engineering Analysis with Boundary Elements, 148, 279-292.
https://doi.org/10.1016/j.enganabound.2022.12.028
Numerical Methods in Civil Engineering
Volume 8, Issue 1
September 2023
Pages 18-26

Files

History

  • Receive Date: 12 March 2023
  • Revise Date: 01 August 2023
  • Accept Date: 15 August 2023

Share

How to cite

Statistics