Free vibration analysis of cracked Kirchhoff-Love plate using the extended radial point interpolation method
Author affiliations
DOI:
https://doi.org/10.15625/2525-2518/59/6/15953Keywords:
fracture, free vibration, Kirchhoff-Love plate, RPIM, XRPIMAbstract
The Kirchhoff-Love plate theory is appropriate for analysing thin plate structures. In a simple form, only one degree of freedom (per node) is needed to describe the behaviour of the plate, thus saving the computational cost. Besides, the analysis of cracked structures is important because it is related to the lifetime of the structures. Therefore, this paper uses the extended radial point interpolation method (XRPIM) to investigate the free vibration of the Kirchhoff-Love plate. The XRPIM is based on RPIM so the requirement for calculating the second-order derivative in Kirchhoff-Love theory is easily done. The numerical results from this study are compared with other researchers to verify the accuracy of the method.Downloads
References
N. Moes, J. Dolbow, T. Belytschko - A finite element method for crack growth without remeshing, Int. J. Numer. Methods Eng. 46 (1999) 131–150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J DOI: https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
J. Dolbow, N. Moes, T. Belytschko - Modeling fracture in mindlin-Reissner plates with the extended finite element method, Int. J. Solids Struct. 37 (2000) 7161–7183. https://doi.org/10.1016/S0020-7683(00)00194-3 DOI: https://doi.org/10.1016/S0020-7683(00)00194-3
J. Li, Z. S. Khodaei, M. H. Aliabadi - Dynamic dual boundary element analysis for cracked Mindlin plates, Int. J. Solids Struct. 152–153 (2018) 248–260. https://doi.org/10.1016/j.ijsolstr.2018.06.033 DOI: https://doi.org/10.1016/j.ijsolstr.2018.06.033
J. Useche - Fracture dynamic analysis of cracked Reissner plates using the boundary element method, Int. J. Solids Struct. 191–192 (2020) 315–332. https://doi.org/10.1016/j.ijsolstr.2020.01.017 DOI: https://doi.org/10.1016/j.ijsolstr.2020.01.017
J. Lasry, Y. Renard, M. Salaun - Stress intensity factors computation for bending plates with extended finite element method, Int. J. Numer. Methods Eng. 91 (2012) 909–928. https://doi.org/10.1002/nme.4292 DOI: https://doi.org/10.1002/nme.4292
M. Petyt - Introduction to Finite Element Vibration Analysis (2nd Edition), Cambridge, 2010. DOI: https://doi.org/10.1017/CBO9780511761195
Vitor M. A. Leitao - A meshless method for Kirchhoff plate bending problems, Int. J. Numer. Methods Eng. 52 (2001) 1107-1130. https://doi.org/10.1002/nme.244 DOI: https://doi.org/10.1002/nme.244
Y. Liu, Y. C. Hon, K. M. Liew - A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems, Int. J. Numer. Methods Eng. 66 (2006) 1153–1178. https://doi.org/10.1002/nme.1587 DOI: https://doi.org/10.1002/nme.1587
N. T. Nguyen, T. Q. Bui, C. Zhang, T. T. Truong - Crack growth modeling in elastic solids by the extended meshfree galerkin radial point interpolation method, Eng. Anal. Bound. Elem. 44 (2014) 87–97. https://doi.org/10.1016/j.enganabound.2014.04.021 DOI: https://doi.org/10.1016/j.enganabound.2014.04.021
N. T. Nguyen, T. Q. Bui, T. T. Truong - Transient dynamic fracture analysis by an extended meshfree method with different crack-tip enrichments, Meccanica 52 (2017) 2363–2390. https://doi.org/10.1007/s11012-016-0589-6 DOI: https://doi.org/10.1007/s11012-016-0589-6
N. T. Nguyen, T. Q. Bui, M. N. Nguyen, T. T. Truong - Meshfree thermomechanical crack growth simulations with new numerical integration scheme, Eng. Fract. Mech. 235 (2020) 107–121. https://doi.org/10.1016/j.engfracmech.2020.107121 DOI: https://doi.org/10.1016/j.engfracmech.2020.107121
H. S. Yang, C. Y. Dong - Adaptive extended isogeometric analysis based on PHT-splines for thin cracked plates and shells with Kirchhoff–Love theory, Appl. Math. Model. 76 (2019) 759–799. https://doi.org/10.1016/j.apm.2019.07.002 DOI: https://doi.org/10.1016/j.apm.2019.07.002
G. R. Liu, X. L. Chen - A mesh-free method for static and free vibration analyses of thin plates of complicated shape, J. Sound Vib. 241 (2001) 839–855. https://doi.org/10.1006/jsvi.2000.3330 DOI: https://doi.org/10.1006/jsvi.2000.3330
S. Shojaee, E. Izadpanah, N. Valizadeh, J. Kiendl - Free vibration analysis of thin plates by using a NURBS-based isogeometric approach, Finite Elem. Anal. Des. 61 (2012) 23–34. https://doi.org/10.1016/j.finel.2012.06.005 DOI: https://doi.org/10.1016/j.finel.2012.06.005
T.V. Vu, N.H. Nguyen, A. Khosravifard, M.R. Hematiyan, S. Tanaka, T.Q. Bui - A simple FSDTbased meshfree method for analysis of functionally graded plates, Eng. Anal. Bound. Elem. 79 (2017) 1–12. https://doi.org/10.1016/j.enganabound.2017.03.002 DOI: https://doi.org/10.1016/j.enganabound.2017.03.002
A. J. M. Ferreira, N. Fantuzzi - Kirchhoff Plates. In: MATLAB Codes for Finite Element Analysis. Solid Mechanics and Its Applications, 157 (2020) Springer, Cham. https://doi.org/10.1007/978-3-030-47952-7_12 DOI: https://doi.org/10.1007/978-3-030-47952-7_12
B. Stahl, L.M. Keer - Vibration and stability of cracked rectangular plates, Int. J.
Solids Struct. 8 (1972) 69–91. https://doi.org/10.1016/0020-7683(72)90052-2 DOI: https://doi.org/10.1016/0020-7683(72)90052-2
K. M. Liew, K. C. Hung, M. K. Lim - A solution method for analysis of cracked plates under vibration, Eng. Fract. Mech. 48 (1994) 393–404. https://doi.org/10.1016/0013-7944(94)90130-9 DOI: https://doi.org/10.1016/0013-7944(94)90130-9
M. Bachene, R. Tiberkak, S. Rechak - Vibration analysis of cracked plates using the extended finite element method, Arch. Appl. Mech. 79 (2009) 249—262. https://doi.org/10.1007/s00419-008-0224-7 DOI: https://doi.org/10.1007/s00419-008-0224-7
T. Nguyen-Thoi, T. Rabczuk , T. Lam-Phat , V. Ho-Huu , P. Phung-Van - Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCSDSG3), Theor. Appl. Fract. Mech. 72 (2014) 150–163. https://doi.org/10.1016/j.tafmec.2014.02.004 DOI: https://doi.org/10.1016/j.tafmec.2014.02.004
C.S. Huang, A.W. Leissa - Vibration analysis of rectangular plates with side
cracks via the Ritz method, J. Sound Vib. 323 (2009) 974–988. https://doi.org/10.1016/j.jsv.2009.01.018 DOI: https://doi.org/10.1016/j.jsv.2009.01.018
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Vietnam Journal of Sciences and Technology (VJST) is an open access and peer-reviewed journal. All academic publications could be made free to read and downloaded for everyone. In addition, articles are published under term of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA) Licence which permits use, distribution and reproduction in any medium, provided the original work is properly cited & ShareAlike terms followed.
Copyright on any research article published in VJST is retained by the respective author(s), without restrictions. Authors grant VAST Journals System a license to publish the article and identify itself as the original publisher. Upon author(s) by giving permission to VJST either via VJST journal portal or other channel to publish their research work in VJST agrees to all the terms and conditions of https://creativecommons.org/licenses/by-sa/4.0/ License and terms & condition set by VJST.
Authors have the responsibility of to secure all necessary copyright permissions for the use of 3rd-party materials in their manuscript.
Vietnam Journal of Science and Technology (VJST) is pleased to notice: