Meshless method and experimental analysis of hyperelastic plates using Mooney-Rivlin strain energy function subjected to concentrated loading

References

• Ahmadi, H., and H. A. Rasheed. 2018. Lateral torsional buckling of anisotropic laminated thin-walled simply supported beams subjected to mid-span concentrated load. Composite Structures 185 (August 2017):348–61. doi:10.1016/j.compstruct.2017.11.027.
   Google Scholar
• Bui, T. K., V. T. Nguyen, T. N. Nguyen, and T. T. Truong. 2020. Meshless radial point interpolation method for hyperelastic materials. Vol. 3, 223–214. doi:10.29007/r7sp.
   Google Scholar
• Cavoretto, R., A. De Rossi, and E. Perracchione. 2018. Optimal selection of local approximants in RBF-PU interpolation. Journal of Scientific Computing 74 (1):1–22. http://arxiv.org/abs/1703.04282. doi:10.1007/s10915-017-0418-7.
   Web of Science ®Google Scholar
• Chen, Y., G. Li, Z. Zhang, and B. Fu. 2010. Bending of thick rectangular plates with different boundaries under concentrated load. Advanced Materials Research 163–167:1440–4. doi:10.4028/www.scientific.net/AMR.163-167.1440.
   Google Scholar
• Civalek, Ö. 2014. Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations. International Journal of Pressure Vessels and Piping 113:1–9. doi:10.1016/j.ijpvp.2013.10.014.
   Web of Science ®Google Scholar
• Civalek, Ö., S. Dastjerdi, and B. Akgöz. 2022. Buckling and free vibrations of CNT-reinforced cross-ply laminated composite plates. Mechanics Based Design of Structures and Machines 50 (6):1914–31. doi:10.1080/15397734.2020.1766494.
   Web of Science ®Google Scholar
• Do, V. N. V., M. T. Tran, and C. H. Lee. 2018. Nonlinear thermal buckling analyses of functionally graded plates by a mesh-free radial point interpolation method. Engineering Analysis with Boundary Elements 87:153–64. doi:10.1016/j.enganabound.2017.12.001.
   Web of Science ®Google Scholar
• Eftekhari, S. A. 2015. A note on mathematical treatment of the Dirac-delta function in the differential quadrature bending and forced vibration analysis of beams and rectangular plates subjected to concentrated loads. Applied Mathematical Modelling 39 (20):6223–42. doi:10.1016/j.apm.2015.01.063.
   Web of Science ®Google Scholar
• Eftekhari, S. A. 2014. A differential quadrature procedure with regularization of the dirac-delta function for numerical solution of moving load problem. Latin American Journal of Solids and Structures 12 (7):1241–65. doi:10.1590/1679-78251417.
   Web of Science ®Google Scholar
• Ersoy, H., K. Mercan, and Ö. Civalek. 2018. Frequencies of FGM shells and annular plates by the methods of discrete singular convolution and differential quadrature methods. Composite Structures 183 (1):7–20. doi:10.1016/j.compstruct.2016.11.051.
   Google Scholar
• Esen, İ. 2015. A new FEM procedure for transverse and longitudinal vibration analysis of thin rectangular plates subjected to a variable velocity moving load along an arbitrary trajectory. Latin American Journal of Solids and Structures 12 (4):808–30. doi:10.1590/1679-78251525.
   Web of Science ®Google Scholar
• Farahani, B. V., J. Berardo, J. Belinha, A. J. M. Ferreira, P. J. Tavares, and P. Moreira. 2017. An optimized RBF analysis of an isotropic mindlin plate in bending. Procedia Structural Integrity 5:584–91. doi:10.1016/j.prostr.2017.07.018.
   Google Scholar
• Ferreira, A. J. M., G. E. Fasshauer, R. C. Batra, and J. D. Rodrigues. 2008. Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter. Composite Structures 86 (4):328–43. doi:10.1016/j.compstruct.2008.07.025.
   Web of Science ®Google Scholar
• Fouaidi, M., M. Jamal, and N. Belouaggadia. 2020. Nonlinear bending analysis of functionally graded porous beams using the multiquadric radial basis functions and a Taylor series-based continuation procedure. Composite Structures 252:112593. doi:10.1016/j.compstruct.2020.112593.
   Web of Science ®Google Scholar
• Fouaidi, M., M. Jamal, A. Hamdaoui, and B. Braikat. 2020. Multiquadric radial basis function approximation method and asymptotic numerical method for nonlinear and linear static analysis of single-walled carbon nanotubes. Engineering Analysis with Boundary Elements 115:40–51. doi:10.1016/j.enganabound.2020.02.010.
   Web of Science ®Google Scholar
• Gherlone, M., L. Iurlaro, and M. Di Sciuva. 2012. A novel algorithm for shape parameter selection in radial basis functions collocation method. Composite Structures 94 (2):453–61. doi:10.1016/j.compstruct.2011.08.001.
   Web of Science ®Google Scholar
• Hosseini, S., and G. Rahimi. 2021. Nonlinear bending analysis of hyperelastic plates using FSDT and meshless collocation method based on radial basis function. International Journal of Applied Mechanics 13 (01):2150007. doi:10.1142/S1758825121500071.
   Google Scholar
• Hosseini, S., G. Rahimi, and Y. Anani. 2021. A meshless collocation method based on radial basis functions for free and forced vibration analysis of functionally graded plates using FSDT. Engineering Analysis with Boundary Elements 125:168–77. doi:10.1016/j.enganabound.2020.12.016.
   Web of Science ®Google Scholar
• Huang, P., Y. Song, Q. Li, X. Liu, and Y. Feng. 2020. A theoretical study of circular orthotropic membrane under concentrated load: The relation of load and deflection. IEEE Access. 8:126127–37. doi:10.1109/ACCESS.2020.3007986.
   Web of Science ®Google Scholar
• Hussein Al-Tholaia, M. M., and H. Jubran Al-Gahtani. 2015. RBF-based meshless method for large deflection of elastic thin plates on nonlinear foundations. Engineering Analysis with Boundary Elements 51:146–55. doi:10.1016/j.enganabound.2014.10.011.
   Web of Science ®Google Scholar
• Joldes, G., G. Bourantas, B. Zwick, H. Chowdhury, A. Wittek, S. Agrawal, K. Mountris, D. Hyde, S. K. Warfield, and K. Miller. 2019. Suite of meshless algorithms for accurate computation of soft tissue deformation for surgical simulation. Medical Image Analysis 56:152–71. doi:10.1016/J.MEDIA.2019.06.004.
   PubMed Web of Science ®Google Scholar
• Khalid, M. S., S. Nisar, S. Z. Khan, M. A. Khan, and A. W. Troesch. 2020. Simulation of blended nonlinear hydrodynamics forces using radial basis function in uniform moving frame. Ocean Engineering 198:106994. doi:10.1016/j.oceaneng.2020.106994.
   Web of Science ®Google Scholar
• Khosrowpour, E., M. R. Hematiyan, and M. Hajhashemkhani. 2019. A strong-form meshfree method for stress analysis of hyperelastic materials. Engineering Analysis with Boundary Elements 109 (June):32–42. doi:10.1016/j.enganabound.2019.09.013.
   Google Scholar
• Li, K., W. Chen, W. Zhang, and G. Ma. 2009. Electromechanical coupling analysis for MEMS featured by stepped-height structure and concentrated load. Microsystem Technologies 15 (4):621–35. doi:10.1007/s00542-008-0751-8.
   Web of Science ®Google Scholar
• Li, X., and S. Li. 2019. A meshless projection iterative method for nonlinear Signorini problems using the moving Kriging interpolation. Engineering Analysis with Boundary Elements 98:243–52. doi:10.1016/j.enganabound.2018.10.025.
   Web of Science ®Google Scholar
• Mercan, K., Ç. Demir, and Ö. Civalek. 2016. Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique. Curved and Layered Structures 3 (1):82–90. doi:10.1515/cls-2016-0007.
   Web of Science ®Google Scholar
• Nakazawa, Y., N. Kogiso, T. Yamada, and S. Nishiwaki. 2016. Robust topology optimization of thin plate structure under concentrated load with uncertain load position. Journal of Advanced Mechanical Design, Systems, and Manufacturing 10 (4):JAMDSM0057. doi:10.1299/jamdsm.2016jamdsm0057.
   Web of Science ®Google Scholar
• Ribeiro, L. G., M. A. Maia, E. Parente, and A. M. C. d. Melo. 2020. Surrogate based optimization of functionally graded plates using radial basis functions. Composite Structures 252:112677. doi:10.1016/j.compstruct.2020.112677.
   Web of Science ®Google Scholar
• Rippa, S. 1999. An algorithm for selecting a good value for the parameter c in radial basis function interpolation. Advances in Computational Mathematics 11 (2/3):193–210. doi:10.1023/A:1018975909870.
   Web of Science ®Google Scholar
• Roque, C. M. C., and J. Grasa. 2021. Geometrically nonlinear analysis of laminated composite plates using RBF-PS meshless method. Composite Structures 267:113830. doi:10.1016/j.compstruct.2021.113830.
   Web of Science ®Google Scholar
• Sarra, S. A., and D. Sturgill. 2009. A random variable shape parameter strategy for radial basis function approximation methods. Engineering Analysis with Boundary Elements 33 (11):1239–45. doi:10.1016/j.enganabound.2009.07.003.
   Web of Science ®Google Scholar
• Singh, J., and K. K. Shukla. 2012a. Nonlinear flexural analysis of functionally graded plates under different loadings using RBF based meshless method. Engineering Analysis with Boundary Elements 36 (12):1819–27. doi:10.1016/j.enganabound.2012.07.001.
   Web of Science ®Google Scholar
• Singh, J., and K. K. Shukla. 2012b. Nonlinear flexural analysis of laminated composite plates using RBF based meshless method. Composite Structures 94 (5):1714–20. doi:10.1016/j.compstruct.2012.01.001.
   Web of Science ®Google Scholar
• Tan, F., and Y. Zhang. 2013. The regular hybrid boundary node method in the bending analysis of thin plate structures subjected to a concentrated load. European Journal of Mechanics - A/Solids 38:79–89. doi:10.1016/j.euromechsol.2012.10.001.
   Web of Science ®Google Scholar
• Tornabene, F., and A. Ceruti. 2013. Free-form laminated doubly-curved shells and panels of revolution resting on winkler-pasternak elastic foundations: A 2-D GDQ solution for static and free vibration analysis. World Journal of Mechanics 03 (01):1–25. doi:10.4236/wjm.2013.31001.
   Google Scholar
• Tornabene, F., N. Fantuzzi, M. Bacciocchi, and E. Viola. 2015. A new approach for treating concentrated loads in doubly-curved composite deep shells with variable radii of curvature. Composite Structures 131:433–52. doi:10.1016/j.compstruct.2015.05.049.
   Web of Science ®Google Scholar
• Tornabene, F., M. Viscoti, and R. Dimitri. 2022. Static analysis of doubly-curved shell structures of smart materials and arbitrary shape subjected to general loads employing higher order theories and generalized differential quadrature method. Computer Modeling in Engineering & Sciences 133 (3):719–98. doi:10.32604/cmes.2022.022210.
   Web of Science ®Google Scholar
• Tornabene, F., M. Viscoti, and R. Dimitri. 2023. Static analysis of anisotropic doubly-curved shell subjected to concentrated loads employing higher order layer-wise theories. Computer Modeling in Engineering & Sciences 134 (2):1393–468. doi:10.32604/cmes.2022.022237.
   Web of Science ®Google Scholar
• Van Do, V. N., and C. H. Lee. 2018. Nonlinear analyses of FGM plates in bending by using a modified radial point interpolation mesh-free method. Applied Mathematical Modelling 57:1–20. doi:10.1016/j.apm.2017.12.035.
   Web of Science ®Google Scholar
• Xiang, S., K. Wang, Y. Ai, Y. Sha, and H. Shi. 2012. Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation. Applied Mathematical Modelling 36 (5):1931–8. doi:10.1016/j.apm.2011.07.076.
   Web of Science ®Google Scholar
• Yan, C., Y. Wang, X. Zhai, and L. Meng. 2020. Strength assessment of curved steel-concrete-steel sandwich shells with bolt connectors under concentrated load. Engineering Structures 212 (September 2019):110465. doi:10.1016/j.engstruct.2020.110465.
   Google Scholar
• Yan, C., Y. Wang, X. Zhai, L. Meng, and H. Zhou. 2019. Experimental study on curved steel-concrete-steel sandwich shells under concentrated load by a hemi-spherical head. Thin-Walled Structures 137 (September 2018):117–28. doi:10.1016/j.tws.2019.01.007.
   Google Scholar
• Yan, J. B., and J. Y. R. Liew. 2016. Design and behavior of steel-concrete-steel sandwich plates subject to concentrated loads. Composite Structures 150:139–52. doi:10.1016/j.compstruct.2016.05.004.
   Web of Science ®Google Scholar
• Zhang, Y., W. Ge, Y. Zhang, Z. Zhao, and J. Zhang. 2018. Topology optimization of hyperelastic structure based on a directly coupled finite element and element-free Galerkin method. Advances in Engineering Software 123:25–37. doi:10.1016/j.advengsoft.2018.05.006.
   Web of Science ®Google Scholar