Sharif University of Technology Scientia Iranica 1026-3098 27 5 2020 10 01 Utilizing new spherical Hankel shape functions to reformulate the deflection, free vibration, and buckling analysis of Mindlin plates based on finite element method 2209 2229 21087 10.24200/sci.2018.5113.1103 EN M. Mohammadi Nia Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, P.O. Box 76169{133, Iran. S. Shojaee Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, P.O. Box 76169{133, Iran. S. Hamzehei-Javaran Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, P.O. Box 76169{133, Iran. Journal Article 2017 09 03 In this study, a new class of shape functions, namely spherical Hankel shape functions, are derived and applied to reformulate the deflection, free vibration, and buckling of Mindlin plates based on finite element method (FEM). In this way, adding polynomial terms to the functional expansion, in which just spherical Hankel radial basis functions (RBFs) are used, leads to obtaining spherical Hankel shape functions. Accordingly, the employment of polynomial and spherical Bessel function fields together results in achieving more robustness and effectiveness. Spherical Hankel shape functions benefit from some useful properties, including infinite piecewise continuity, partition of unity, and Kronecker delta property. In the end, the accuracy of the proposed formulation is investigated through several numerical examples for which the same degrees of freedom are selected in both the presented formulation and the classical finite element method. Finally, it can be concluded that a higher accuracy is reachable by utilizing spherical Hankel shape functions in comparison with the Lagrangian FEM. https://scientiairanica.sharif.edu/article_21087_e0486134d53afffd48f4305975e8acda.pdf