Mohammadi Nia, M., Shojaee, S., Hamzehei-Javaran, S. (2018). Utilizing new spherical Hankel shape functions to reformulate the deflection, free vibration, and buckling analysis of Mindlin plates based on finite element method. Scientia Iranica, (), -. doi: 10.24200/sci.2018.5113.1103
Majid Mohammadi Nia; Saeed Shojaee; Saleh Hamzehei-Javaran. "Utilizing new spherical Hankel shape functions to reformulate the deflection, free vibration, and buckling analysis of Mindlin plates based on finite element method". Scientia Iranica, , , 2018, -. doi: 10.24200/sci.2018.5113.1103
Mohammadi Nia, M., Shojaee, S., Hamzehei-Javaran, S. (2018). 'Utilizing new spherical Hankel shape functions to reformulate the deflection, free vibration, and buckling analysis of Mindlin plates based on finite element method', Scientia Iranica, (), pp. -. doi: 10.24200/sci.2018.5113.1103
Mohammadi Nia, M., Shojaee, S., Hamzehei-Javaran, S. Utilizing new spherical Hankel shape functions to reformulate the deflection, free vibration, and buckling analysis of Mindlin plates based on finite element method. Scientia Iranica, 2018; (): -. doi: 10.24200/sci.2018.5113.1103
Utilizing new spherical Hankel shape functions to reformulate the deflection, free vibration, and buckling analysis of Mindlin plates based on finite element method
1Civil Engineering Department, Faculty of Engineering, Shahid Bahonar University of Kerman, Iran
2Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University, Kerman, Iran
3Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, 22 Bahman Blvd, Kerman, Iran
Abstract
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.
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