Spherical Hankel-Based Free Vibration Analysis of Cross-ply Laminated Plates Using Refined Finite Element Theories

Abstract

In this paper, spherical Hankel basis functions and Carrera unified formulation (CUF) are utilized for the free vibration analysis of laminated composite plates. The spherical Hankel shape functions are derived from the corresponding radial basis function. These functions have excellent ability to satisfy the first and second kind of Bessel function as well as polynomial function fields which leads to more accurate results. Also, CUF presents an effective formulation to employ any order of Taylor expansion to expand solution field. Higher-order theories supposed by CUF are free from Poisson locking phenomenon, and they do not need any shear correction factor. Therefore, coupling spherical Hankel basis functions and CUF ends in a suitable methodology to analyze laminated plates. To investigate the proposed approach, several numerical examples are provided and the superiority and robustness of the suggested approach are shown.

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Correspondence to Saleh Hamzehei-Javaran.

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Alesadi, A., Shojaee, S. & Hamzehei-Javaran, S. Spherical Hankel-Based Free Vibration Analysis of Cross-ply Laminated Plates Using Refined Finite Element Theories. Iran J Sci Technol Trans Civ Eng 44, 127–137 (2020). https://doi.org/10.1007/s40996-019-00242-6

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Keywords

  • Spherical Hankel basis functions
  • Free vibration
  • Composite laminates
  • Carrera unified formulation