Steel and Composite Structures

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A semi-analytical FE method for the 3D bending analysis of nonhomogeneous orthotropic toroidal shells

  • Wu, Chih-Ping (Department of Civil Engineering, National Cheng Kung University) ;
  • Li, En (Department of Civil Engineering, National Cheng Kung University)
  • Received : 2020.06.08
  • Accepted : 2021.04.15
  • Published : 2021.05.10
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Abstract

Based on Reissner's mixed variational theorem (RMVT), the authors develop a semi-analytical finite element (FE) method for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to uniformly-distributed loads. In this formulation, the toroidal shell is divided into several finite annular prisms (FAPs) with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridianradial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAP methods shows that their solutions converge rapidly, and the convergent FAP solutions closely agree with the 3D elasticity solutions available in the literature.

Keywords

Acknowledgement

This work was supported by the Ministry of Science and Technology of the Republic of China through Grant MOST 109-2221-E-006-015-MY3.

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