Abstract
AbstractWe present a simple methodology to design curved shell finite elements based on Nzengwa-Tagne’s shell equations. The element has three degrees of freedom at each node. The displacements field of the element satisfies the exact requirement of rigid body modes in a ‘shifted-Lagrange’ polynomial basis. The element is based on independent strain assumption insofar as it is allowed by the compatibility equations. The element developed herein is first validated on analysis of benchmark problems involving a standard shell with simply supported edges. Examples illustrating the accuracy improvement are included in the analysis. It showed that reasonably accurate results were obtained even when using fewer elements compared to other shell elements. The element is then used to analyse spherical roof structures. The distribution of the various components of deflection is obtained. Furthermore, the effect of introducing concentrated load on a cylindrical clamped ends structure is investigated. It is found that the CSFE3-sh element considered is a very good candidate for the analysis of general shell structures in engineering practice in which the ratio h/R ranges between 1/1000 and 2/5.
Highlights
A great number of research works has been expended over the past five decades on the development of shell finite elements methods for the analysis of curved structures [1, 2]
We present a simple methodology to design curved shell finite elements based on Nzengwa-Tagne’s shell equations
The objective of this paper is to develop CSFE triangular shell finite elements that can be practically used for N-T shell equations which are more general for shell structures
Summary
A great number of research works has been expended over the past five decades on the development of shell finite elements methods for the analysis of curved structures [1, 2]. The formulation of simple and robust finite elements has become one of the most important research fields in structural mechanics [3], like high order elements of Carrera et al [4]; Keshava Kumar S. et al [5]. Grafton and Strome [15] developed conical segments for the analysis of shell of revolution. Curved rectangular and cylindrical shell elements were developed by [17, 18]. To model a spherical shape shells using the finite element method, triangular and rectangular spherical shell elements are needed [19,20,21]
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