Generalised assumed strain curved shell finite elements (CSFE-sh) with shifted-Lagrange and applications on N-T’s shells theory

Abstract

We 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.

Keywords

• double curved
• shells
• shifted-lagrange
• strain approach
• deflexion
• convergence