Shallow Spherical Shell Rectangular Finite Element for Analysis of Cross Shaped Shell Roof

Abstract

A new spherical rectangular finite element based on shallow shell formulation is developed in this paper. The element has six degrees of freedom at each corner node, five of which are the essential external degrees of freedom and the additional sixth is associated with the in-plane shell rotation. The displacement fields of the element satisfy the exact requirement of rigid body modes of motion. The element is based on independent strain assumption insofar as it is allowed by the compatibility equations. The element developed herein is first validated by applying it to the analysis of a benchmark problem involving a standard spherical shell with simply supported edges. A reliable finite element package program, ANSYS, is used for structural analysis. The results of the analysis showed that reasonably accurate results were obtained even when modeling the shells using fewer elements compared to other shell element types. The element is then used in a finite element model to analyze cross shaped spherical roof structures. The distribution of the various components of deflection and stress is obtained. Furthermore, the effect of introducing circular arched beams as stiffeners spanning the two diagonally opposite end corners is investigated. It is found that the stiffeners reduced the deflections and the stresses in the roof structure by considerable value