A quadrilateral flat-shell element for the static and dynamic analysis of composite and sandwich cylindrical, spherical and conical shell panels

Abstract

A quadrilateral flat-shell element is developed for analysing the deflections, stresses and natural frequencies along with their allied mode shapes of cylindrical, spherical, and conical shell panels made up of layered composite and sandwich material. The developed element (DKZigTS1) is based on zigzag theory and has seven local as well as global DOF per node. The concept of obtaining transformation matrix is used for transforming actions and reactions from local to global direction to convert the plate bending into a flat-shell element. The two separate coordinate systems are used to transform rotational and translational degrees-of-freedom (DOF), from local to global direction. The local translational DOF are transformed to global Cartesian coordinates (x, y, z) and the local rotational DOF are transformed to the surface coordinate system (ξ1, ξ2, ξ3), in which ξ3 is perpendicular to the surface. The DKZigTS1 element gives fairly accurate results that align with the 2D analytical and the 3D elasticity solutions, reported in the literature for moderately thick and thick shell panel. The present results are also in good agreement with the 3D finite element solutions for shallow and deep shell panels having various material properties, boundary restrained environments, and geometrical shapes considered in this study.

Keywords

• transformation
• zigzag theory
• free vibration
• static analysis
• composite
• sandwich