Static and free vibration analysis of sandwich shell panels using quadrilateral flat shell finite element

Abstract

A quadrilateral flat-shell element with nine DOF (Degrees of Freedom) per node is developed for the static (deflections and stresses) and free vibration analysis (natural frequencies and accompanying mode shapes) of sandwich cylindrical and globular shell panels. The element is based on zigzag theory and is augmented using the discrete Kirchhoff quadrilateral bending plate element having seven DOF per node. It is vital to convert the rotations and translations degrees of freedom from local to global direction for the plate bending element to transform into a flat shell element. DKZigTS is developed by adding two fictitious degrees of freedom and has nine local and global DOF per node. The transformation matrix of size 36 × 36 is used for DKZigTS. It does not face the problem of the ill-conditioned stiffness matrix. The developed element is judged for its performance for simply supported and clamped shell panels. The DKZigTS element’s result are compared with results gotten using the 3 D finite element (FE) results of ANSYS (Mechanical APDL). To establish the confidence the comparison is also done with those 2 D analytical, 2 D numerical and 3 D elasticity results available in the literature. The numerical evaluation with DKZigTS element exhibits a very satisfactory performance for the static and free vibration response of moderately thick and thick sandwich spherical and cylindrical shell panels.