An assessment of refined hierarchical kinematic models for the bending and free vibration analyses of laminated and functionally graded sandwich cylindrical panels

Abstract

An effort is made in this study to systematically develop and evaluate two-dimensional (2D) displacement-based higher order theories for stress and vibration analyses of moderately thick laminated and functionally graded (FG) sandwich cylindrical shell panels. Comparison of various displacement models is presented in order to assess the contribution of thickness stretching effects in laminated and sandwich shells. The equivalent single layer (ESL) approach is followed and a refined thickness criterion is adopted to enhance the accuracy of present formulation for moderately thick to thick cylindrical shell panels. Contribution of membrane and bending deformations is examined using the hierarchical kinematic models. Governing set of equations is obtained using energy minimization based on a variational approach and solution is obtained subsequently with Navier’s method for cylindrical shells with all edges on diaphragm (simple) supports. Effective FG material properties are obtained using Voigt’s rule of mixture with power law gradation. Solutions are compared with the available three dimensional (3D) solutions and a comparative assessment is done for different higher order theories. The present study accentuates the necessity of including transverse normal strain in the theory for FG sandwich panels.