Deformation of laminated and sandwich cylindrical shell with covered or embedded piezoelectric layers under compression and electrical loading

Abstract

A three-dimensional (3D) theory of elasticity is presented for the solution of the generalized displacements and stresses in the composite laminated and sandwich cylindrical shell structures with covered or embedded piezoelectric layers based on the scaled boundary finite element method (SBFEM). The SBFEM is a weak-form differential technique, which can lead to accurate results performing discretization only on the middle plane of shell structures so that the considered model can be treated as a two-dimensional (2D) discretizated problem. A new type 2D high order spectral element shape function is introduced both for approximations of geometry model and basis variables in the scaled boundary coordinate system. Employing the weighted residual principle in conjunction with Green’s theorem to the normalized static equilibrium equations of each layer leads to the SBFEM governing equation with respect to the radial generalized displacement fields. Then a system of a first-order ordinary differential equation is obtained by introducing a dual variable and analytically solved by using the precise integration technique (PIT). As a result, the major advantage of the proposed formulations for solving the bending problem of the composite laminated and sandwich cylindrical piezoelectric shell is no need to discretize the 3D model with a great deal of degrees of freedom while ensures the computational accuracy. Two test examples are carried out to demonstrate the adaptability and reliability of the present method and illustrate very good agreements and rapid convergence with the solutions based on the finite element approach only using a small number of elements. Numerical examples about the sandwich cylindrical piezoelectric shell are presented to investigate the parametric effects of the thickness ratio as well as the stacking sequence on the variation of generalized displacements and stresses. The results show that both the thickness ratio and stacking sequence have significant influence on the bending behaviors of the sandwich cylindrical piezoelectric shells.