Dynamic analysis of linear viscoelastic cross-ply laminated shallow spherical shells

Abstract

This paper aims to propose an alternative approach for response of viscoelastic cross-ply laminated shallow spherical shells. In the proposed approach, the governing differential equations of cross-ply laminated shallow spherical shell are derived using the dynamic version of the principle of virtual displacements. Following this Laplace transform is employed in the transient analysis of laminated shell problem. In the transformed domain damping can be incorporated very easily. The transformed time-independent problem in spatial coordinate is solved numerically by Gauss elimination. Inverse transformation of the results into the time domain is performed by the modified Durbin’s method. Verification of the presented method is carried out by comparing the results with those obtained by Newmark method and ANSYS finite element software. Materials of the shell laminates are assumed to be linear elastic or viscoelastic. The novelty of the present study lies in the fact that a combination of Laplace transform and Navier method is employed in the analysis of damped response of laminated shells. The numerical sample results have proved that the presented method constitutes a highly accurate and efficient solution and it can be easily applied to the laminated composite shell problems.