A 3D time-domain solution for the bending of viscoelastic shells

Abstract

This article presents a time domain analysis of viscoelastic doubly curved shallow shells employing 3D solution based on equilibrium equations. The constitutive equation is transformed into Laplace domain in order to avoid the time domain integration. The partial differential equations are solved for the mid-surface variables by applying the Navier Technique. The thickness equations are solved using the differential quadrature method (DQM). Lagrange interpolation polynomial are employed as basis functions. Each layer of the panel is discretized by the Chebyshev–Gauss–Lobatto grid distribution. The time-domain displacements are obtained by using the inverse Laplace transformation in an approximate numerical manner. The 3D solution is compared with references in the literature. Given the inclusion of comprehensive 3D time domain solutions, these results can be considered as a benchmark for reference.