3D hygro-elastic shell model for the analysis of composite and sandwich structures

Abstract

The present work proposes the study of the hygrometric loading effects in the static analysis of multilayered composite and sandwich plates and shells. The employed model is based on a general exact 3D shell theory valid for one-layered and multilayered sandwich and composite plates, cylinders and cylindrical/spherical shell panels. The employed 3D equilibrium equations are developed in an orthogonal mixed curvilinear coordinate system for spherical shells in order to obtain the other simpler geometries as particular cases. A layer-wise approach is employed and equilibrium equations are solved in the thickness direction via the exponential matrix method. The partial derivatives in the in-plane directions are exactly calculated by assuming simply-supported edges and harmonic forms for the variables. The presented 3D shell model is extended to hygro-elastic cases by considering moisture content amplitudes imposed at the external surfaces of the structures in steady-state conditions. The moisture content profile through the thickness of the structures can be included in the 3D shell model using three different methodologies: it can be calculated by solving the steady-state 3D or 1D version of the Fick diffusion law, or it can be “a priori” assumed as linear through the thickness. Therefore, the developed system includes three non-homogeneous second order differential equilibrium equations that are solved after the introduction of opportune mathematical layers to consider the curvature effects through the thickness. The reduction to a first order differential equation system is obtained by redoubling the number of variables. The exponential matrix method is employed to accurately define both general and particular solutions. The implemented 3D hygro-elastic shell model is firstly validated and then it is employed with confidence for new benchmarks where the effects of thickness ratio, geometry, lamination scheme, material, thickness layer and imposed moisture content values at the external surfaces are investigated for composite and sandwich plates and shells. Showed results demonstrate the importance of an accurate developing of the elastic part of the 3D shell model combined with an appropriate evaluation of the moisture content profile through the thickness. Assumed linear moisture content profiles are correct only for thin one-layered isotropic structures, the use of the 1D Fick diffusion law allows only the correct definition of the material layer effect, the use of its 3D version allows the correct definition of both material and thickness layer effects.