Linear response of thin axysimmetric cross-ply structure under a static load: Numerical and analythical comparisons

Abstract

Abstract. Thin-walled mechanical components, such as beams, plates and shells, are widely used as structural components in several engineering fields, in particular mechanical, aeronautical and aerospace sectors. The purpose of this work is to analyse the cross-ply bending behaviour of cylindrical and spherical shell structures using the finite element method. Hence, numerical models, realized using commercial software, were realized using the shell and solid approaches and were compared with numerical and analytical methods to appreciate their advantages. In this research, a Navier solution in close form for high-order theories, developed using the Carrera Unified Formulation (CUF) approach, has been reported, where the high-order elastic shell model has been developed using the variational principle of virtual work for three-dimensional linear theory equations and the analytical results were obtained using the Mathematica software. The results furnished by the numerical method such as the elasticity solutions given in the literature using Navier’s method are used as a benchmark for comparing the finite element method results in terms of maximum displacement and stress distribution along the principal structure direction. However, the numerical shell model cannot provide sufficient data to describe the tensional and deformational state at all points and especially along the laminate thickness. Wishing to obtain a complete description of the plate's mechanical behaviour, it is necessary to use a three-dimensional approach with the associated increase in calculation time. In contrast, the numerical solution based on the CUF approach shows a very efficient description of the composite structure behaviour and its use should be preferred to the classical lamination approach if an accurate description of the structure is necessary.