Evaluation of refined theories for multilayered shells via Axiomatic/Asymptotic method

Abstract

This paper is devoted to refined shell theories for the analysis of isotropic and laminated shells. Refined theories are built by assuming higher expansion order for the displacement field in the shell thickness directions. The implementation of these theories is made according to the Carrera unified formulation (CUF) which makes it possible to obtain shell governing equations in terms of fundamental nuclei whose form is independent of the chosen theory shell. Equivalent single layer and layer wise schemes are used. The axiomatic/ asymptotic technique is employed to evaluate the effectiveness of each displacement variable in the adopted displacement expansion. The error introduced by each term deactivation is evaluated with respect to a reference solution and according to a given error criterion; if the error computed does not exceed an a priori defined threshold the term is considered as not relevant and discarded. In this way it is possible to construct reduced models for each stress/displacement component. Attention has been restricted to closed form Navier type solutions and simply supported orthotropic shells are considered in the numerical investigation. Analysis of the displacement variables relevance is performed considering the influence of the kind of material and of the geometry, specifically isotropic and laminated materials and thick and thin shells. “Best”′ reduced models are proposed and related distributions are discussed.