Refined One-Dimensional Formulations for Laminated Structure Analysis

Abstract

This paper proposes one-dimensional formulations based on hierarchical expansions of the unknown displacement variables for the analysis of multilayered structures made of anisotropic composite layers. The hierarchical technique shows variable kinematic properties and it is based on the Carrera unified formulation. Two different classes of refined theories are proposed: the first expands the unknown variables in terms of power polynomials of the cross-sectional coordinates (it consists of a Taylor-like expansion); the second class of onedimensional theories uses Lagrange polynomials (Lagrange expansion) and subdomain discretizations of the cross section, and it leads to only pure displacements as the unknown variables. Taylor-like expansion is used to develop equivalent single-layer formulations, and Lagrange expansion is used to construct both equivalent single-layer and layerwise descriptions. The finite element method is employed to develop numerical applications. Using the Carrera unified formulation, finite element matrices are obtained in terms of a few fundamental nuclei that are formally independent of all the considered one-dimensional formulations. A number of numerical examples are given concerning on beams, plates, and more complex structures. Comparisons with results from plate and solid models are provided. The following has been concluded: 1) The proposed formulation represents a reliable, compact, and accurate method to develop refined one-dimensional models. 2) The present one-dimensional models are very effective at detecting both global and local responses of composite structures. 3) Shell-and solidlike results are obtained with a significant reduction in the computational costs.