Analysis of composite beams, plates, and shells using Jacobi polynomials and NDK models

Abstract

Abstract. In this work, hierarchical Jacobi-based expansions are explored for the static analysis of multilayered beams, plates, and shells as structural theories as well as shape functions. Jacobi polynomials, denoted as P_p^((γ,θ) ), belong to the family of classical orthogonal polynomials and depend on two scalars parameters 𝛾 and 𝜃, with p being the polynomial order. Regarding the structural theories, layer wise and equivalent single-layer approaches can be used. It is demonstrated that the parameters 𝛾 and 𝜃 of the Jacobi polynomials are not influential for the calculations. These polynomials are employed in the framework of the Carrera Unified Formulation (CUF), which allows to generate of finite element stiffness matrices straightforwardly. Furthermore, Node-dependent Kinematics is used in the CUF framework to build global-local models to save computational costs and obtain reliable results simultaneously.