Finite element models with node-dependent kinematics based on Legendre polynomials for the global–local analysis of compact and thin walled beams

Abstract

In the present work, enhanced one-dimensional finite elements with node-dependent kinematics are proposed for the static analysis. Finite element governing equations are derived by applying the Carrera Unified Formulation. This framework subdivides the three-dimensional displacement field into a cross-section domain and an axis domain. The dimension along the beam is discretized by using Lagrange-based shape functions. At each node of the element, an independent structural theory can be imposed, thus obtaining a node-dependent kinematic model. This method permits to focus on the finite element node. In this way, several combinations of kinematics can be used together. In particular, Taylor-based and Legendre-based expansions have been adopted in this paper to create global–local models without using special coupling methods. The results have been compared with well-established benchmarks from the literature. Compact section and thin-walled beams have been taken into account. Results have been given in terms of displacements and stresses. It is shown that the present model provides high accuracy with a reduced number of degrees of freedom.