Comparisons between 1D (Beam) and 2D (Plate/Shell) Finite Elements to Analyze ThinWalled Structures

This paper compares 1D and 2D assumptions for the analysis of isotropic thin-walled structures. Refined 1D (beam) and 2D (shell) models were exploited. These models are based on a variable kinematic approach which means that the displacement field assumed can be refined to any extent since the orders of the polynomial expansions are taken as free parameters. The Finite Element (FE) approach was used to provide numerical results. FEM is, in fact, the most popular technique used in the analysis of structures in engineering. The Carrera Unified Formulation (CUF) was adopted in order to write finite element matrices of 1D and 2D models in a concise form based on the so-called fundamental nuclei. In this work, 1D models are used to assessing well-established benchmarks which are often used to solve shell problems, such as the pinched shell problem. 1D and 2D models were compared in terms of accuracy and computational costs. Furthermore, locking phenomena are discussed. It is concluded that some of the well-known shell problems, including those that are usually used as ’benchmarks’ in FE shell developments, can be dealt with 1D refined models. The use of 1D refined models results in minor numerical locking, much lower computational efforts and comparable accuracy with shell models.