Geometrically nonlinear analysis of beam structures via hierarchical one-dimensional finite elements
type: Item
instance of: scholarly article
title: Geometrically nonlinear analysis of beam structures via hierarchical one-dimensional finite elements
zbMATH Open document ID: 1427.74166
DOI: 10.1155/2018/4821385
author: Y. Hui
author: A. Pagani
author: Giuseppe de Pietro
author: Gaetano Giunta
author: Salim Belouettar
author: Heng Hu
author: Erasmo Carrera
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 7019033
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/4821385
OpenAlex ID: W2902427535
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Wikidata QID: Q128898115
description: scientific article; zbMATH DE number 7019033