A corotational formulation based on Hamilton's principle for geometrically nonlinear thin and thick planar beams and frames
type: Item
instance of: scholarly article
title: A corotational formulation based on Hamilton's principle for geometrically nonlinear thin and thick planar beams and frames
zbMATH Open document ID: 1426.74180
DOI: 10.1155/2018/2670462
author: Hesham A. Elkaranshawy
author: Ahmed A. H. Elerian
author: Walied I. Hussien
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: A corotational finite element formulation for two-dimensional beam elements with geometrically nonlinear behavior is presented. The formulation separates the rigid body motion from the pure deformation which is always small relative to the corotational element frame. The stiffness matrices and the mass matrices are evaluated using both Euler-Bernoulli and Timoshenko beam models to reveal the shear effect in thin and thick beams and frames. The nonlinear equilibrium equations are developed using Hamilton's principle and are defined in the global coordinate system. A MATLAB code is developed for the numerical solution. In static analysis, the code employed an iterative method based on the full Newton-Raphson method without incremental loading, while, in dynamic analysis, the Newmark direct integration implicit method is also utilized. Several examples of flexible beams and frames with large displacements are presented. Not only is the method simple and time-saving, but it is also highly effective and highly accurate.
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 70H25
zbMATH DE Number: 7018682
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/2670462
OpenAlex ID: W2885905407
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description: scientific article; zbMATH DE number 7018682