Beam Element with a 3D Response for Shear Effects
Publication: Journal of Engineering Mechanics
Volume 144, Issue 1
Abstract
This paper presents a beam element for which the cross section remains neither plane nor orthogonal to the beam axis. The cross section with arbitrary geometry is modeled by two-dimensional (2D) finite elements. The element kinematics is defined by the displacement shapes of the cross sections and the axial functions of their corresponding averaged movements. The deformed displacement shapes are obtained by minimizing the potential energy of a beam slice submitted to the compatibility constraints of the kinematics framework. The recursive procedure that yields the higher-order deformed displacement shapes is initiated with the rigid-body components of the displacement field. The mechanical model is validated through examples of linear-elastic materials with isotropic and nonisotropic cross sections. Higher-order beam elements yield three-dimensional (3D) stresses and strains that correspond to elasticity solutions and 3D solid element models, for concentrated and distributed loads. The beam elements do not require shear coefficients. The first-order formulation is extended to nonlinear materials.
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Acknowledgments
The writer thanks Prof. Benjamin Ernani Diaz, Prof. Maria Paola Santisi d’Avila, and Prof. Jose Kimio Ando for their valuable comments.
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©2017 American Society of Civil Engineers.
History
Received: Sep 6, 2016
Accepted: Jun 7, 2017
Published online: Oct 31, 2017
Published in print: Jan 1, 2018
Discussion open until: Mar 31, 2018
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