A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGE ROTATION AND DEFORMATION PROBLEMS

By Mohamed A. Omar, Ahmed A Shabana. 2001

301 citations recorded by the source corpus.

Subfields: Computational Mechanics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1a1f99f818a71529b575a550528fdd9b84b2ce44

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In Computational Mechanics

In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation (2011, methodology): “In the original shear deformable ANCF element by Omar and Shabana [10], the strain energy is defined with a St. Venant–Kirchhoff material law, which uses a linear relation between the Green strain tensor and the second Piola–Kirchhoff stress tensor.”
A geometrically exact beam element based on the absolute nodal coordinate formulation (2008, methodology): “In the original shear deformable ANCF beam [ 14 ], the concept of virtual work of elastic forces follows from the continuum mechanics based formulation for the arbitrary deformation of a mechanical solid, using the fully nonlinear Green strain tensor and the second Piola–Kirchhoff stress tensor.”
Simulation of planar flexible multibody systems with clearance and lubricated revolute joints (2010, unknown): “To consider the shear deformation effect, Omar and Shabana [ 35 ] firstly proposed a planar dimensional ANCF-based shear deformable beam element.”
Use of B-Spline in the Finite Element Analysis: Comparison With ANCF Geometry (2012, unknown): “The shape function matrix for the element considered in this section is defined as 1 2 3 4 5 6 j s s s s s sS I I I I I I (4) where the shape functions , 1,2, ,6is i are defined as (Omar and Shabana, 2001) 2 3 2 3 1 2 3 2 3 2 3 4 5 6 1 3 2 , 2 , 1 , 3 2 , , s s l s l s s l s l”
State of the Art of ANCF Elements Regarding Geometric Description, Interpolation Strategies, Definition of Elastic Forces, Validation and the Locking Phenomenon in Comparison with Proposed Beam Finite Elements (2014, methodology): “In the classical ANCF 2D and 3D beam elements by [84,139] the interpolation of shear and bending deformation is not of the same order.”
Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods (2009, methodology): “In order to consider the shear deformation effect, the two-dimensional ANCF-based shear deformable beam element [28] is adopted, as shown in Fig.”