Analysis of shear locking in Timoshenko beam elements using the function space approach

2001 ◽  
Vol 17 (6) ◽  
pp. 385-393 ◽  
Author(s):  
Somenath Mukherjee ◽  
Gangan Prathap
Keyword(s):  
Function Space ◽  
Timoshenko Beam ◽  
Shear Locking ◽  
Beam Elements ◽  
Space Approach

A Function Space Approach to Spectral Related Problems

2019 ◽  
Vol 10 (6) ◽  
pp. 1220-1222
Author(s):  
T. Venkatesh ◽  
Karuna Samaje
Keyword(s):  
Function Space ◽  
Space Approach

On a hierarchy of conforming timoshenko beam elements

1981 ◽  
Vol 14 (3-4) ◽  
pp. 335-344 ◽  
Author(s):  
A. Tessler ◽  
S.B. Dong
Keyword(s):  
Timoshenko Beam ◽  
Beam Elements

The Effects of Airfoil Camber on Flutter Suppression Regarding Timoshenko Beam Theory

2011 ◽  
Vol 110-116 ◽  
pp. 1531-1538
Author(s):  
Abbas Rahi ◽  
Mortaza Shahravi ◽  
Darvish Ahmadi
Keyword(s):  
Timoshenko Beam ◽  
Free Stream ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Real Component ◽  
State Space Approach ◽  
Suppression Effect ◽  
Flutter Suppression ◽  
Time Marching ◽  
Space Approach

The application of Timoshenko beam theory is presented, thereby the effects of airfoil camber can be investigated analytically and numerically by considering rotary inertia and shear deformation in addition to moment of inertia, aerodynamic loading and bending/torsion coupling. Regarding a tuned blisk, the analysis is simplified to a single blade with plunge and pitch DOF. Pressure distribution of the airfoil surfaces and the resulting aerodynamic forces are calculated with ‘ANSYS/FLOTRAN’ during one-cycle time marching at several reduced frequencies. A parametric relation is then achieved by Roger’s approximation including quasi-inertia, quasi-damping, quasi-elastic and lag terms. The final aeroelastic equations are established by bending-torsion and aerodynamics-structure coupling which is solved by state space approach. This procedure is repeated at several free stream velocities until the real component of an eigenvalue equals zero. The latest velocity is the flutter speed. Following this procedure, flutter characteristics of two similar aeroleastic cases are determined considering only one difference in blade configuration; one with cambered and the other with uncambered airfoil. Comparison of these two cases shows the considerable suppression effect of airfoil camber on flutter.

Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
A. L. Schwab ◽  
J. P. Meijaard
Keyword(s):  
Dynamic Analysis ◽  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Flexible Beam ◽  
Element Formulation ◽  
Shear Locking ◽  
Elastic Line ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Bending Mode

Three formulations for a flexible spatial beam element for dynamic analysis are compared: a Timoshenko beam with large displacements and rotations, a fully parametrized element according to the absolute nodal coordinate formulation (ANCF), and an ANCF element based on an elastic line approach. In the last formulation, the shear locking of the antisymmetric bending mode is avoided by the application of either the two-field Hellinger–Reissner or the three-field Hu–Washizu variational principle. The comparison is made by means of linear static deflection and eigenfrequency analyses on stylized problems. It is shown that the ANCF fully parametrized element yields too large torsional and flexural rigidities, and shear locking effectively suppresses the antisymmetric bending mode. The presented ANCF formulation with the elastic line approach resolves most of these problems.

scholarly journals Study on the Size Effect of Auxetic Cellular Materials

2017 ◽  
Vol 22 (3) ◽  
pp. 749-757
Author(s):  
M. Janus-Michalska
Keyword(s):  
Computer Simulations ◽  
Timoshenko Beam ◽  
Scale Effects ◽  
Cellular Materials ◽  
Boundary Effects ◽  
Simple Shearing ◽  
Material Microstructure ◽  
Beam Elements ◽  
Material Sample ◽  
Auxetic Structure

AbstractThe objective of this paper is to investigate the effects of scale of an auxetic cellular material sample on the evaluation of elastic properties. Size and boundary effects are studied in detail. This is achieved by conducting computer simulations of the auxetic structure under the typical loading exerted by the compression and simple shearing test performed by means of ABAQUS FEA. The material microstructure is discretized by the plane network of Timoshenko beam elements. The results of the studies give insight to the scale effects. Structures with designed properties can be potentially used for engineering applications.

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