A Theory of Torsional and Coupled Bending Torsional Waves in Thin-Walled Open Section Beams

1967 ◽  
Vol 34 (2) ◽  
pp. 337-343 ◽  
Author(s):  
H. R. Aggarwal ◽  
E. T. Cranch
Keyword(s):  
Transverse Shear ◽  
Torsion Theory ◽  
Transverse Shear Deformation ◽  
Governing Equations ◽  
High Frequencies ◽  
Wave Velocities ◽  
Open Section ◽  
Torsional Waves ◽  
Torsion Theories ◽  
Thin Walled

An appropriate torsion or coupled bending torsion theory is developed for the dynamic behavior of thin-walled open section beams. A new, more accurate set of governing equations is established which eliminate the short-wavelength defects of both the Saint-Venant and Timoshenko torsion theories. This theory, which includes warping and associated effects of longitudinal inertia and transverse shear deformation, while agreeing with previous theories for large wavelengths, leads to satisfactory finite wave velocities for short wavelengths and high frequencies. Dispersion and group velocity curves for wide-flanged and channel sections are displayed.

A Procedure for the Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation

2007 ◽  
Author(s):  
Aki Mikkola ◽  
Oleg Dmitrochenko ◽  
Marko Matikainen
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Transverse Shear Deformation ◽  
High Frequencies ◽  
Absolute Nodal Coordinate ◽  
Numerical Performance ◽  
The Absolute ◽  
Shear Deformable

In this study, a procedure to account for transverse shear deformation in the absolute nodal coordinate formulation is presented. In the absolute nodal coordinate formulation, shear deformation is usually defined by employing the slope vectors in the element transverse direction. This leads to the description of deformation modes that are, in practical problems, associated with high frequencies. These high frequencies, in turn, complicate the time integration procedure burdening numerical performance. In this study, the description of transverse shear deformation is accounted for in a two-dimensional beam element based on the absolute nodal coordinate formulation without the use of transverse slope vectors. In the introduced shear deformable beam element, slope vectors are replaced by vectors that describe the rotation of the beam cross-section. This procedure represents a simple enhancement that does not decrease the accuracy or numerical performance of elements based on the absolute nodal coordinate formulation. Numerical results are presented in order to demonstrate the accuracy of the introduced element in static and dynamic cases. The numerical results obtained using the introduced element agree with the results obtained using previously proposed shear deformable beam elements.

Some Remarks on Spherical Shells

1965 ◽  
Vol 32 (1) ◽  
pp. 121-128
Author(s):  
C. N. DeSilva ◽  
H. Cohen
Keyword(s):  
Asymptotic Solution ◽  
Spherical Shell ◽  
Variable Thickness ◽  
Transverse Shear ◽  
Correction Term ◽  
Transverse Shear Deformation ◽  
Governing Equations ◽  
Spherical Shells ◽  
Annular Disk ◽  
Thickness Function

The present paper treats the deformation of a spherical shell within the framework of a linear bending theory which includes the effect of transverse-shear deformation. A two-term asymptotic solution of the governing equations is obtained which embraces all terms of an order retained in the formulation of the theory. The solution is valid within a physically important domain of the shell and reduces to the previously known one-term asymptotic solution of the classical bending theory. The problem of variable thickness is also discussed. The behavior of the thickness function may be such as to require in the solution a correction term which may contribute significantly to the deformation. This solution is applied to a treatment of the deformation of a rotating, completely closed spherical shell stiffened by an annular disk located normal to the axis of the spin.

Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation

2008 ◽  
Vol 4 (1) ◽  
Author(s):  
Aki Mikkola ◽  
Oleg Dmitrochenko ◽  
Marko Matikainen
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Transverse Shear Deformation ◽  
High Frequencies ◽  
Absolute Nodal Coordinate ◽  
Numerical Performance ◽  
The Absolute ◽  
Shear Deformable

In this study, a procedure to account for transverse shear deformation in the absolute nodal coordinate formulation is presented. In the absolute nodal coordinate formulation, shear deformation is usually defined by employing the slope vectors in the element transverse direction. This leads to the description of deformation modes that are, in practical problems, associated with high frequencies. These high frequencies, in turn, complicate the time integration procedure burdening numerical performance. In this study, the description of transverse shear deformation is accounted for in a two-dimensional beam element based on the absolute nodal coordinate formulation without the use of transverse slope vectors. In the introduced shear deformable beam element, slope vectors are replaced by vectors that describe the orientation of the beam cross-section. This procedure represents a simple enhancement that does not decrease the accuracy or numerical performance of elements based on the absolute nodal coordinate formulation. Numerical results are presented in order to demonstrate the accuracy of the introduced element in static and dynamic cases. The numerical results obtained using the introduced element agree with the results obtained using previously proposed shear deformable beam elements.

Effect of the Transverse Shear Deformation on the Free Vibration of Rotating Blades Modeled as Thin-Walled Composite Beams

2015 ◽  
Vol 798 ◽  
pp. 119-124
Author(s):  
Serhat Yilmaz ◽  
Seher Eken ◽  
Metin Orhan Kaya
Keyword(s):  
Transverse Shear ◽  
Fiber Orientation ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Transverse Shear Deformation ◽  
Combined Effects ◽  
Shear Deformations ◽  
Thin Walled ◽  
Good Agreement

In this paper, vibration analysis of a blade modeled as an anisotropic composite thin-walled beam is carried out. The analytical formulation of the beam is derived for the flapwise bending, chordwise bending and transverse shear deformations. The equations of motion are solved by applying the extended Galerkin method (EGM) for anti-symmetric lay-up configuration that is also referred as Circumferentially Uniform Stiffness (CUS). Consequently, the natural frequencies are validated by making comparisons with the results in literature and it is observed that there is a good agreement between the results. Combined effects of transverse shear, fiber orientation, and rotational speed on the natural frequencies are further investigated.

scholarly journals Non-linear analysis of laminated plates

2002 ◽  
Vol 24 (4) ◽  
pp. 197-208
Author(s):  
Dao Huy Bich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Linear Analysis ◽  
Laminated Plates ◽  
Transverse Shear Deformation ◽  
Governing Equations ◽  
Non Linear

The governing equations of laminates plates taking into account the transverse shear deformation effects for large deformation are given. The formulation of Ritsz method and finite element method for non-linear analysis of this problem is presented

Pure Bending, Stretching, and Twisting of Anisotropic Cylindrical Shells

1972 ◽  
Vol 39 (1) ◽  
pp. 148-154 ◽  
Author(s):  
E. Reissner ◽  
W. T. Tsai
Keyword(s):  
Recent Work ◽  
Cross Section ◽  
Transverse Shear ◽  
Constitutive Equations ◽  
Middle Surface ◽  
Transverse Shear Deformation ◽  
Thin Shells ◽  
Pure Bending ◽  
Explicit Formulas ◽  
Thin Walled

This paper considers the problem of determining stresses and deformations in elastic thin-walled, prismatical beams, subject to axial end forces and end bending and twisting moments, within the range of applicability of linear theory. The analysis, which generalizes recent work on the problem of torsion [1], is based on the differential equations of equilibrium and compatibility of thin shells in the form given by Gunther [2], together with constitutive equations given by the first-named author [3]. The technically most significant aspect of the work has to do with the analysis of the effect of anisotropy of the material, which is associated with previously not determined modes of coupling between stretching, bending, and twisting. Use of the general formulas of the theory is illustrated for a class of shells consisting of an “ordinary” material (unable to support stress moments with axes normal to the middle surface of the shell, and unable to undergo transverse shear deformation). Here explicit formulas are obtained for certain types of open as well as of closed-cross-section beams.

Transient Solutions of a Longitudinally Impacted Conical Shell

1971 ◽  
Vol 38 (2) ◽  
pp. 545-547 ◽  
Author(s):  
R. W. Mortimer ◽  
A. Blum
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Conical Shell ◽  
Method Of Characteristics ◽  
Shell Theory ◽  
Experimental Results ◽  
Transverse Shear Deformation ◽  
Longitudinal Impact ◽  
Governing Equations ◽  
Transient Solutions

A thin conical shell theory, which includes the effects of transverse and rotary inertias and transverse shear deformation, is used to analyze the response of a conical shell to longitudinal impact. The governing equations of this theory are solved by the method of characteristics and the results are compared to published experimental results.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

2020 ◽  
Vol 22 (4) ◽  
pp. 939-958
Author(s):  
Indrajit Roy ◽  
D. P. Acharya ◽  
Sourav Acharya
Keyword(s):  
Surface Stress ◽  
Incident Angle ◽  
Plane Waves ◽  
Three Dimensional ◽  
Elastic Fibre ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Rotation Surface ◽  
Wave Velocities ◽  
Magnetic Field Rotation

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

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