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.

On Pure Bending and Stretching of Orthotropic Laminated Cylindrical Shells

1974 ◽  
Vol 41 (1) ◽  
pp. 168-172 ◽  
Author(s):  
E. Reissner ◽  
W. T. Tsai
Keyword(s):  
Cross Section ◽  
Analogous Result ◽  
Cylindrical Shells ◽  
Bending Stiffness ◽  
Thin Shells ◽  
Pure Bending ◽  
Laminated Shells ◽  
Thin Walled ◽  
Laminated Cylindrical Shells

The paper considers pure bending and stretching of axially uniform, orthotropic nonhomogeneous (laminated) thin-walled beams, as a problem of the theory of thin shells. In analyzing this problem, it is found that the stretching and bending stiffness factors for such shells are generally different for closed-cross-section shells and for longitudinally slit shells. While an analogous result for torsion of (homogeneous) shells is well known, the significance of the present results for the problems of bending and stretching of laminated shells lies in the fact that no such effect exists for homogeneous shells.

Part II. The Flattening of Monocoque Cylinders

1938 ◽  
Vol 42 (328) ◽  
pp. 302-319
Keyword(s):  
Variational Method ◽  
Potential Energy ◽  
Cross Section ◽  
Radial Displacement ◽  
Bending Moment ◽  
Experimental Investigations ◽  
Pure Bending ◽  
Centre Line ◽  
Thin Walled ◽  
The Cross

It is known from both theoretical and experimental investigations that St. Venant's assumption on the constancy of the shape of the cross section of girders in pure bending does not hold true in case of thin-walled sections. The greater flexibility than calculated according to ordinary bending theory of initially curved tubes, as experimentally found by Professor Bantlin, was perfectly explained by Professor von Kármán in 1911 on the assumption of a flattening of the section.In 1927 Brazier with the aid of the variational method determined exactly that the shape of an originally circular thin-walled bent cylinder corresponding to the least potential energy is quasi elliptical and that the cross section of the cylinder, therefore, must flatten, even if the centre line of the cylinder was originally straight. In consequence of the flattening St. Venant's linear law for the curvature loses its validity and the curvature increases more rapidly than the bending moment. For a certain value of the curvature the bending moment is a maximum, and after this value was reached the curvature increases even if the applied moment remains unchanged or decreases, fulfilling thereby the criterion of instability. This instability occurs when the rate of flattening, i.e., the maximum radial displacement of any point of the circumference of the tube divided by the original radius of the tube, will equal 2/9.

The Distortion and Buckling of Long Viscoelastic Cylinders in Pure Bending

1976 ◽  
Vol 18 (4) ◽  
pp. 167-174
Author(s):  
S. G. Croll
Keyword(s):  
Cross Section ◽  
Pure Bending ◽  
Bending Radius ◽  
Oval Cross Section ◽  
Thin Walled

The behaviour in pure bending of moderately thick polypropylene cylinders is examined. The distortion into an oval cross-section is measured as the bulging and flattening displacements. The bending radius at buckling is also determined. When compared with an existing theory for thin-walled Hookean cylinders both the distortion and buckling are found to be functions of a single reduced parameter involving the tube dimensions and the bending curvature, as predicted. However, the amount of distortion and the buckling radius are both less than the theoretical values. These discrepancies are explained by the mechanical nonlinearity of polypropylene.

On Finite Symmetrical Deflections of Thin Shells of Revolution

1969 ◽  
Vol 36 (2) ◽  
pp. 267-270 ◽  
Author(s):  
Eric Reissner
Keyword(s):  
Differential Equations ◽  
Nonlinear Theory ◽  
Transverse Shear ◽  
Shell Theory ◽  
Middle Surface ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Shear Deformations ◽  
Linear Shell Theory ◽  
Classical Subject

Recent simplifications of linear shell theory through consideration of transverse shear deformations and stress moments with axes normal to the shell middle surface suggest analogous approaches to the corresponding problem of nonlinear theory. As a first step in this direction consideration is given here to the classical subject of finite symmetrical deformations of shells of revolution. The principal new results of the present analysis concern the form of strain-displacement and compatibility differential equations.

scholarly journals Vibration and Stability of Variable Cross Section Thin-Walled Composite Shafts with Transverse Shear

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Ma Jing-min ◽  
Ren Yong-sheng
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Transverse Shear ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Rotating Speed ◽  
Composite Shaft ◽  
Variational Asymptotic ◽  
Finite Element Package ◽  
Thin Walled

A dynamic model of composite shaft with variable cross section is presented. Free vibration equations of the variable cross section thin-walled composite shaft considering the effect of shear deformation are established based on a refined variational asymptotic method and Hamilton’s principle. The numerical results calculated by Galerkin method are analyzed to indicate the effects of ply angle, taper ratio, and transverse shear deformation on the first natural frequency and critical rotating speed. The results are compared with those obtained by using finite element package ANSYS and available in the literature using other models.

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.

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.

Shear Deformation in Beams on Elastic Foundations

1962 ◽  
Vol 29 (2) ◽  
pp. 313-317 ◽  
Author(s):  
F. Essenburg
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Cross Section ◽  
Transverse Shear ◽  
Elastic Beam ◽  
Practical Significance ◽  
Transverse Shear Deformation ◽  
Concentrated Load ◽  
Infinite Beam ◽  
Concentrated Couple

The importance of the effect of transverse shear deformation in the flexure of an elastic beam of symmetric cross section, constrained by a Winkler-type elastic foundation, is found to depend upon both the elastic properties of the beam and the foundation and the geometry of the beam cross section. Under certain conditions the form of the solution is substantially altered and the periodic character predicted by the classical treatment is not present. The practical significance of these modifications is illustrated by means of the specific examples of an infinite beam under concentrated load and an infinite beam under concentrated couple.

Instability of Monocoque Structures in Pure Bending

1938 ◽  
Vol 42 (328) ◽  
pp. 291-346 ◽  
Author(s):  
N. J. Hoff
Keyword(s):  
Total Cross Section ◽  
Cross Section ◽  
Smooth Surfaces ◽  
Pure Bending ◽  
Thin Walled Structures ◽  
Ultimate Failure ◽  
Thin Walled

The growing demand for aerodynamically advantageous forms, for smooth surfaces, and last but not least for a better ratio of useful cross section to total cross section of fuselages lead to an increasing application of monocoque structures in aircraft construction. Unlike ordinary beams the behaviour of such thin walled structures under loads and their ultimate failure is influenced a great deal by instability phenomena. In the present paper these problems are dealt with in some detail for the case of pure bending.

Sign in / Sign up

Export Citation Format

Share Document