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.

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.

Structural bionic design for thin-walled cylindrical shell against buckling under axial compression

2011 ◽  
Vol 225 (11) ◽  
pp. 2619-2627 ◽  
Author(s):  
D Xing ◽  
W Chen ◽  
J Ma ◽  
L Zhao
Keyword(s):  
Cylindrical Shell ◽  
Axial Compression ◽  
Cross Section ◽  
Cylindrical Shells ◽  
High Load ◽  
Vascular Bundles ◽  
Bionic Design ◽  
Load Bearing ◽  
Thin Walled ◽  
The Cross

In nature, bamboo develops an excellent structure to bear nature forces, and it is very helpful for designing thin-walled cylindrical shells with high load-bearing efficiency. In this article, the cross-section of bamboo is investigated, and the feature of the gradual distribution of vascular bundles in bamboo cross-section is outlined. Based on that, a structural bionic design for thin-walled cylindrical shells is presented, of which the manufacturability is also taken into consideration. The comparison between the bionic thin-walled cylindrical shell and a simple hollow one with the same weight showed that the load-bearing efficiency was improved by 44.7 per cent.

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.

scholarly journals Effect of local stiffeners and warping constraints on the buckling of symmetric open thin-walled beams with high warping stiffness

Meccanica ◽  
2021 ◽  
Author(s):  
G. Piana ◽  
E. Lofrano ◽  
A. Carpinteri ◽  
G. Ruta
Keyword(s):  
Cross Section ◽  
Bending Stiffness ◽  
Dimensional Model ◽  
One Dimensional ◽  
Practical Applications ◽  
Thin Walled ◽  
Compressive Buckling ◽  
The Way

AbstractLocal stiffeners affect the behaviour of thin-walled beams (TWBs). An in-house code based on a one-dimensional model proved effective in several instances of compressive buckling of TWBs but gave counterintuitive results for locally stiffened TWBs. To clarify the matter, we investigated TWBs with multi-symmetric double I cross-section, widely used in practical applications where high bending stiffness is required. Several samples were manufactured and stiffened on purpose, closing them over a small portion of the axis at different places. The samples were tested with end constraints accounting for various warping conditions. The experimental and numerical outputs from a commercial FEM code gave a key to overcome the unexpected results by the in-house code, paving the way for further studies.

THERMAL STRESS IN LONG CYLINDRICAL SHELLS DUE TO TEMPERATURE VARIATION ROUND THE CIRCUMFERENCE, AND THROUGH THE WALL

1937 ◽  
Vol 15a (4) ◽  
pp. 49-58 ◽  
Author(s):  
J. N. Goodier
Keyword(s):  
Thermal Stress ◽  
Circular Cylinder ◽  
Temperature Variation ◽  
Cross Section ◽  
Maximum Stress ◽  
Cylindrical Shells ◽  
Axial Direction ◽  
Temperature Distributions ◽  
Thin Walled ◽  
The Cross

The thermal stress in thin-walled cylinders of any cross section has been investigated for internal and external temperatures each varying in any manner round the circumference but not in the axial direction. The thickness also may vary round the circumference.A method is given for calculating the stress from given temperature distributions, whatever the shape of the cross section. The stress is evaluated for uniform, but different, inside and outside temperatures.The circular cylinder is treated in detail and the stress found for the general case of circumferential variation. It is shown that the maximum stress will depend only on the temperature distributions and the material, and not on the thickness or diameter of the cylinder.

EVALUATION OF THE PERTURBATION SENSITIVITY OF COMPOSITE LAMINATED SHELLS

2010 ◽  
Vol 10 (04) ◽  
pp. 779-790 ◽  
Author(s):  
DIETER DINKLER ◽  
JENS PONTOW
Keyword(s):  
Cylindrical Shells ◽  
Load Level ◽  
Imperfection Sensitivity ◽  
Limit Loads ◽  
Laminated Shells ◽  
Specific Modification ◽  
Energy Concept ◽  
Perturbation Energy ◽  
The Stability ◽  
Laminated Cylindrical Shells

Imperfection sensitivity and its influence on the limit loads of shells are widely discussed phenomena. Both phenomena may be classified with respect to the type of imperfection, which may be generalized to a perturbation. As perturbations influence the stability of shells, the identification of unfavorable perturbations is essential for the design of shells. The perturbation energy concept enables one to identify unfavorable perturbations of different kinds and to evaluate the sensitivity of fundamental states against buckling by the perturbation energy. This paper discusses the perturbation sensitivity of unstiffened composite laminated cylindrical shells consisting of unidirectional layers. Moreover, an approach for a load-level-specific modification of the perturbation sensitivity is introduced.

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.

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