On the Uniform Deformation in Two Dimensions of a Cylindrical Shell of Finite Thickness, with Application to the General Theory of Deformation of Thin Shells

2011 ◽  
pp. 280-287
Author(s):  
John William Strutt
1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.


1950 ◽  
Vol 17 (4) ◽  
pp. 396-398
Author(s):  
W. R. Osgood ◽  
J. A. Joseph

Abstract In the general theory of shells expressions are obtained for the changes of curvature and the twist, and revisions are introduced in the equations of equilibrium.


1974 ◽  
Vol 96 (1) ◽  
pp. 44-46
Author(s):  
C. K. McDonald ◽  
R. E. McDonald

The effect of large displacements on the flexural edge stresses in thin cylindrical shells with flat head closures subjected to axisymmetric loads is considered. Results are presented which show that neglecting this nonlinear effect leads to nonconservative results. However, it is shown that these effects can usually be safely neglected except for very thin shells or for shells with a low modulus of elasticity. Curves are given which illustrate this effect for selected shell parameters.


Author(s):  
Roustem N. Miftahof ◽  
Hong Gil Nam
Keyword(s):  

1965 ◽  
Vol 32 (4) ◽  
pp. 793-802 ◽  
Author(s):  
P. Mann-Nachbar ◽  
W. Nachbar

The chessboard buckle pattern in the solution of the linearized Donnell equations for buckling of a thin, cylindrical shell under axial compression is so sensitive to uncertainties in shell dimensions that the number of circumferential waves and the aspect ratio of the buckles is indeterminate. This problem is treated statistically. Shell dimensions are treated as random variables with probability distributions dependent on nominal values and manufacturing tolerances. Distributions for aspect ratio and number of circumferential waves are found by a Monte-Carlo technique. It is found that the linear theory does contain a mechanism for distinguishing among buckle modes. There is always a preferred buckle mode. For thin shells and attainable manufacturing tolerances, the aspect ratio of the preferred mode is closer to one than that of any other possible mode, and the corresponding number of buckles is large.


Author(s):  
William S. Oakley

<p class="abstract">The long standing major issue in physics has been the inability to unify the two main theories of quantum electro-dynamics (QED) and the general theory of relativity (GTR), both of which are well proven and cannot accommodate significant change. The problem is resolved by combining the precepts of GTR and QED in a conceptual model describing the electron as electromagnetic (EM) energy localized in relativistic quantum loops near an event horizon. EM energy is localized by propagating in highly curved space-time of closed geometry, the local metric index increases, and the energy is thus relativistic to the observer at velocity v &lt; c, with the curved space-time thereby evidencing gravity. The presence of gravity leads to the observer notion of mass. Particle energy is in dynamic equilibrium with relativistic loop circumferential metric strain at the strong force scale opposed by radial metric strain. The resulting particle is a quantum black hole with the circumferential strong force in the curved metric orthogonal in two dimensions to all particle radials. The presence of energy E is thus evident in observer space reduced by c<sup>2</sup> to E/c<sup>2</sup> = mass. The circumferential strain diminishes as it extends into the surrounding metric as the particle’s gravitational field. The radial strain projects outward into observer space and is therein evident as electric field. Gravity, unit charge, and their associated fields are emergent properties and Strong and electric forces are equal within the particle, quantizing gravity and satisfying the Planck scale criteria of force equality. A derived scaling factor produces the gravity effect experienced by the observer and the GRT-QED unification issue is thereby largely resolved.</p>


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