On the General Theory of Thin Shells

1950 ◽  
Vol 17 (4) ◽  
pp. 396-398
Author(s):  
W. R. Osgood ◽  
J. A. Joseph
Keyword(s):  
General Theory ◽  
Thin Shells ◽  
Theory Of Shells

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.

General Theory of Thin Shells

2011 ◽  
pp. 51-64
Author(s):  
Roustem N. Miftahof ◽  
Hong Gil Nam
Keyword(s):  
General Theory ◽  
Thin Shells

A General Theory of Shells and the Complementary Potentials

1986 ◽  
Vol 53 (4) ◽  
pp. 881-885 ◽  
Author(s):  
G. Wempner
Keyword(s):  
Finite Elements ◽  
General Theory ◽  
Linear Function ◽  
Transverse Shear ◽  
Surface Deformation ◽  
Reference Surface ◽  
Shear Deformations ◽  
Theory Of Shells

This theory incorporates the attributes which are essential to the approximation of shells by finite elements. It is limited only by one assumption: Displacement is a linear function of distance along the normal to a reference surface. Deformation is decomposed into rotation and strain; the rotation carries elements of the reference surface to the same surface in any subsequent state. Transverse-shear deformations accommodate simple elements. The theory is couched in the potential Pv and in the complementary potential Pc; these have the property, Pv + Pc= 0 for all admissible (equilibrated) states. The theory is also cast in the complementary functional P¯c of stress and displacement, and the functional P¯v of displacement, strain and stress; P¯c and P¯v are akin to the functionals of Hellinger-Reissner and Hu-Washizu. These alternate functionals provide the means to develop various hybrid elements.

Free Vibrations of Circular Cylindrical Web-Stiffened Sandwich Shells

1973 ◽  
Vol 17 (01) ◽  
pp. 43-49
Author(s):  
David Ranlet ◽  
Youl-Nan Chen ◽  
Joseph Kempner
Keyword(s):  
Natural Frequencies ◽  
Free Vibrations ◽  
Thin Shells ◽  
Rotatory Inertia ◽  
Variational Functional ◽  
The Core ◽  
Discrete Nature ◽  
Sandwich Shells ◽  
The Mathematical Model ◽  
Theory Of Shells

An analysis of the free vibrations of simply supported and clamped, web-stiffened, circular, cylindrical sandwich shells is presented. The mathematical model formulated includes the effect of translatory and rotatory inertia in each layer of the sandwich, and treats the two face layers as thin shells in which the classical (Donnell) theory of shells applies. However, shear deformations are permitted in the core, which is treated as a layer of inhomogeneous, orthotropic material. In the analysis, the discrete nature of the webs is maintained, except for the inclusion of an average secondary shear modulus induced by the bending of the webs and faces. The effect of smearing-out, or averaging, a given web-stiffened core is also investigated. A Galerkin procedure is employed to determine the natural frequencies from a variational functional generated by means of Hamilton's principle.

On the Derivation of Shell Theories by Direct Approach

1974 ◽  
Vol 41 (1) ◽  
pp. 173-176 ◽  
Author(s):  
A. E. Green ◽  
P. M. Naghdi
Keyword(s):  
General Theory ◽  
Direct Approach ◽  
Recent Developments ◽  
Cosserat Surface ◽  
Theory Of Shells

A constrained theory of shells by a direct approach, based on a general theory of a Cosserat surface, is derived and its relation to other recent developments obtained by direct procedures is indicated.

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