Stress-deformation state of thick shells and plates. Three-dimensional theory (review)

1991 ◽  
Vol 27 (11) ◽  
pp. 1035-1055
Author(s):  
Yu. N. Nemish ◽  
I. Yu. Khoma
Keyword(s):  
Three Dimensional ◽  
Dimensional Theory ◽  
Deformation State ◽  
Stress Deformation ◽  
Thick Shells ◽  
Theory Review

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

Three-Dimensional Elasticity Solution of a Composite Beam

1967 ◽  
Vol 1 (2) ◽  
pp. 122-135 ◽  
Author(s):  
Staley F. Adams ◽  
M. Maiti ◽  
Richard E. Mark
Keyword(s):  
Three Dimensional ◽  
Solid Wood ◽  
Theory Of Elasticity ◽  
Orthotropic Materials ◽  
Stress And Strain ◽  
Cantilever Beams ◽  
Dimensional Theory ◽  
Reinforced Plastics ◽  
Three Dimensional Elasticity ◽  
Moduli Of Elasticity

This investigation was undertaken to develop a rigorous mathe matical solution of stress and strain for a composite pole con sisting of a reinforced plastics jacket laminated on a solid wood core. The wood and plastics are treated as orthotropic materials. The problem of bending of such poles as cantilever beams has been determined by the application of the principles of three- dimensional theory of elasticity. Values of all components of the stress tensor in cylindrical coordinates are given for the core and jacket. Exact values for the stresses have been obtained from computer results, using the basic elastic constants—Poisson's ratios, moduli of elasticity and moduli of rigidity—for each ma terial. A comparison of the numerical results of the exact solu tion with strength of materials solutions has been completed.

scholarly journals A three-dimensional theory of wind pumping

1991 ◽  
Vol 37 (125) ◽  
pp. 89-96 ◽  
Author(s):  
Garry K. C. Clarke ◽  
Edwin D. Waddington
Keyword(s):  
Heat Source ◽  
Surface Pressure ◽  
Air Flow ◽  
Pressure Fluctuations ◽  
Normal Component ◽  
Three Dimensional ◽  
Lower Atmosphere ◽  
Dimensional Theory ◽  
Theoretical Formulation ◽  
Near Surface

AbstractQuantitative understanding of the processes that couple the lower atmosphere to the upper surface of ice sheets is necessary for interpreting ice-core records. Of special interest are those processes that involve the exchange of energy or atmospheric constituents. One such process, wind pumping, entails both possibilities and provides a possible mechanism for converting atmospheric kinetic energy into a near-surface heat source within the firn layer. The essential idea is that temporal and spatial variations in surface air pressure, resulting from air motion, can diffuse into permeable firn by conventional Darcy flow. Viscous friction between moving air and the solid firn matrix leads to energy dissipation in the firn that is equivalent to a volumetric heat source.Initial theoretical work on wind pumping was aimed at explaining anomalous near-surface temperatures measured at sites on Agassiz Ice Cap, Arctic Canada. A conclusion of this preliminary work was that, under highly favourable conditions, anomalous warming of as much as 2°C was possible. Subsequent efforts to confirm wind-pumping predictions suggest that our initial estimates of the penetration depth for pressure fluctuations were optimistic. These observations point to a deficiency of the initial theoretical formulation — the surface-pressure forcing was assumed to vary temporally, but not spatially. Thus, within the firn there was only a surface-normal component of air flow. The purpose of the present contribution is to advance a three-dimensional theory of wind pumping in which air flow is driven by both spatial and temporal fluctuations in surface pressure. Conclusions of the three-dimensional analysis are that the penetration of pressure fluctuations, and hence the thickness of the zone of frictional interaction between air and permeable firn, is related to both the frequency of the pressure fluctuations and to the spatial coherence length of turbulence cells near the firn surface.

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