scholarly journals How to use reactive stresses to improve plate-theory approximations of the stress field in a linearly elastic plate-like body

2007 ◽  
Vol 44 (5) ◽  
pp. 1337-1369 ◽  
Author(s):  
Marzio Lembo ◽  
Paolo Podio-Guidugli
Keyword(s):  
Stress Field ◽  
Elastic Plate ◽  
Plate Theory

General Solutions for the Statics of Anisotropic, Transversely Inhomogeneous Elastic Plates in Terms of Complex Functions

2006 ◽  
Vol 11 (6) ◽  
pp. 596-628 ◽  
Author(s):  
Kostas P. Soldatos
Keyword(s):  
General Solution ◽  
Elastic Plate ◽  
Plate Theory ◽  
High Order ◽  
Transverse Strain ◽  
Elastic Plates ◽  
General Solutions ◽  
Material Inhomogeneity ◽  
Complex Functions ◽  
Anisotropic Elastic

This paper develops the general solution of high-order partial differential equations (PDEs) that govern the static behavior of transversely inhomogeneous, anisotropic, elastic plates, in terms of complex functions. The basic development deals with the derivation of such a form of general solution for the PDEs associated with the most general, two-dimensional (“equivalent single-layered”), elastic plate theory available in the literature. The theory takes into consideration the effects of bending–stretching coupling due to possible un-symmetric forms of through-thickness material inhomogeneity. Most importantly, it also takes into consideration the effects of both transverse shear and transverse normal deformation in a manner that allows for a posteriori, multiple choices of transverse strain distributions. As a result of this basic and most general development, some interesting specializations yield, as particular cases, relevant general solutions of high-order PDEs associated with all of the conventional, elastic plate theories available in the literature.

Response of a Plate Supported by a Fluid Half Space to a Moving Pressure

1970 ◽  
Vol 37 (4) ◽  
pp. 1050-1054 ◽  
Author(s):  
D. H. Y. Yen ◽  
C. C. Chou
Keyword(s):  
Half Space ◽  
Elastic Plate ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Integral Transforms ◽  
Classical Plate Theory ◽  
Plate Deflection

The response of an elastic plate supported by a fluid half space to a steadily moving pressure is studied. The Timoshenko plate theory is used in the study. By the method of integral transforms, solutions for both the plate deflection and the interaction fluid pressure are obtained. The results are then compared in detail with those obtained previously using the classical plate theory.

scholarly journals Transient dynamics of an elastic Hele-Shaw cell due to external forces with application to impact mitigation

2016 ◽  
Vol 800 ◽  
pp. 517-530 ◽  
Author(s):  
A. Tulchinsky ◽  
A. D. Gat
Keyword(s):  
Elastic Plate ◽  
Plate Theory ◽  
Applied Pressure ◽  
Elastic Interaction ◽  
External Pressure ◽  
Transient Dynamics ◽  
Impact Mitigation ◽  
Order Of Magnitude ◽  
External Forces ◽  
Hele Shaw Cell

We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure field. We model the flow field via the lubrication approximation and the plate deformation by the Kirchhoff–Love plate theory. We obtain a self-similarity solution for the case of an external point force acting on the elastic plate. The pressure and deformation field during and after the application of the external force are derived and presented by closed-form expressions. We examine a distributed external pressure, spatially uniform and linearly increasing with time, acting on the elastic plate over a finite region and during a finite time period, similar to the viscous–elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by an order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure. The results thus suggest that elastic Hele-Shaw configurations may be used to achieve significant impact mitigation.

Investigation of Fixed-Free Annular Plate Resonant Frequency Predictions

1988 ◽  
Vol 110 (3) ◽  
pp. 408-410 ◽  
Author(s):  
Alison Flatau ◽  
G. A. Flandro ◽  
W. K. Van Moorhem
Keyword(s):  
Free Boundary ◽  
Resonant Frequency ◽  
Elastic Plate ◽  
Annular Plate ◽  
Plate Theory ◽  
Outer Radius ◽  
Resonant Frequencies ◽  
Free Boundary Conditions ◽  
Annular Plates ◽  
Analytical Frequency

Nondimensional frequency parameters for predicting the resonant frequencies of annular plates with fixed-free boundary conditions as the plate inner to outer radius ratio approaches unity have been investigated experimentally. Frequency parameters have been determined by using modal analysis to measure resonant frequencies for annular plates of varied materials, thicknesses, and with radius ratios of 0.5 to 0.9. The data are compared to two different analytical frequency predictions which have been presented as solutions for resonance of fixed-free annular plates based on classical elastic plate theory.

Some mechanical aspects of pingo growth and failure, western Arctic coast, Canada

1987 ◽  
Vol 24 (6) ◽  
pp. 1108-1119 ◽  
Author(s):  
J. Ross Mackay
Keyword(s):  
Elastic Plate ◽  
Plate Theory ◽  
Early Growth ◽  
Thin Elastic Plate ◽  
Normal Faulting ◽  
Overburden Thickness ◽  
Changing Roles ◽  
Western Arctic ◽  
Arctic Coast ◽  
Spring Flow

Many closed-system pingos are underlain by sub-pingo water lenses, and the same is probably true of numerous open-system pingos. In the early growth stage the bending of the frozen overburden of a pingo by a sub-pingo water lens can be compared to the bending of a thin elastic plate. Although the assumptions of elastic plate theory do not apply fully to a growing pingo, because time-dependent plastic and creep deformation are involved, the application of elastic plate theory nevertheless helps to explain the peripheral normal faulting and spring flow of pingos, summit failure, the ease with which elongated pingos appear to collapse, and the changing roles played by the radius and overburden thickness of pingos from early growth to the cessation of growth.

scholarly journals Breakage of Ice Sheets by Underwater Explosions

1977 ◽  
Vol 19 (81) ◽  
pp. 661-663
Author(s):  
E. Vittoratos ◽  
M. E. Charles
Keyword(s):  
Elastic Plate ◽  
High Speed ◽  
Plate Theory ◽  
Ice Sheets ◽  
Theoretical Development ◽  
Small Scale ◽  
Theory Approach ◽  
Classical Plate Theory ◽  
Theoretical Understanding ◽  
Deformation And Failure

AbstractWe have attempted to develop a theoretical understanding of the field experience on the destruction of floating ice sheets by explosives, by performing small-scale laboratory explosions and developing a theory based on the elastic plate. Glass spheres 4.5 × 10¯2 m in diameter and c. 4 × 10¯4 m thick were immersed in water underneath a floating ice sheet c. 2 × 10¯2 m in thickness. The air pressure was raised till the sphere burst at pressures around 15 atmospheres. A high-speed camera (up to several thousand frames per second) recorded the details of the explosion: the growth of the gas bubble and the corresponding deformation and failure of the ice. We observed radial and circumferential cracks develop within 2 ms of the bursting of the sphere.As a first step in the theoretical development, we have considered the response of an infinite elastic plate to impulsive pressure loading due to an underwater explosion. We have assumed potential, incompressible flow which is a valid approximation for the case of the above experiments and the analogous compressed-gas blasting in the field (Mellor and Kovacs, 1972). However the effects caused by the intense shock wave that is radiated by the detonation of a high explosive are thus not considered. We relate the maxima in the tensile stress with the crack pattern and the eventual damage, and have achieved qualitative agreement with the laboratory observations. The model does reproduce and clarify some aspects of the field data, in particular the role of the thickness (Mellor, unpublished); but it fails to relate the crater diameter to the weight of the explosive. It appears that at optimum blasting conditions with high explosives an incompressible-fluid, classical-plate-theory approach is inadequate.

scholarly journals Breakage of Ice Sheets by Underwater Explosions

1977 ◽  
Vol 19 (81) ◽  
pp. 661-663
Author(s):  
E. Vittoratos ◽  
M. E. Charles
Keyword(s):  
Elastic Plate ◽  
High Speed ◽  
Plate Theory ◽  
Ice Sheets ◽  
Theoretical Development ◽  
Small Scale ◽  
Theory Approach ◽  
Classical Plate Theory ◽  
Theoretical Understanding ◽  
Deformation And Failure

Abstract We have attempted to develop a theoretical understanding of the field experience on the destruction of floating ice sheets by explosives, by performing small-scale laboratory explosions and developing a theory based on the elastic plate. Glass spheres 4.5 × 10¯2 m in diameter and c. 4 × 10¯4 m thick were immersed in water underneath a floating ice sheet c. 2 × 10¯2 m in thickness. The air pressure was raised till the sphere burst at pressures around 15 atmospheres. A high-speed camera (up to several thousand frames per second) recorded the details of the explosion: the growth of the gas bubble and the corresponding deformation and failure of the ice. We observed radial and circumferential cracks develop within 2 ms of the bursting of the sphere. As a first step in the theoretical development, we have considered the response of an infinite elastic plate to impulsive pressure loading due to an underwater explosion. We have assumed potential, incompressible flow which is a valid approximation for the case of the above experiments and the analogous compressed-gas blasting in the field (Mellor and Kovacs, 1972). However the effects caused by the intense shock wave that is radiated by the detonation of a high explosive are thus not considered. We relate the maxima in the tensile stress with the crack pattern and the eventual damage, and have achieved qualitative agreement with the laboratory observations. The model does reproduce and clarify some aspects of the field data, in particular the role of the thickness (Mellor, unpublished); but it fails to relate the crater diameter to the weight of the explosive. It appears that at optimum blasting conditions with high explosives an incompressible-fluid, classical-plate-theory approach is inadequate.

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