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 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.

EXACT SOLUTION FOR BENDING OF AN ELASTIC PLATE CONTAINING A CRACK AND SUBJECTED TO A CONCENTRATED MOMENT

2007 ◽  
Vol 04 (02) ◽  
pp. 265-281
Author(s):  
LALITHA CHATTOPADHYAY ◽  
S. SRIDHARA MURTHY ◽  
S. VISWANATH
Keyword(s):  
Stress Intensity Factor ◽  
Elastic Plate ◽  
Integral Transform ◽  
Plate Theory ◽  
Infinite Plate ◽  
Bending Moment ◽  
Single Line ◽  
Bending Stress ◽  
Single Crack ◽  
Classical Plate Theory

The problem of estimating the bending stress distribution in the vicinity of cracks located on a single line in an elastic plate subjected to concentrated moment is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in detail for the case in which there is a single crack in an infinite plate, and the bending stress intensity factor is determined in a closed form. Two examples are considered to illustrate the present approach.

The Effect of a Rigid Elliptic Inclusion on the Bending of a Thick Elastic Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 379-382
Author(s):  
Fu Chow
Keyword(s):  
Stress Concentration ◽  
Elastic Plate ◽  
Plate Theory ◽  
Circular Inclusion ◽  
Elliptic Inclusion ◽  
Focal Distance ◽  
Classical Plate Theory ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Rigid Circular Inclusion

The effect of a rigid elliptic inclusion on both plain bending and pure twist of a thick elastic plate is investigated on the basis of Reissner’s plate theory [1, 2]. Comparison is made for the limiting cases of vanishing focal distance of the elliptic inclusion (a rigid circular inclusion), and vanishing thickness (Poisson-Kirchhoff plate theory), with the solutions of C. Pai [3], R. A. Hirsch [4], and M. Goland [5]. The stress-concentration factors are lower than those predicted by the classical plate theory.

Bending of a Cantilever Plate Supported From an Elastic Half Space

1961 ◽  
Vol 28 (3) ◽  
pp. 387-394 ◽  
Author(s):  
N. C. Small
Keyword(s):  
Half Space ◽  
Plate Theory ◽  
Free Edge ◽  
Fourier Integral ◽  
Elastic Half Space ◽  
Cantilever Plate ◽  
Classical Plate Theory ◽  
Small Deviations ◽  
Shear Effects ◽  
The Moment

A solution is obtained for an infinitely long cantilever plate supported from an elastic half space. The junction conditions between the elasticity approach for the half space and the classical plate theory (no-shear) approach for the plate are based upon the use of assumed equilibrium surface tractions for the half space. The formal Fourier integral results for the example of a concentrated free-edge load are evaluated using an IBM 704 computer. The correlation with the deflection results of a steel model test is shown to be very good. The small deviations from the theoretical values are primarily due to shear effects in the model. It is also shown that, except for very stubby plates, it is sufficiently accurate to neglect the shear effects along the half space, and to assume that the rotation is proportional to the moment in the conventional “Winkler” sense.

The Effect of a Rigid Circular Inclusion on the Bending of a Thick Elastic Plate

1952 ◽  
Vol 19 (1) ◽  
pp. 28-32
Author(s):  
R. A. Hirsch
Keyword(s):  
Plane Strain ◽  
Elastic Plate ◽  
Plate Theory ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Inclusion Size ◽  
Circular Inclusion ◽  
Stress Concentrations ◽  
Classical Plate Theory ◽  
Rigid Circular Inclusion

Abstract The three-dimensional problem of the effect of a rigid circular inclusion on the bending of a thick elastic plate is solved approximately by the method of E. Reissner (1, 2). Comparison is made for the limiting cases of vanishing inclusion size, (plane strain), and vanishing thickness (Poisson-Kirchoff plate theory), with the work of J. N. Goodier (3) and M. Goland (4). Graphs showing the transition from the plane-strain solution to the Poisson-Kirchoff solution are given. Stress concentrations are calculated and plotted versus the inclusion diameter-plate thickness ratio. The stress concentrations are found to be less than predicted by the classical plate theory when the inclusion diameter approaches the same order of magnitude as the plate thickness.

ISOGEOMETRIC SIMULATION FOR BUCKLING, FREE AND FORCED VIBRATION OF ORTHOTROPIC PLATES

2013 ◽  
Vol 05 (02) ◽  
pp. 1350017 ◽  
Author(s):  
N. VALIZADEH ◽  
T. Q. BUI ◽  
V. T. VU ◽  
H. T. THAI ◽  
M. N. NGUYEN
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Isogeometric Analysis ◽  
Plate Theory ◽  
Present Formulation ◽  
Orthotropic Plates ◽  
Classical Plate Theory ◽  
Numerical Examples ◽  
Nurbs Basis Function ◽  
Plate Deflection

Buckling, free and forced vibration analyses of orthotropic plates are studied numerically using Isogeometric analysis. The present formulation is based on the classical plate theory (CPT) while the NURBS basis function is employed for both the parametrization of the geometry and the approximation of plate deflection. An efficient and easy-to-implement technique is used for imposing the essential boundary conditions. Numerical examples for free and forced vibration and buckling of orthotropic plates with different boundary conditions and configurations are considered. The numerical results are compared with other existing solutions to show the efficiency and accuracy of the proposed approach for such problems.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

1989 ◽  
Vol 56 (2) ◽  
pp. 251-262 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Contact Region ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Complete Contact ◽  
The One ◽  
Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

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