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.

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.

Fracture Analysis of Adhesively Bonded Sheets

1976 ◽  
Vol 43 (4) ◽  
pp. 652-656 ◽  
Author(s):  
L. M. Keer ◽  
C. T. Lin ◽  
T. Mura
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Transform ◽  
Crack Tip ◽  
Fracture Analysis ◽  
Single Crack ◽  
Adhesively Bonded ◽  
Transform Methods ◽  
Coplanar Cracks

The problem of adhesively bonded sheets, one of which is cracked, is formulated by the utilization of integral transform methods. The objective of the investigation is to calculate the stress-intensity factor at the crack tip for the cracked sheets. Results are obtained when the cracked sheet has a single crack and an array of identical, equally spaced, coplanar cracks. Results tend to indicate that the growth of crack implies a reduction in the stress-intensity factor.

Diffraction of harmonic flexural waves in a cracked elastic plate carrying electrical current

2005 ◽  
Vol 461 (2063) ◽  
pp. 3543-3560 ◽  
Author(s):  
Damodar R Ambur ◽  
Davresh Hasanyan ◽  
Liviu Librescu ◽  
Zhanming Qin
Keyword(s):  
Intensity Factor ◽  
Integral Equations ◽  
Incident Wave ◽  
Elastic Plate ◽  
Plate Theory ◽  
Bending Moment ◽  
Singular Integral Equations ◽  
Electrical Current ◽  
Flexural Waves ◽  
Dual Integral Equations

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal x -axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

The Effect of Transverse Shear Deformation on the Bending of Elastic Plates

1945 ◽  
Vol 12 (2) ◽  
pp. A69-A77 ◽  
Author(s):  
Eric Reissner
Keyword(s):  
General Solution ◽  
Rectangular Plate ◽  
Transverse Shear ◽  
Plate Theory ◽  
Infinite Plate ◽  
Present Theory ◽  
System Of Equations ◽  
Elastic Plates ◽  
Classical Plate Theory

Abstract A system of equations is developed for the theory of bending of thin elastic plates which takes into account the transverse shear deformability of the plate. This system of equations is of such nature that three boundary conditions can and must be prescribed along the edge of the plate. The general solution of the system of equations is obtained in terms of two plane harmonic functions and one function which is the general solution of the equation Δψ − (10/h2)ψ = 0. The general results of the paper are applied (a) to the problem of torsion of a rectangular plate, (b) to the problems of plain bending and pure twisting of an infinite plate with a circular hole. In these two problems important differences are noted between the results of the present theory and the results obtained by means of the classical plate theory. It is indicated that the present theory may be applied to other problems where the deviations from the results of classical plate theory are of interest. Among these other problems is the determination of the reactions along the edges of a simply supported rectangular plate, where the classical theory leads to concentrated reactions at the corners of the plate. These concentrated reactions will not occur in the solution of the foregoing problem by means of the theory given in the present paper.

Stress Intensity Factors for Plate Bending and Shearing Problems

1994 ◽  
Vol 61 (3) ◽  
pp. 719-722 ◽  
Author(s):  
A. T. Zehnder ◽  
Chung-Yuen Hui
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Plate Theory ◽  
Infinite Plate ◽  
Bending Moment ◽  
Far Field ◽  
Intensity Factors ◽  
Arbitrary Angle ◽  
Cracked Plate ◽  
Finite Crack

Stress intensity factors for a finite crack in an infinite plate are calculated assuming Kirchhoff plate theory. Two problems are considered: a cracked plate subjected to uniform far-field shearing, and a cracked plate subjected to uniform far-field bending moment. In both cases the crack is oriented at an arbitrary angle to the axis of loading.

Contact Between Plates and Unilateral Supports

1984 ◽  
Vol 51 (2) ◽  
pp. 324-328 ◽  
Author(s):  
J. P. Dempsey ◽  
L. M. Keer ◽  
N. B. Patel ◽  
M. L. Glasser
Keyword(s):  
Integral Transform ◽  
Plate Theory ◽  
Classical Plate Theory ◽  
Dual Series Equations ◽  
Receding Contact ◽  
Finite Integral ◽  
Simple Supports ◽  
Square Plate ◽  
Laterally Loaded ◽  
Support Reactions

The tendency of a laterally loaded, unilaterally constrained, rectangular plate to separate from its simple supports motivates one to consider the actual extent of contact. In the case of a square plate, an appropriately chosen finite integral transform converts the dual series equations that result from the Levy-Nadai approach to one singular integral equation which can be solved by standard methods. Being a receding contact problem, the extent of contact depends on the geometry and elastic properties of the plate only. The support reactions are integrated to confirm that total equilibrium is obtained using classical plate theory.

Generalized Bending of a Large, Shear Deformable Isotropic Plate Containing a Circular Hole or Rigid Inclusion

2000 ◽  
Vol 68 (2) ◽  
pp. 230-233 ◽  
Author(s):  
C. W. Bert ◽  
H. Zeng
Keyword(s):  
Circular Hole ◽  
Isotropic Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Circular Inclusion ◽  
Experimental Result ◽  
Classical Plate Theory ◽  
Geometric Ratio ◽  
Three Dimensional Elasticity

The problem of a large isotropic plate with a circular hole or rigid circular inclusion is considered here. The plate experiences transverse shear deformation and is subjected to an arbitrary bending field. By using Reissner’s plate theory, a general solution, in terms of Poisson’s ratio ν, a geometric ratio, and bending moment ratio B, is obtained to satisfy both the boundary conditions along the edge and at great distances from the edge. The stress couple concentration factors are calculated and compared with classical plate theory, three-dimensional elasticity theory, higher-order plate theory, and an experimental result.

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