On the Flexure of an Infinite Elastic Plate Containing a Large Unstressed Circular Hole

1968 ◽  
Vol 16 (1) ◽  
pp. 109-125 ◽  
Author(s):  
E. E. Burniston
Keyword(s):  
Circular Hole ◽  
Elastic Plate

The Bending and Twisting of a Flat Elastic Plate with a Reinforced Circular Hole

1960 ◽  
Vol 11 (2) ◽  
pp. 137-158 ◽  
Author(s):  
R. Hicks
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Circular Hole ◽  
Classical Theory ◽  
Elastic Plate ◽  
Radial Stress ◽  
Lateral Loading ◽  
Stress Variation ◽  
Wide Range

SummaryThis paper considers the problem of a reinforced circular hole in a bent or twisted flat elastic plate having small deflections. The reinforcement is chosen so that the ratio of its radial width to the diameter of the hole is small; this implies that there is no radial stress variation across sections of the reinforcement. Using the classical theory for bending, expressions are obtained for the boundary conditions at the junction of the reinforcement and plate. The expressions are general in so far as they are also applicable to plates under the action of lateral loading. The following particular problems are considered: —(a) uniform bending about one or two axes, (b) uniform twisting about two axes. For the particular case of uniform bending about one axis, data has been obtained for the stress concentration around holes for plates and reinforcements having a reasonably wide range of practical dimensions.

Stress Distribution in an Edge-Stiffened Semi-infinite Elastic Plate Containing a Circular Hole

1992 ◽  
Vol 59 (4) ◽  
pp. 789-795 ◽  
Author(s):  
Eung J. Lee ◽  
Eric C. Klang
Keyword(s):  
Shear Stress ◽  
Stress Concentration ◽  
Circular Hole ◽  
Elastic Plate ◽  
Stress Condition ◽  
Mapping Technique ◽  
System Of Equations ◽  
Stress Distributions ◽  
Bipolar Coordinates ◽  
In Series

An edge-stiffened semi-infinite elastic plate containing a circular hole under tension at infinity has been studied using a conformal mapping technique. Melan ’s stiffener condition in Cartesian coordinates has been newly formulated as a resultant shear stress condition in bipolar coordinates. The solution is sought in series form, and by truncating the system of equations, it is numerically solved. Pertinent stress distributions are examined to illustrate the roll of the stiffener under the presence of a circular hole near the straight edge. It has been concluded that the stiffener contributes to indirectly suppressing the stress concentration around the hole.

On energy changes due to the formation of a circular hole in an elastic plate

2006 ◽  
Vol 76 (11-12) ◽  
pp. 681-697 ◽  
Author(s):  
R. Kienzler ◽  
F. D. Fischer ◽  
P. Fratzl
Keyword(s):  
Circular Hole ◽  
Elastic Plate

Plane-Stress Unloading Waves Emanating From a Suddenly Punched Hole in a Stretched Elastic Plate

1960 ◽  
Vol 27 (1) ◽  
pp. 165-171 ◽  
Author(s):  
Julius Miklowitz
Keyword(s):  
Laplace Transform ◽  
Circular Hole ◽  
Plane Stress ◽  
Elastic Plate ◽  
Circumferential Stress ◽  
Radial Pressure ◽  
Compressional Waves ◽  
Stress Solution ◽  
Laplace Transform Technique ◽  
The Laplace Transform

The present paper points out that Kromm’s [1] plane-stress solution, for compressional waves in an infinite elastic plate subjected to radial pressure in a circular hole at its center, has application to still another problem of interest. This is the problem of a stretched elastic plate in which a circular hole is suddenly punched. The plane-stress solution for the tensile circumferential stresses, generated by the unloading mechanism in punching, is given here. This solution is derived independently of Kromm’s work in which a rather special Laplace-transform technique was used. The derivation given here also makes use of the Laplace transform but in a more direct manner, employing the inversion integral and a contour integration. It is also shown that the present inversion technique offers important simplifying features over that used by Selberg [3] in the closely related plane-strain problem. The numerical results presented are of interest in fragmentation studies. It is shown that the dynamic circumferential stress field in the vicinity of the punched hole is quite severe; which would be important to the creation and propagation of radial cracks.

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