scholarly journals On the stresses in the neighbourhood of a circular hole in a strip under tension

1930 ◽  
Vol 229 (670-680) ◽  
pp. 49-86 ◽  
Keyword(s):  
Circular Hole ◽  
Practical Importance ◽  
Infinite Plate ◽  
Two Dimensions ◽  
Theoretical Interest ◽  
Circular Boundary ◽  
Applied Tension ◽  
Circular Holes ◽  
Special Solutions ◽  
Maximum Stresses

The problem of determining the stresses in a plate under tension when the material is pierced by one or more circular holes is one of both theoretical interest and practical importance. Provided that the plate may be regarded as infinitely extended in two dimensions, the solution for a single hole is easily found and is well known. The presence of the hole leads to the occurrence of stresses equal to three times the tension at infinity, these maximum stresses occurring at the edge of the hole and on the diameter perpendicular to the direction of the applied tension. More general stress systems, corresponding to the presence of tractions at the edge of the hole, may be studied by similar methods, not only when the plate is infinite but also when there is a second circular boundary concentric with the first. A number of special solutions for the infinite plate have recently been published by BICKLEY. The solution for a semi-infinite plate with one circular hole was obtained by JEFFREY, using bipolar co-ordinates,§ which may be applied also to the case of an infinite plate pierced by two holes

Note on General Bi-Harmonic Analysis for a Plate Containing Circular Holes

1941 ◽  
Vol 37 (1) ◽  
pp. 29-33 ◽  
Author(s):  
A. E. Green
Keyword(s):  
General Solution ◽  
Harmonic Analysis ◽  
Circular Hole ◽  
Elastic Constants ◽  
Infinite Plate ◽  
Stress Distributions ◽  
Zero Force ◽  
Circular Holes

In a previous paper a general solution was given for problems of stress distributions in a plate containing circular holes of varying sizes arranged in any manner. This work was a generalization of special methods used by various writers for particular arrangements of holes. The types of stress distributions were, however, confined to those which produce zero force resultants on each hole and the solutions were therefore independent of the elastic constants. Bickley has studied distributions of stress round one circular hole in an infinite plate when the force resultants on the hole are no longer zero, and a few other problems of this type have been dealt with by other writers.

Curvature Effects on Stress Concentrations at Reinforced Circular Holes

1968 ◽  
Vol 12 (02) ◽  
pp. 142-152
Author(s):  
Peter Van Dyke
Keyword(s):  
Boundary Conditions ◽  
Practical Importance ◽  
Complex Problem ◽  
Stress Concentrations ◽  
Aerospace Vehicles ◽  
Curvature Effects ◽  
Circular Boundary ◽  
Influence Coefficients ◽  
Circular Holes ◽  
Direct Use

The primary purposes of this paper are: first, to present a summary of the results of recent investigations into the effects of the curvature on the stress conditions at circular boundaries in shallow cylindrical shells; and second, to apply these results, in the form of influence coefficients at the circular boundary in the shell, to a more complex problem of practical importance which might be encountered in the design of advanced marine or aerospace vehicles. When the boundary conditions at the shell edge specify either the stresses, deformations, or mixtures of both, solutions are obtained through direct use of the influence coefficients. When the stresses and deformations are linked elastically, as exemplified by problems concerning reinforced holes, solutions are more complex in nature. Results for stresses at the intersection of a shell with a flat circular reinforcement are presented here as a function of shell curvature for particular material and geometric properties of the shell and reinforcement. Also, the formulation of the problem where both reinforcement and shell are curved is included.

scholarly journals On the stresses induced by flexure in a deep rectangular beam

1934 ◽  
Vol 143 (849) ◽  
pp. 271-284 ◽  
Keyword(s):  
Stress Distribution ◽  
Practical Importance ◽  
Sufficient Accuracy ◽  
Elastic Instability ◽  
Theoretical Interest ◽  
Close Approximation ◽  
Rectangular Section ◽  
Apparent Paradox ◽  
State Of Stress ◽  
Radial Forces

1. When a straight cylindrical rod is bent into a circle by couples applied at its ends, the resulting state of stress is given, with sufficient accuracy for practical purposes, by the well-known theory of St. Venant. In that theory qunatities of the second and higher orders in therms of strain are neglected, and the resulting solution asserts that the stress is purely longitudinal, so that the rod may be thought of as an assembly of cylindrical fibres, each of which behaves independently of its neighbours. It is evident that this description cannot be exact; for a fibre bent into a circle cannot be kept in tension unless radial forces operate to maintain equilibrium, and in the case considered such forces can come only from actions between adjacent fibres. The apparent paradox is explained by the consideration that those action are of the second order in terms of the curvature, and accordingly are neglected in St. Venant's theory. In connection with a certain problem of elastic instability it was thought desirable to attempt a more accurate description for a particular case, namely, a rod of deep and thin rectangular section. It was found that the equations of equilibrium can be integrated independently of any simplifying assumption, and the stress-distribution determined for curvature of any magnitude. The results have no great practical importance, sice they show that St. Venant's theory gives a close approximation to the facts within that range of strains which actual materials can sustain elastically; but they have some theoretical interest, and accordingly are presented in this paper.

Stresses Due to Diametral Forces on a Circular Disk With an Eccentric Hole

1955 ◽  
Vol 22 (2) ◽  
pp. 263-266
Author(s):  
A. M. Sen Gupta
Keyword(s):  
Circular Hole ◽  
Normal Force ◽  
Infinite Plate ◽  
Circular Disk ◽  
Outer Edge

Abstract In this paper stresses in a circular disk with an eccentric circular hole have been determined when the disk is compressed along the line of centers by two equal and opposite forces acting on its outer edge, the inner edge being unstressed. From the results obtained, the solution of the problem of a semi-infinite plate acted on by a concentrated normal force on its straight boundary and containing an unstressed circular hole has been deduced.

A Rapid Method for the Determination of Principal Stresses Across Sections of Symmetry From Photoelastic Data

1938 ◽  
Vol 5 (1) ◽  
pp. A24-A28
Author(s):  
M. M. Frocht
Keyword(s):  
Free Boundary ◽  
Rapid Method ◽  
Circular Hole ◽  
Characteristic Curve ◽  
Principal Stresses ◽  
Recent Improvement ◽  
Tangential Stresses ◽  
Circular Holes ◽  
Photoelastic Data

Abstract The author discusses: (a) Mesnager’s theorem of isoclinics, (b) the characteristic curve of tangential stresses across a section of symmetry, (c) a formula for the maximum tangential stresses for the case of a central circular hole between fields of pure tension, (d) the slope of the p curve at a point corresponding to a cupic point, (e) recent improvement in the determination of free boundary stresses, and (f) formulas for the position of cupic points for two cases. A new method for the determination of the principal stresses across sections of symmetry from photoelastic data is illustrated with three examples: (1) Bars in tension or compression with central circular holes, (2) grooved beams in bending, and (3) rings or disks with circular central holes subjected to two concentrated diametral loads.

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