The Effect of a Circular Hole on the Pure Twist of an Infinite Strip

1957 ◽  
Vol 24 (1) ◽  
pp. 115-121
Author(s):  
Osamu Tamate
Keyword(s):  
Perturbation Method ◽  
Circular Hole ◽  
Successive Approximation ◽  
Maximum Stress ◽  
Hole Diameter ◽  
Thin Plates ◽  
Width Ratio ◽  
Infinite Strip ◽  
Plate Material ◽  
Kirchhoff Theory

Abstract In a previous paper by the author (1), a theoretical solution for an infinite strip with a circular hole under plain bending is given by the method of successive approximation. This method demands laborious calculations. However, it seems that the labor can be diminished by employing the method of perturbation. In this paper, the effect of a circular hole in an infinite strip under the state of pure twist is investigated with the help of the perturbation method. The maximum deflections on the rim of the hole and the maximum stress couples in the strip are calculated and plotted versus hole-diameter strip-width ratio and Poisson’s ratio of the plate material. Here the strip is considered subjected to the limitation of the Poisson-Kirchhoff theory of bending of thin plates.

Large Deflections of Elliptical Plates

1956 ◽  
Vol 23 (1) ◽  
pp. 21-26
Author(s):  
N. A. Weil ◽  
N. M. Newmark
Keyword(s):  
Circular Plate ◽  
Maximum Stress ◽  
Large Deflection ◽  
Ritz Method ◽  
Constant Thickness ◽  
Infinite Strip ◽  
Elliptical Plate ◽  
Arbitrary Dimensions ◽  
Center Deflection ◽  
Large Deflection Problem

Abstract A solution is obtained by means of the Ritz method for the “large-deflection” problem of a clamped elliptical plate of constant thickness, subjected to a uniformly distributed load. Two shapes of elliptical plate are treated, in addition to the limiting cases of the circular plate and infinite strip, for which the exact solutions are known. Center deflections as well as total stresses at the center and edge decrease as one proceeds from the infinite strip through the elliptical shapes to the circular plate, holding the width of the plates constant. The relation between edge-stress at the semiminor axis (maximum stress in the plate) and center deflection is found to be practically independent of the proportions of the elliptical plate. Hence the governing stress may be determined from a single curve for a given load on an elliptical plate of arbitrary dimensions, if the center deflection is known.

On the Stresses in a Strip Under Tension and Containing Two Equal Circular Holes Placed Longitudinally

1956 ◽  
Vol 23 (4) ◽  
pp. 555-562
Author(s):  
A. Atsumi
Keyword(s):  
Perturbation Method ◽  
Longitudinal Axis ◽  
Infinite Strip ◽  
Circular Holes ◽  
Finite Breadth

Abstract A problem of determining the stresses in an infinite strip of finite breadth under tension and containing two equal circular holes placed on the longitudinal axis is studied theoretically. Stresses are calculated by a perturbation method, in each case the radius of the circle and the distance between the centers of two holes being varied. From consideration of the results obtained, some conclusions are made regarding the effects of the straight boundaries and the holes.

Green’s Functions for Infinite and Semi-infinite Anisotropic Thin Plates

2003 ◽  
Vol 70 (2) ◽  
pp. 260-267 ◽  
Author(s):  
Z.-Q. Cheng ◽  
J. N. Reddy
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Infinite Plate ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Green Functions ◽  
Real Form ◽  
Concentrated Forces ◽  
Anisotropic Elastic ◽  
Kirchhoff Theory

This paper presents fundamental solutions of an anisotropic elastic thin plate within the context of the Kirchhoff theory. The plate material is inhomogeneous in the thickness direction. Two systems of problems with non-self-equilibrated loads are solved. The first is concerned with in-plane concentrated forces and moments and in-plane discontinuous displacements and slopes, and the second with transverse concentrated forces. Exact closed-form Green’s functions for infinite and semi-infinite plates are obtained using the recently established octet formalism by the authors for coupled stretching and bending deformations of a plate. The Green functions for an infinite plate and the surface Green functions for a semi-infinite plate are presented in a real form. The hoop stress resultants are also presented in a real form for a semi-infinite plate.

Characterization of Notched Ductile Failure With Continuum Damage Mechanics

1990 ◽  
Vol 112 (4) ◽  
pp. 412-421 ◽  
Author(s):  
C. L. Chow ◽  
K. Y. Sze
Keyword(s):  
Ductile Fracture ◽  
Circular Hole ◽  
Damage Mechanics ◽  
Damage Model ◽  
Ductile Failure ◽  
Continuum Damage Mechanics ◽  
Thin Plates ◽  
Continuum Damage ◽  
Anisotropic Model ◽  
Aluminum Alloy 2024

A recently developed anisotropic model of continuum damage mechanics has been applied successfully to characterize ductile fracture of cracked plates under mode I and mixed mode failures. The damage model is further extended in this investigation to examine its applicability to include notch ductile fracture of thin plates containing a circular hole. Two hole sizes of 16 mm and 24 mm diameters are chosen and the specimen material is aluminum alloy 2024-T3. Fracture loads of the plates are predicted by the damage model and compared satisfactorily with those determined experimentally. This investigation provides an important confirmation that not only the anisotropic model of continuum damage mechanics but also the same failure criterion developed can be effectively employed to characterize both ductile fracture for plates containing an isolated macro-crack or circular hole which would otherwise not be possible using the conventional theory of fracture mechanics. The successful development of the unified approach to characterize ductile failure provides a vital impetus for design engineers in the general application of the theory of continuum damage mechanics to solve practical engineering problems.

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