Stress Concentration Around an Ellipsoidal Cavity in an Infinite Body Under Arbitrary Plane Stress Perpendicular to the Axis of Revolution of Cavity

1947 ◽  
Vol 14 (3) ◽  
pp. A191-A201 ◽  
Author(s):  
M. A. Sadowsky ◽  
E. Sternberg
Keyword(s):  
Stress Concentration ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Infinite Body ◽  
Plane State ◽  
Ellipsoidal Cavity ◽  
State Of Stress ◽  
Ellipsoid Of Revolution ◽  
Arbitrary Plane ◽  
Uniform Plane

Abstract This paper contains an exact closed solution for the stress distribution around a cavity in the shape of an ellipsoid of revolution in an infinite elastic body which is otherwise in an arbitrary uniform plane state of stress perpendicular to the axis of revolution of the cavity. The solution is based upon an extension to orthogonal curvilinear co-ordinates of the classical three-function approach to three-dimensional problems of the theory of elasticity. The technically important features of the ensuing stress concentration are discussed in detail.

Using the Palm Computer to Augment the Design of Machine Elements

2000 ◽  
Author(s):  
Terry E. Shoup
Keyword(s):  
Stress Concentration ◽  
Stress Analysis ◽  
Three Dimensional ◽  
The Other ◽  
Machine Design ◽  
State Of Stress ◽  
Machine Elements ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Computational Processes

Abstract This paper discusses the utility of the palm sized computers for augmenting the design of machine elements. Two palm computer programs are presented for handling frequently occurring problems in stress analysis in order to demonstrate the utility of the palm computer in this environment. One of these programs handles the manipulation of a three dimensional state of stress and the other program handles stress concentration factors. These modules facilitate computational processes that would not be possible with a traditional hand-held calculator. These programs are useful for students of machine design and practitioners as well.

Long Cylindrical Tube Subjected to Two Diametrically Opposite Loads

1969 ◽  
Vol 20 (4) ◽  
pp. 365-381 ◽  
Author(s):  
J. C. Yao
Keyword(s):  
Stress State ◽  
Stress Concentration ◽  
Stress Function ◽  
Radial Displacement ◽  
Theoretical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Theory Of Elasticity ◽  
Test Results ◽  
Dimensional Theory

SummaryA theoretical study is made of the problem of a long, thick cylindrical tube subjected to two equal and diametrically opposite normal loads. The stress state is analysed by the three-dimensional theory of elasticity, with the Papkovich and Neuber stress-function approach. Numerical results for stresses and radial displacement are obtained to show the nature of stress concentration in the neighbourhood of the load. Some related experiments using the photoelasticity technique are also accomplished. Favourable correlation is shown between the theory and the test results.

Stress Concentration Around a Triaxial Ellipsoidal Cavity

1949 ◽  
Vol 16 (2) ◽  
pp. 149-157
Author(s):  
M. A. Sadowsky ◽  
E. Sternberg
Keyword(s):  
Stress Concentration ◽  
Elliptic Functions ◽  
The Body ◽  
Stress Concentrations ◽  
Principal Stresses ◽  
Jacobian Elliptic Functions ◽  
Ellipsoidal Cavity ◽  
Internal Cavities ◽  
Ellipsoid Of Revolution ◽  
Principal Directions

Abstract Previous investigations have been concerned with the stress concentrations around internal cavities in the shape of an ellipsoid of revolution. This paper contains an exact closed solution, in terms of Jacobian elliptic functions, for the stress distribution around a general triaxial ellipsoidal cavity in an infinite elastic body. The body at infinity is in a uniform state of stress whose principal directions are parallel to the axes of the cavity, the magnitudes of the principal stresses at infinity being arbitrary. The solution covers as limiting cases the known results for spherical and spheroidal cavities. The technically important aspects of the ensuing stress concentration are discussed in detail.

Three-Dimensional Solution for the Stress Concentration Around a Circular Hole in a Plate of Arbitrary Thickness

1949 ◽  
Vol 16 (1) ◽  
pp. 27-38
Author(s):  
E. Sternberg ◽  
M. A. Sadowsky
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Ritz Method ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Uniform State ◽  
Arbitrary Thickness

Abstract This paper contains an approximate three-dimensional solution for the stress distribution around a circular cylindrical hole in an infinite plate of arbitrary thickness, which is otherwise in a uniform state of plane stress parallel to the bounding planes. The approach used rests on a modification of the Ritz method in the theory of elasticity. A knowledge of the triaxial characteristics of the ensuing stress concentration is held important in connection with modern views on failure. The results furthermore illuminate critically the significance of two-dimensional analysis in problems of the type under consideration.

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