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.

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.

Jacobian elliptic functions and a family of bivariate peak polynomials

2021 ◽  
Vol 97 ◽  
pp. 103371
Author(s):  
Shi-Mei Ma ◽  
Jun Ma ◽  
Yeong-Nan Yeh ◽  
Roberta R. Zhou
Keyword(s):  
Elliptic Functions ◽  
Jacobian Elliptic Functions

ANALYTICAL STUDY ON NONLINEAR DIFFERENTIAL–DIFFERENCE EQUATIONS VIA A NEW METHOD

2010 ◽  
Vol 24 (08) ◽  
pp. 761-773
Author(s):  
HONG ZHAO
Keyword(s):  
Difference Equations ◽  
Elliptic Function ◽  
Analytical Study ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobian Elliptic Function ◽  
Jacobian Elliptic Functions ◽  
Periodic Wave Solutions ◽  
Trigonometric Function Solutions

Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third elliptic function solutions, were obtained. Furthermore, the solitonic solutions and trigonometric function solutions were also obtained within the limit conditions in this paper.

Analysis of Stress Concentrations in Thick Cylinders With Sideholes and Crossholes

1972 ◽  
Vol 94 (3) ◽  
pp. 815-824 ◽  
Author(s):  
J. C. Gerdeen
Keyword(s):  
Stress Concentration ◽  
Stress Concentrations ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Experimental Values ◽  
Pressure Stress ◽  
Shrink Fit ◽  
Outside Diameter ◽  
Theoretical Results

An approximate theoretical analysis is presented for the determination of stress concentration factors in thick walled cylinders with sideholes and crossholes. The cylinders are subjected to both internal pressure and external shrink-fit pressure. Stress concentration factors are plotted as functions of the geometrical ratios of outside diameter-to-bore diameter, and bore diameter-to-sidehole diameter. Theoretical results are compared to experimental values available in the literature and results of experiments described in a separate paper.

Stress concentrations due to axial tension and bending of loaded axisymmetric projections

1983 ◽  
Vol 18 (1) ◽  
pp. 7-14 ◽  
Author(s):  
T H Hyde ◽  
B J Marsden
Keyword(s):  
Stress Concentration ◽  
Diameter Ratio ◽  
The Finite Element Method ◽  
Stress Concentrations ◽  
Axial Tension ◽  
Bending Loads ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
D Values ◽  
Existing Data

The finite element method has been used to investigate the behaviour of axisymmetric loaded projections (e.g., bolts) subjected to axial tension and bending. The results show that existing data for stepped shafts, which have the axial tension and bending loads applied remote from the region of the step, cannot be applied to loaded projections with the same geometry. For h/d (head thickness to shank diameter ratio) values greater than 0.66 and 0.41 for axial tension and bending, respectively, the stress concentration factors are independent of h/d, load position, and D/d (head diameter to shank diameter ratio) for D/d in the range 1.5 ≤ D/d ≤ 2.0. Smaller h/d values result in large increases in the stress concentration factors due to dishing of the head.

Elastic Stress Concentrations for the Torsion of Hollow Shouldered Shafts Determined by an Electrical Analogue

1964 ◽  
Vol 15 (1) ◽  
pp. 83-96 ◽  
Author(s):  
K. R. Rushton
Keyword(s):  
Stress Concentration ◽  
Elastic Stress ◽  
Plastic Region ◽  
Stress Concentrations ◽  
Electrical Analogue ◽  
Shoulder Diameter ◽  
Concentration Factors ◽  
Stress Concentration Factors

SummaryThe elastic stress concentration factors for the torsion of solid and hollow shouldered shafts have been determined by means of a pure resistance electrical analogue. Fillet radii ranged from 0.05 to 1.0 times the diameter of the smaller shaft, and the shoulder diameter increased from 1.0 to 8.10 times the diameter of the smaller shaft. A comparison is made with the results of other techniques. A study has also been made of the formation of a plastic region in the neighbourhood of the fillet.

The Jacobian Elliptic Functions

2008 ◽  
pp. 671-684
Author(s):  
Keith B. Oldham ◽  
Jan C. Myland ◽  
Jerome Spanier
Keyword(s):  
Elliptic Functions ◽  
Jacobian Elliptic Functions
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