Stress Distribution Around a Circular Inclusion in a Semi-Infinite Elastic Plate

1958 ◽  
Vol 25 (1) ◽  
pp. 129-135
Author(s):  
E. M. Saleme
Keyword(s):  
Elastic Plate ◽  
Elastic Moduli ◽  
Infinite Plate ◽  
Circular Inclusion ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Uniform Tension ◽  
Method Of Solution ◽  
In Series ◽  
Axis Of Symmetry

Abstract This paper contains an exact two-dimensional solution in series form for the stresses and displacements around a circular inclusion perfectly bonded to a semi-infinite elastic plate. At infinity the plate is assumed to be in a state of uniform tension parallel to the straight boundary. It should be emphasized, however, that the method of solution presented may be applied to other types of loading. Numerical results are given for the variation along the axis of symmetry of the normal stress which is parallel to the straight boundary, for a given geometry, and various ratios of the elastic moduli of the plate and the inclusion. Finally, the known solutions corresponding to an infinite plate with a circular inclusion and to a semi-infinite plate with a circular hole are obtained as limiting cases.

The Approximate Distribution of Stress in a Finite Plate Having a Stress-Free Circular Cut-Out

1964 ◽  
Vol 68 (639) ◽  
pp. 204-208 ◽  
Author(s):  
H. Waters
Keyword(s):  
Outer Boundary ◽  
Practical Importance ◽  
Infinite Plate ◽  
Approximate Solutions ◽  
Finite Width ◽  
Infinite Length ◽  
Uniform Tension ◽  
Approximate Distribution ◽  
Axis Of Symmetry ◽  
Distribution Of Stress

The distribution of stress in a flat plate having a circular cut-out and subjected to known forces at its outer boundary is of considerable practical importance. Assuming that (i) the plate is thin, so that the problem is one of plane stress, and (ii) the material of which it is formed is isotropic and obeys Hooke's law, exact or approximate solutions have been obtained for a limited number of particular cases. Most of these solutions relate to a plate which is infinite in extent in one or more directions. The case of a plate of finite width and infinite length having a circular hole on the axis of symmetry was discussed by Howland, and by Howland and Stevenson. Wang gave an approximate solution for a perforated shear web, and Mindlin investigated the stress distribution around a hole near the edge of a semi-infinite plate under uniform tension.

Stress Concentration Due to a Hemispherical Pit at a Free Surface

1954 ◽  
Vol 21 (1) ◽  
pp. 57-62
Author(s):  
R. A. Eubanks
Keyword(s):  
Free Surface ◽  
Present Method ◽  
Infinite Medium ◽  
The Body ◽  
Hydrostatic Tension ◽  
Rotationally Symmetric ◽  
Method Of Solution ◽  
In Series ◽  
Axis Of Symmetry ◽  
Plane At Infinity

Abstract This paper contains a solution in series form for the stresses and displacements around a hemispherical pit at a free surface of an elastic body. The problem is idealized by considering a semi-infinite medium which otherwise is bounded by a plane. At infinity the body is assumed to be in a state of plane hydrostatic tension perpendicular to the axis of symmetry of the pit. The present method of solution may be generalized to loadings which are not rotationally symmetric. Numerical results are given for the variation along the axis of symmetry of the normal stress which is parallel to the tractions at infinity; these results are compared with the known corresponding numerical values appropriate to the two-dimensional analog of the present problem.

Steady flow through distorted rectangular tubes of large aspect ratio

1983 ◽  
Vol 385 (1788) ◽  
pp. 107-127 ◽  
Keyword(s):  
Aspect Ratio ◽  
Boundary Layers ◽  
Rectangular Cross Section ◽  
Two Dimensional ◽  
Large Aspect Ratio ◽  
Dimensional Solution ◽  
Method Of Solution ◽  
Flow Through ◽  
High Reynolds ◽  
Sharp Corners

High Reynolds number ( Re ) flows through large aspect ratio ( λμ ) tubes of rectangular cross section are studied. One wall of the tube is slightly deformed to produce a two-dimensional distortion of length λ . We determine conditions for the flow at the centre of the tube and near the distortion to approximate the appropriate two-dimensional solution: namely, λμ ≫ ( λ -1 Re ) 1/6 if Re 1/7 ≲ λ and μ ≫ 1 if Re 1/7 ≳ λ . However, the latter condition needs to be strengthened to λμ ≫ Re 1/7 if the flow is additionally to be approximately two-dimensional far up- and down-stream. The method of solution includes a numerical calculation for the flow in the sharp corners of the tube. We deduce that for sufficiently short distortions ( λ ≪ Re 1/9 (ln Re ) 11/9 ), the sharp corners can effectively isolate disturbances in the wall boundary layers from each other. However, for larger distortions the disturbances in the boundary layers are all of comparable magnitude owing to interactions at the corners. Our examination of the corner regions also enables us to confirm a hypothesis, due to Hocking (1977) and others, that to leading order the pressure is constant in approximately square regions at the sides of the tube.

Effect of Thickness on the Stresses in a Plate With an Elliptic Hole

1977 ◽  
Vol 99 (2) ◽  
pp. 401-403 ◽  
Author(s):  
M. N. Bapu Rao
Keyword(s):  
Circular Hole ◽  
Thick Plate ◽  
Maximum Stress ◽  
Semimajor Axis ◽  
Plate Thickness ◽  
Elliptic Hole ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Uniform Tension

A three-dimensional analysis is presented for the stresses around an elliptic hole in an infinitely long thick plate subjected to uniform tension and shear. The maximum stress is found to depend on the ratio of plate thickness to the length of the semimajor axis of the hole, as well as on Poisson’s ratio. In the limiting cases the solution reduces to that of the circular-hole problem and the two-dimensional solution of the elliptic-hole problem.

Stress Solutions for an Infinite Plate With Triangular Inlay

1956 ◽  
Vol 23 (3) ◽  
pp. 336-338
Author(s):  
R. M. Evan-Iwanowski
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Unit Circle ◽  
Complex Variable ◽  
Boundary Value ◽  
Infinite Plate ◽  
Mapping Function ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Uniform Tension

Abstract The method of solving two-dimensional problems in elasticity by means of the functions of complex variable, essentially developed by É. Goursat (1), and N. I. Muskhelishvili (2-4), has been applied to the following cases: (a) An infinite plate with a rigid triangular inlay under uniform tension at infinity; (b) A concentrated force; and (c) a moment acting on a triangular inlay in an infinite plate. All these problems are second boundary-value problems; i.e., the displacements are prescribed on the boundary. The first boundary-value problem for a triangular opening in an infinite plate was treated by Hu-Nan Chu (7). The mapping function used in this paper is z = ω ( ζ ) = K ( ζ + n ζ 2 ) , K is real, and 0 < n < 1/2 and real, and it maps an exterior of a triangle with rounded corners, Fig. 1, in the z-plane into an exterior of a unit circle in the ζ-plane [for detailed discussion of this mapping refer to (4)].

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.

The Elastic Moduli of Silver Thin Films Measured with a New Microtensile Tester

1991 ◽  
Vol 239 ◽  
Author(s):  
J. Ruud ◽  
D. Josell ◽  
A. L. Greer ◽  
F. Spaepen
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Diffraction Grating ◽  
Strain Measurement ◽  
Elastic Moduli ◽  
Two Dimensional ◽  
Bulk Crystals ◽  
Free Standing ◽  
Tensile Direction ◽  
Silver Thin Films

ABSTRACTA new design for a thin film microtensile tester is presented. The strain is measured directly on the free-standing thin film from the displacement of laser spots diffracted from a thin grating applied to its surface by photolithography. The diffraction grating is two-dimensional, allowing strain measurement both along and transverse to the tensile direction. In principle, both Young's modulus and Poisson's ratio of a thin film can be determined. Ag thin films with strong <111> texture were tested. The measured Young moduli agreed with those measured on bulk crystals, but the measured Poisson ratios were low, most likely due to slight transverse folding of the film that developed during the test.

scholarly journals Elastic Moduli of Collagen Gels Can Be Predicted from Two-Dimensional Confocal Microscopy

2009 ◽  
Vol 97 (7) ◽  
pp. 2051-2060 ◽  
Author(s):  
Ya-li Yang ◽  
Lindsay M. Leone ◽  
Laura J. Kaufman
Keyword(s):  
Confocal Microscopy ◽  
Elastic Moduli ◽  
Two Dimensional ◽  
Collagen Gels
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