The effect of a hole on certain stress distributions in aeolotropic and isotropic plates

1944 ◽  
Vol 40 (2) ◽  
pp. 172-188 ◽  
Author(s):  
S. Holgate
Keyword(s):  
Circular Hole ◽  
Infinite Plate ◽  
Complex Stress ◽  
Stress Distributions ◽  
Finite Form ◽  
Isotropic Materials ◽  
Isotropic Plates ◽  
General Manner ◽  
Alternative Method ◽  
Stress Functions

1. The problems of stress distributions in an infinite plate containing a circular hole were solved in a general manner by Bickley(1) for isotropic materials. An alternative method, using complex stress functions, was later given by Green(5) and extended so as to apply to aeolotropic materials. In the present paper Green's method is employed to determine the stress distributions that arise when the stresses are produced by isolated forces acting at points on, or near to, the edge of the circular hole, and though some of the solutions are cumbersome they are all obtained in finite form.

Forces on a Circular Hole Located in Functionally Graded Material

2011 ◽  
Vol 704-705 ◽  
pp. 631-635
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Circular Hole ◽  
Constant Term ◽  
Complex Stress ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Dimensional Problem ◽  
Stress Components ◽  
Graded Material ◽  
Stress Functions ◽  
Stress Function Method

The complex stress function method is used in this study to formulate the 2-dimensional problem for nonhomogeneous materials. The Young’s modulus E varies linearly with the coordinate x and the Poisson’s ratio of the material is assumed constant and. The stress components and the boundary conditions are expressed in terms of two complex stress functions in explicit forms. It is noted that the constant term in stress functions has an influence on the stress components, which is different from the homogeneous material case. Subsequently, the problem of a nonhomogeneous plane containing a circular hole subjected to a uniform internal pressure is studied.

Contact Stress Analysis Around Elliptic Pin-Loaded Holes in Orthotropic Plates

2010 ◽  
Author(s):  
O. Aluko ◽  
H. A. Whitworth
Keyword(s):  
Coulomb Friction ◽  
Complex Stress ◽  
Stress Distributions ◽  
Orthotropic Plates ◽  
Carbon Fiber Reinforced Plastics ◽  
Reinforced Plastics ◽  
Method Of Solution ◽  
Stress Functions ◽  
Fiber Reinforced Plastics ◽  
Lower Magnitude

This analysis utilizes the complex stress function approach to obtain the stress distribution in pin loaded composite joints with elliptic openings. The stress functions were derived from assumed displacement expressions that satisfy the boundary conditions around the hole. In the method of solution Coulomb friction was used to determine the prescribed displacements at the boundary. The material properties of graphite/epoxy and carbon fiber reinforced plastics laminates were used in this investigation and the results also compared with available data for joints with circular openings. It was revealed that the stress distributions followed the same pattern in both geometries but with lower magnitude in elliptical shape and the reduction in stress distributions caused by changing the pin/hole shape from circular to elliptic depend on friction.

Notes on problems in hexagonal aeolotropic materials

1951 ◽  
Vol 47 (2) ◽  
pp. 401-409 ◽  
Author(s):  
R. T. Shield
Keyword(s):  
General Solution ◽  
Stress Function ◽  
Harmonic Functions ◽  
Present Note ◽  
Three Dimensional ◽  
Stress Distributions ◽  
Axially Symmetric ◽  
Isotropic Materials ◽  
Stress Functions ◽  
Single Stress

Three-dimensional stress distributions in hexagonal aeolotropic materials have recently been considered by Elliott(1, 2), who obtained a general solution of the elastic equations of equilibrium in terms of two ‘harmonic’ functions, or, in the case of axially symmetric stress distributions, in terms of a single stress function. These stress functions are analogous to the stress functions employed to define stress systems in isotropic materials, and in the present note further problems in hexagonal aeolotropic media are solved, the method in each case being similar to that used for the corresponding problem in isotropic materials. Because of this similarity detailed explanations are unnecessary and only the essential steps in the working are given below.

scholarly journals Stress systems in aeolotropic plates. IV

1942 ◽  
Vol 180 (981) ◽  
pp. 173-208 ◽  
Keyword(s):  
Circular Hole ◽  
Elastic Constants ◽  
Complex Variable ◽  
Isotropic Plate ◽  
Poisson's Ratio ◽  
Stress Distributions ◽  
Numerical Work ◽  
Zero Force ◽  
Isotropic Materials ◽  
Method Of Solution

Stress distributions in an aeolotropic plate containing a circular hole are discussed theoretically when the material of the plate has two directions of sym metry at right angles to one another. Some examples of stress distributions are included which have non-zero force resultants on the edge of the hole, corresponding to cases in isotropic materials for which the solution is dependent on Poisson’s ratio. The use of the complex variable makes the method of solution comparatively simple, and as an introduction to the work for an aeolotropic material the same method is applied to problems of stresses in an isotropic plate containing a circular hole in order to obtain results which Bickley previously found by another method. Numerical work is carried out using the elastic constants found in experiments with specimens cut from the highly aeolotropic materials spruce and oak.

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.

Bonded Bi-material Half-Planes With Semi-elliptical Notch Under Tension Along the Interface

1992 ◽  
Vol 59 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Norio Hasebe ◽  
Mikiya Okumura ◽  
Takuji Nakamura
Keyword(s):  
Stress Concentration ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Approximate Expression ◽  
Complex Stress ◽  
Stress Distributions ◽  
Rational Mapping ◽  
Stress Functions ◽  
Elliptical Holes ◽  
Stress Concentration Factors

A problem of two bonded, dissimilar half-planes containing an elliptical hole on the interface is solved. The external load is uniform tension parallel to the interface. A rational mapping function and complex stress functions are used and an analytical solution is obtained. Stress distributions are shown. Stress concentration factors are also obtained for arbitrary lengths of debonding and for several material constants. In addition, an approximate expression of the stress concentration factor is given for elliptical holes and the accuracy is investigated.

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.

Accurate Calculation of Stress Distributions in Multiholed Plates

1965 ◽  
Vol 87 (3) ◽  
pp. 331-335 ◽  
Author(s):  
L. E. Hulbert ◽  
F. W. Niedenfuhr
Keyword(s):  
Computer Program ◽  
Plane Stress ◽  
Symmetric Groups ◽  
Thin Plates ◽  
Stress Distributions ◽  
Accurate Calculation ◽  
Point Matching ◽  
Shallow Shells ◽  
Matching Technique ◽  
Stress Functions

This paper discusses the application of the point-matching technique in obtaining the solution of many problems involving multiholed thin plates undergoing generalized plane stress. The stress functions appropriate to plates with symmetric groups of holes are described. A large number of problems solved by a computer program are described and compared with published results. Problems are solved also for which there are no known published results. Two interesting new problems are discussed in detail. The results show the power and flexibility of the technique. The extension of the methods to permit the solution of problems in the deflection of thin, multiholed plates and shallow shells is discussed.

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