scholarly journals ANALYTICAL STUDY ABOUT THE BENDING OF ELASTIC PLATES WITH OPENING HOLE UNDER UNIFORM LOAD : Part 1 : Square Plates with Eccentic Circular Hole

1979 ◽  
Vol 280 (0) ◽  
pp. 39-51
Author(s):  
TERUZI IWAHARA
Keyword(s):  
Circular Hole ◽  
Analytical Study ◽  
Elastic Plates ◽  
Uniform Load

scholarly journals Stress Intensity Factors for a Non-Circular Hole with Inclusion Layer Embedded in a Cracked Matrix

Aerospace ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 17
Author(s):  
Chenchun Chiu ◽  
Shaochen Tseng ◽  
Chingkong Chao ◽  
Jheyuan Guo
Keyword(s):  
Stress Intensity ◽  
Circular Hole ◽  
Composite Structures ◽  
Failure Behavior ◽  
Uniform Load ◽  
Intensity Factors ◽  
Variable Theory ◽  
Complex Variable Theory ◽  
The Matrix ◽  
Stress Functions

The failure analysis of a non-circular hole with an inclusion layer embedded in an infinite cracked matrix under a remote in-plane uniform load is presented. In this study, a series solution of stress functions for both the matrix and inclusion layer is obtained using the complex variable theory in conjunction with the method of conformal mapping. The stress intensity factor (SIF) can then be determined numerically by solving the singular integral equation (SIE) for the interaction among different crack sites, material properties, and geometries of irregular holes with an inclusion layer. In particular, the failure behavior of composite structures associated with an approximately triangular hole and an approximately square hole with inclusion layers, such as those of oxides, nitrides, and sulfides, is examined in detail. The results demonstrate that a softer layer would enhance the SIF and a stiffer layer would restrain the SIF when a crack is near the inclusion layer. It can be concluded that crack propagation would be suppressed by a stiffer layer even when a micro-defect such as a hole resides in the inclusion layer.

Bending of an Annularly Loaded Square Plate With a Central Circular Hole

1982 ◽  
Vol 104 (3) ◽  
pp. 544-550
Author(s):  
L. K. Oja ◽  
G. L. Kinzel ◽  
A. W. Leissa
Keyword(s):  
Circular Hole ◽  
Systematic Approach ◽  
Bending Moment ◽  
Outer Edge ◽  
Loading Conditions ◽  
Uniform Load ◽  
Approximate Methods ◽  
Point Matching ◽  
Plate Size ◽  
Plate Bending Problem

Although uniformly loaded square plates with round holes are analyzed in several references, a systematic approach to the analysis for a ring load does not appear to have been presented before. As in the case of the uniform load, the exact solution to the plate bending problem for an annular load about a central circular hole cannot be developed in closed form; however, accurate approximate methods can be developed. The method employed in this paper uses least-squares point-matching for the boundary conditions along the straight edges and the singularity-function approach for the radially discontinuous loading conditions. Deflection and bending-moment results in the form of curves are presented for selected ratios of hole diameter to plate size and for different annular loading conditions. Both simply supported and clamped boundaries at the outer edge are considered while the inner edge is assumed to be free.

scholarly journals An Analytical Approach to Obtaining the Stress Field of a Cylindrical Shell with a Circular Hole under Tension

2021 ◽  
pp. 64-75
Author(s):  
S. V Kashtanova ◽  
A. V Rzhonsnitskiy
Keyword(s):  
Cylindrical Shell ◽  
Circular Hole ◽  
Main Parameter ◽  
Analytical Approach ◽  
Analytical Study ◽  
Infinite System ◽  
Basis Functions ◽  
Exact Equation ◽  
Algebraic Equations ◽  
Mechanical Nature

The problem of a cylindrical shell with a circular hole under uniaxial tension is considered. The main obstacle of solving this problem is the necessity to find such coefficients in the expansion of the solution into a sum of basis functions, for which this solution satisfies the boundary conditions. The study of the classical works led to understanding that none of the so far proposed approaches can be considered successfully, and the results of these approaches differ, so it is not clear, which results can be used as a basis. In the present paper, a new analytical approach to studying this issue is proposed. It allows expanding the range of applicability of the solution and gives the opportunity for the analytical study of the stress state. The idea consists in expanding each of the basis functions in a Fourier series by dividing the variables, which allows obtaining explicitly an infinite system of algebraic equations for finding coefficients. One of the important steps of this research is that the authors were able to prove which exact equation is a linear combination of the others and exclude, which made it possible to compose a reduced system for finding unknown coefficients. The proposed approach, in contrast to most classical works, does not impose mathematical restrictions on the values of the main parameter characterizing the cylindrical shell. The existing restrictions are of mechanical nature, as larger cutouts require another model. Moreover, the numerical results obtained by the new method are presented in a fairly complete manner and they are compared with the results of the classical works.

scholarly journals Ray analysis and punching problems for stretched elastic plates

1982 ◽  
Vol 24 (1) ◽  
pp. 98-119 ◽  
Author(s):  
T. Bryant Moodie ◽  
R. J. Tait ◽  
D. W. Barclay
Keyword(s):  
Uniaxial Tension ◽  
Circular Hole ◽  
Transversely Isotropic ◽  
Simple Algebra ◽  
Numerical Results ◽  
Graphical Form ◽  
Elastic Plates ◽  
Ray Method ◽  
Propagation Process ◽  
Isotropic Plates

AbstractThe present paper presents a ray analysis for a problem of technical importance in fragmentation studies. The problem is that of suddenly punching a circular hole in either isotropic or transversely isotropic plates subjected to a uniaxial tension field. The ray method, which involves only differentiation, integration, and simple algebra, is shown to be particularly useful in clarifying the propagation process of the resulting unloading waves and obtaining the attendant discontinuities of the various quantities involved. Numerical results obtained from the ray analysis are presented in graphical form and compared with those obtained by more elaborate schemes.

scholarly journals X. The distribution of stress round a circular hole in a plate

1928 ◽  
Vol 227 (647-658) ◽  
pp. 383-415 ◽  
Keyword(s):  
Circular Hole ◽  
Stress Function ◽  
Elastic Solid ◽  
Point Of View ◽  
Engineering Practice ◽  
Elastic Plates ◽  
Circular Boundary ◽  
Tension Member ◽  
Method Of Solution ◽  
Paper Plane

The study of stress distributions in elastic plates would seem to have many important applications in engineering practice, and from this point of view it is, at first sight, surprising that our knowledge of the subject is not more detailed than it is at present. True, the fact that the stresses are derivable from a stress-function, and the equation satisfied by this stress-function, have long been known; particular solutions, satisfying the types of boundary condition met with in practice are, however, rare. Jeffery, in his paper, “Plane Stress and Plane Strain in Bipolar Co-ordinates, says that in the problem of the equilibrium of an elastic solid“ knowledge comes by patient accumulation of special solutions rather than by the establishment of great general propositions ”and later, that“ it is of considerable importance that the two-dimensional problems should be worked out more thoroughly The present paper is an attempt to fill one gap by a fairly full examination of the stresses round a circular hole in an otherwise infinite elastic plate of uniform thickness, due to prescribed tractions in the plane of the plate, acting on the circular boundary. A general solution is obtained and particular cases are examined in detail, these cases being chosen to combine, as far as possible, mathematical simplicity with some semblance of the type of distribution of traction likely to occur in practice ; the analysis is also applied to examine some experimental results obtained in the Engineering Laboratories of University College by Prof. E. G. Coker and T. Fukuda. The attention of the author was first turned to this type of problem in 1919 by Prof. Coker , whose experimental method of solution is now well known. He suggested an attempt to calculate mathematically the stresses in the neighbourhood of a circular hole in a tension member. An exact solution was not obtained, and an approximate one is only applicable when the diameter of the hole is very small compared to the width of the member. In the course of the investigation, however, it became necessary to find the stresses due to a simple distribution of traction on the circular boundary, and difficulties were met with when the traction did not form a system in equilibrium.

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