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.

Stress Concentration Factors at an Elliptical Hole on the Interface Between Bonded Dissimilar Half-Planes Under Bending Moment

1996 ◽  
Vol 63 (1) ◽  
pp. 7-14 ◽  
Author(s):  
Mohamed Salama ◽  
Norio Hasebe
Keyword(s):  
Stress Concentration ◽  
Elliptical Hole ◽  
Bending Moment ◽  
Mapping Function ◽  
Complex Stress ◽  
Function Technique ◽  
Rational Mapping ◽  
Stress Functions ◽  
Stress Concentration Factors ◽  
Thin Plate Bending

The problem of thin plate bending of two bonded half-planes with an elliptical hole on the interface and interface cracks on its both sides is presented. A uniformly distributed bending moment applied at the remote ends of the interface is considered. The complex stress functions approach together with the rational mapping function technique are used in the analysis. The solution is obtained in closed form. Distributions of bending and torsional moments, the stress concentration factor as well as the stress intensity factor, are given for all possible dimensions of the elliptical hole, various material constants, and rigidity ratios.

A Point Dislocation Interacting with an Elliptical Hole Located at a Bi-Material Interface

2012 ◽  
Vol 151 ◽  
pp. 75-79 ◽  
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe ◽  
P.B.N. Prasad
Keyword(s):  
Conformal Mapping ◽  
Unit Circle ◽  
Half Plane ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Complex Stress ◽  
Complex Variables ◽  
Material Interface ◽  
Rational Mapping ◽  
Point Dislocation

The problem of a point dislocation interacting with an elliptical hole at the interface of two bonded half-planes is studied. Complex stress potentials are obtained by applying the methods of complex variables and conformal mapping. A rational mapping function that maps a half plane with a semi-elliptical notch onto a unit circle is used for mapping the bonded half-planes. The solution derived can serve as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

Debondings at a Semielliptic Rigid Inclusion on the Rim of a Half Plane

1988 ◽  
Vol 55 (3) ◽  
pp. 574-579 ◽  
Author(s):  
N. Hasebe ◽  
S. Tsutsui ◽  
T. Nakamura
Keyword(s):  
Half Plane ◽  
Rigid Inclusion ◽  
Mixed Boundary ◽  
Mapping Function ◽  
Singular Values ◽  
Complex Stress ◽  
Uniform Compression ◽  
Rational Mapping ◽  
Stress Functions ◽  
Clamped Edge

An elastic half plane with a semielliptic rigid inclusion is analyzed as a mixed boundary value problem with a clamped edge. A rational mapping function of a sum of fractional expressions and the complex stress functions are used for the analysis. The debondings emanated from both ends of the semielliptic inclusion under uniform tension is examined and singular values of the stress at the debonded tips are obtained. By using these values, it is examined for some elliptical shapes how the debonding propagates. The stress values at the base of the semielliptic inclusion are also examined. Even if the loading is uniform compression, the debonding may occur at the base.

Compressibility of Two-Dimensional Cavities of Various Shapes

1986 ◽  
Vol 53 (3) ◽  
pp. 500-504 ◽  
Author(s):  
R. W. Zimmerman
Keyword(s):  
Closed Form Solution ◽  
Mapping Function ◽  
Complex Stress ◽  
Form Solution ◽  
Hydrostatic Compression ◽  
Biaxial Compression ◽  
Cavity Surface ◽  
Uniform Pressure ◽  
Two Dimensional ◽  
Stress Functions

Muskhelishvili-Kolosov complex stress functions are used to find the stresses and displacements around two-dimensional cavities under plane strain or plane stress. The boundary conditions considered are either uniform pressure at the cavity surface with vanishing stresses at infinity, or a traction-free cavity surface with uniform biaxial compression at infinity. A closed-form solution is obtained for the case where the mapping function from the interior of the unit circle to the region outside of the cavity has a finite number of terms. The area change of the cavity due to hydrostatic compression at infinity is examined for a variety of shapes, and is found to correlate closely with the square of the perimeter of the hole.

Analysis of the Second Mixed Boundary Value Problem for a Thin Plate

1994 ◽  
Vol 61 (3) ◽  
pp. 555-559 ◽  
Author(s):  
Norio Hasebe ◽  
Takuji Nakamura ◽  
Yoshihiro Ito
Keyword(s):  
Boundary Value Problem ◽  
Thin Plate ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mapping Function ◽  
Complex Stress ◽  
Mixed Boundary Value Problem ◽  
Rational Mapping ◽  
Before And After ◽  
External Forces

The second mixed boundary value problem is solved by the classical theory of thin plate bending. The mixed boundary consists of a boundary (M) on which one respective component of external force and deflective angle are given, and on the remaining boundary the external forces are given. The boundary (M) is straight and the remaining boundary is arbitrary configuration. A closed solution is obtained. Complex stress functions and a rational mapping function are used. A half-plane with a crack is analyzed under a concentrated torsional moment. Stress distributions before and after the crack initiation, and stress intensity factors are obtained for from short to long cracks and for some Poisson’s ratio.

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.

Engineering Procedure for Calculation of Elastic Stress Concentration Factors of Bearing Pad Fretting Flaws

2009 ◽  
Author(s):  
Bogdan S. Wasiluk ◽  
Douglas A. Scarth
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Crack Initiation ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Elastic Stress ◽  
Elliptical Hole ◽  
Flat Bottom ◽  
Concentration Factors ◽  
Stress Concentration Factors

Procedures to evaluate volumetric bearing pad fretting flaws for crack initiation are in the Canadian Standard N285.8 for in-service evaluation of CANDU® pressure tubes. The crack initiation evaluation procedures use equations for calculating the elastic stress concentration factors. Newly developed engineering procedure for calculation of the elastic stress concentration factor for bearing pad fretting flaws is presented. The procedure is based on adapting a theoretical equation for the elastic stress concentration factor for an elliptical hole to the geometry of a bearing pad fretting flaw, and fitting the equation to the results from elastic finite element stress analyses. Non-dimensional flaw parameters a/w, a/c and a/ρ were used to characterize the elastic stress concentration factor, where w is wall thickness of a pressure tube, a is depth, c is half axial length, and ρ is root radius of the bearing pad fretting flaw. The engineering equations for 3-D round and flat bottom bearing pad fretting flaws were examined by calculation of the elastic stress concentration factor for each case in the matrix of source finite element cases. For the round bottom bearing pad fretting flaw, the fitted equation for the elastic stress concentration factor agrees with the finite element results within ±3.7% over the valid range of flaw geometries. For the flat bottom bearing pad fretting flaw, the fitted equation agrees with the finite element results within ±4.0% over the valid range of flaw geometries. The equations for the elastic stress concentration factor have been verified over the valid range of flaw geometries to ensure accurate results with no anomalous behavior. This included comparison against results from independent finite element calculations.

Bearing Strength Analysis of Pin-Loaded Elliptical Holes in Laminated Composite Joints

2011 ◽  
Author(s):  
O. Aluko ◽  
H. A. Whitworth
Keyword(s):  
Characteristic Curve ◽  
Laminated Composite ◽  
Complex Stress ◽  
Strength Analysis ◽  
Orthotropic Plates ◽  
Bearing Strength ◽  
Mode Of Failure ◽  
Curve Model ◽  
Stress Functions ◽  
Elliptical Holes

An analysis was performed to predict bearing strength and mode of failure of pin loaded orthotropic plates with elliptic holes of varying sizes using two dimensional stress analyses and a characteristic curve model. The stresses required to analyze joint failure were obtained by utilizing complex stress functions that were determined from assumed displacement expressions that satisfy the boundary conditions around the hole. Three different joint geometries with major-to-minor diameter ratios ranging from 1 to 5 were evaluated and the analysis revealed that the joint strength was found to vary with increasing major-to-minor diameter ratios. The material properties of graphite/epoxy laminates were used in this investigation.

Howland’s isotropic Kts curve for plates with circular holes as a master curve for Kts in orthotropic plates with elliptical holes

2017 ◽  
Vol 52 (3) ◽  
pp. 152-161 ◽  
Author(s):  
Nando Troyani ◽  
Milagros Sánchez
Keyword(s):  
Stress Concentration ◽  
Master Curve ◽  
Orthotropic Materials ◽  
Finite Width ◽  
Rectangular Plates ◽  
Analysis And Design ◽  
Circular Holes ◽  
Elliptical Holes ◽  
Concentration Factors ◽  
Stress Concentration Factors

The importance of the role played by the so-called stress concentration factors (or symbolically referred to as Kts) in analysis and design in both mechanical and structural engineering is a well-established fact, and accuracy and ease in their estimation result in significant aspects related to engineering costs, and additionally on both the reliability in the design of parts and/or in the analysis of failed members. In this work, rectangular finite width plates of both isotropic and orthotropic materials with circular and elliptical holes are considered. Based on two key observations reported herein, it is shown in a partially heuristic engineering sense, that Howland’s solution curve for the stress concentration factors for finite width plates with circular holes subjected to tension can be viewed as a master curve; accordingly, it can be used as a basis to rather accurately estimate stress concentration factors for isotropic finite width tension rectangular plates with centered elliptical holes and also rather accurately used to estimate stress concentration factors for orthotropic finite width rectangular plates under tension with centered elliptical holes. Two novel concepts are defined and presented to this effect: geometric scaling and material scaling. In all the examined and reported cases, the specific numerical results can be obtained accurately using a hand-held calculator making virtually unnecessary the need to program and/or use other complex programs based on the finite element method, just as an example. The maximum recorded average error for all the considered cases being 2.62% as shown herein.

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