Solution of the Displacement Boundary Value Problem of an Interface Between Two Dissimilar Half-Planes and a Rigid Elliptic Inclusion at the Interface

1998 ◽  
Vol 65 (4) ◽  
pp. 880-888 ◽  
Author(s):  
V. Boniface ◽  
N. Hasebe
Keyword(s):  
Stress Concentration ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Function Technique ◽  
Bimaterial Interface ◽  
Radius Of Curvature ◽  
Elliptic Inclusion ◽  
Displacement Boundary ◽  
Concentration Factors ◽  
Stress Concentration Factors

The displacement boundary value problem of a bimaterial interface is solved using the complex stress function technique. A rational mapping function is used to map the two half-planes into unit circles and analysis is carried out in the mapped plane. The symmetric bimaterial problem is considered and the particular case of a rigid elliptic inclusion at the interface is solved. Uniform remote tensions both along and normal to the interface are considered. Stress distributions on the inclusion boundary are shown. Stress concentration factors at the inclusion tips are obtained and are expressed in terms of the radius of curvature using an approximate form of a general expression. These results are used to predict the likelihood of debonding/cracking at the tips. Also, stress concentration factors at the tips of an elliptic inclusion and elliptic void are compared. Stress intensity factors at the tips of a thin rigid elliptic inclusion are also determined.

Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jialu Wang ◽  
Xiaoyuan Liu
Keyword(s):  
Stress Concentration ◽  
Radius Of Curvature ◽  
Tension Stress ◽  
Generalized Equations ◽  
Stress Concentrations ◽  
Minimum Thickness ◽  
Flexure Hinges ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Maximum Stresses

The flexure hinges are the most vulnerable parts in a flexure-based mechanism due to their smaller dimensions and stress concentration characteristics, therefore evaluating the maximum stresses generated in them is crucial for assessing the workspace and the fatigue life of the mechanism. Stress concentration factors characterize the stress concentrations in flexure hinges, providing an analytical and efficient way to evaluate the maximum stress. In this work, by using the ratio of the radius of curvature of the stress-concentrating feature to the minimum thickness as the only fitting variable, generalized equations for both the bending and tension stress concentration factors were obtained for two generalized models, the conic model and the elliptic-arc-fillet model, through fitting the finite element results. The equations are applicable to commonly used flexure hinges including circular, elliptic, parabolic, hyperbolic, and various corner-fillet flexure hinges, with acceptable errors. The empirical equations are tractable and easy to be employed in the design and optimization of flexure-based mechanisms. The case studies of the bridge-type displacement amplifiers demonstrated the effectiveness of the generalized equations for predicting the maximum stresses in flexure-based mechanisms.

The Effect of a Rigid Elliptic Inclusion on the Bending of a Thick Elastic Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 379-382
Author(s):  
Fu Chow
Keyword(s):  
Stress Concentration ◽  
Elastic Plate ◽  
Plate Theory ◽  
Circular Inclusion ◽  
Elliptic Inclusion ◽  
Focal Distance ◽  
Classical Plate Theory ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Rigid Circular Inclusion

The effect of a rigid elliptic inclusion on both plain bending and pure twist of a thick elastic plate is investigated on the basis of Reissner’s plate theory [1, 2]. Comparison is made for the limiting cases of vanishing focal distance of the elliptic inclusion (a rigid circular inclusion), and vanishing thickness (Poisson-Kirchhoff plate theory), with the solutions of C. Pai [3], R. A. Hirsch [4], and M. Goland [5]. The stress-concentration factors are lower than those predicted by the classical plate theory.

scholarly journals Stress Concentration Factors for Welded Plate T-Joints Subjected to Tensile, Bending and Shearing Loads

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 546
Author(s):  
Krzysztof L. Molski ◽  
Piotr Tarasiuk
Keyword(s):  
Stress Concentration ◽  
Plate Thickness ◽  
Percentage Error ◽  
Geometrical Parameters ◽  
T Joints ◽  
Loading Mode ◽  
Weld Toe ◽  
Concentration Factors ◽  
Parametric Expression ◽  
Stress Concentration Factors

The paper deals with the problem of stress concentration at the weld toe of a plate T-joint subjected to axial, bending, and shearing loading modes. Theoretical stress concentration factors were obtained from numerical simulations using the finite element method for several thousand geometrical cases, where five of the most important geometrical parameters of the joint were considered to be independent variables. For each loading mode—axial, bending, and shearing—highly accurate closed form parametric expression has been derived with a maximum percentage error lower than 2% with respect to the numerical values. Validity of each approximating formula covers the range of dimensional proportions of welded plate T-joints used in engineering applications. Two limiting cases are also included in the solutions—when the weld toe radius tends to zero and the main plate thickness becomes infinite.

Stress Analysis of Holes in Thick Plates

2004 ◽  
Vol 1-2 ◽  
pp. 153-158 ◽  
Author(s):  
S. Quinn ◽  
Janice M. Dulieu-Barton
Keyword(s):  
Stress Concentration ◽  
Stress Analysis ◽  
Uniaxial Tension ◽  
Plane Stress ◽  
Plate Surface ◽  
Flat Plates ◽  
Thick Plates ◽  
Concentration Factors ◽  
Stress Concentration Factors

A review of the Stress Concentration Factors (SCFs) obtained from normal and oblique holes in thick flat plates loaded in uniaxial tension has been conducted. The review focuses on values from the plate surface and discusses the ramifications of making a plane stress assumption.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

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