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.

Analysis of Stress Concentrations in Thick Cylinders With Sideholes and Crossholes

1972 ◽  
Vol 94 (3) ◽  
pp. 815-824 ◽  
Author(s):  
J. C. Gerdeen
Keyword(s):  
Stress Concentration ◽  
Stress Concentrations ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Experimental Values ◽  
Pressure Stress ◽  
Shrink Fit ◽  
Outside Diameter ◽  
Theoretical Results

An approximate theoretical analysis is presented for the determination of stress concentration factors in thick walled cylinders with sideholes and crossholes. The cylinders are subjected to both internal pressure and external shrink-fit pressure. Stress concentration factors are plotted as functions of the geometrical ratios of outside diameter-to-bore diameter, and bore diameter-to-sidehole diameter. Theoretical results are compared to experimental values available in the literature and results of experiments described in a separate paper.

Stress concentrations due to axial tension and bending of loaded axisymmetric projections

1983 ◽  
Vol 18 (1) ◽  
pp. 7-14 ◽  
Author(s):  
T H Hyde ◽  
B J Marsden
Keyword(s):  
Stress Concentration ◽  
Diameter Ratio ◽  
The Finite Element Method ◽  
Stress Concentrations ◽  
Axial Tension ◽  
Bending Loads ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
D Values ◽  
Existing Data

The finite element method has been used to investigate the behaviour of axisymmetric loaded projections (e.g., bolts) subjected to axial tension and bending. The results show that existing data for stepped shafts, which have the axial tension and bending loads applied remote from the region of the step, cannot be applied to loaded projections with the same geometry. For h/d (head thickness to shank diameter ratio) values greater than 0.66 and 0.41 for axial tension and bending, respectively, the stress concentration factors are independent of h/d, load position, and D/d (head diameter to shank diameter ratio) for D/d in the range 1.5 ≤ D/d ≤ 2.0. Smaller h/d values result in large increases in the stress concentration factors due to dishing of the head.

Elastic Stress Concentrations for the Torsion of Hollow Shouldered Shafts Determined by an Electrical Analogue

1964 ◽  
Vol 15 (1) ◽  
pp. 83-96 ◽  
Author(s):  
K. R. Rushton
Keyword(s):  
Stress Concentration ◽  
Elastic Stress ◽  
Plastic Region ◽  
Stress Concentrations ◽  
Electrical Analogue ◽  
Shoulder Diameter ◽  
Concentration Factors ◽  
Stress Concentration Factors

SummaryThe elastic stress concentration factors for the torsion of solid and hollow shouldered shafts have been determined by means of a pure resistance electrical analogue. Fillet radii ranged from 0.05 to 1.0 times the diameter of the smaller shaft, and the shoulder diameter increased from 1.0 to 8.10 times the diameter of the smaller shaft. A comparison is made with the results of other techniques. A study has also been made of the formation of a plastic region in the neighbourhood of the fillet.

Stress Concentrations in a Hybrid Composite Sheet

1983 ◽  
Vol 50 (4a) ◽  
pp. 845-848 ◽  
Author(s):  
H. Fukuda ◽  
T. W. Chou
Keyword(s):  
Stress Concentration ◽  
Hybrid Composite ◽  
Fiber Strength ◽  
Series Representation ◽  
High Modulus ◽  
Composite Sheet ◽  
Stress Concentrations ◽  
Low Modulus ◽  
Concentration Factors ◽  
Stress Concentration Factors

This paper examines the load redistribution in a hybrid composite sheet due to fiber breakage. The hybrid composite contains both high modulus and low modulus fibers arranged in alternating positions. Stress concentration factors for both types of fibers immediately adjacent to a group of fractured fibers have been evaluated. The method of influence function and Fourier series representation are adopted. Results of stress concentration factors are presented in terms of the number of fractured fibers and their geometric arrangements. Reduction of the stress concentration factor of the high modulus fibers when dispersed among the low modulus fibers provides a theoretical explanation of the observed “hybrid effect.” The present analysis can be readily incorporated into a failure model taking into account the statistical nature of fiber strength.

Stress concentrations at an oblique hole in a thick flat plate under an arbitrary in-plane biaxial loading

1993 ◽  
Vol 28 (3) ◽  
pp. 223-235 ◽  
Author(s):  
P Stanley ◽  
B J Day
Keyword(s):  
Stress Concentration ◽  
Flat Plate ◽  
Biaxial Loading ◽  
Plate Thickness ◽  
Diameter Ratio ◽  
Hole Diameter ◽  
Stress Concentrations ◽  
Photoelastic Investigation ◽  
Concentration Factors ◽  
Stress Concentration Factors

The results of an extensive ‘frozen-stress’ photoelastic investigation of the stresses at isolated oblique holes in thick wide plates subjected to uniform uniaxial tension are used to provide stress concentration factors at holes resulting from any form of biaxial in-plane loading. The work covers plate thickness/hole diameter ratios from 1.3 to 3.0 and hole obliquity angles up to 60 degrees. Over these ranges the effects of changes in the plate thickness/hole diameter ratio are not of major importance but the effects of changes in the angle of obliquity are considerable.

Stress-Concentration Factors in Shafts With Transverse Holes as Found by the Electroplating Method

1955 ◽  
Vol 22 (2) ◽  
pp. 193-196
Author(s):  
H. Ōkubo ◽  
S. Satō
Keyword(s):  
Stress Concentration ◽  
Outer Surface ◽  
Maximum Stress ◽  
Accurate Determination ◽  
Slicing Method ◽  
Concentration Factors ◽  
Mathematical Difficulties ◽  
Stress Concentration Factors ◽  
Maximum Stresses

Abstract In this paper the torsion of shafts with transverse holes has been investigated experimentally. Usual methods for stress measurements, such as the method of brittle coatings and the use of sensitive extensometers, are not applied effectively to the present problem because the maximum stress occurs in the bore and does not occur on the outer surface of the shaft. The stress may be measured by the stress-freezing and slicing method but we cannot expect too much from this method for the accurate determination of the stress when the diameter of the hole is comparatively small. In treating the problem theoretically, considerable mathematical difficulties are encountered on account of its axially nonsymmetrical nature. The electroplating method recently developed by one of the authors (1), however, has been proved to be useful in this case, so the maximum stresses in shafts are measured by this method and the stress-concentration factors are found for various diameters of the hole.

Stress Concentrations in DT/X Square-to-Square and Square-to-Round Tubular Joints

1994 ◽  
Vol 116 (2) ◽  
pp. 49-55 ◽  
Author(s):  
A. K. Soh ◽  
C. K. Soh
Keyword(s):  
Stress Concentration ◽  
Bending Moment ◽  
Bending Moments ◽  
Axial Loads ◽  
Stress Concentrations ◽  
Tubular Joints ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Plane Bending ◽  
Stress Concentration Factors

A parametric stress analysis of DT/X square-to-square and square-to-round tubular joints subjected to axial loads, in-plane, and out-of-plane bending moments has been performed using the finite element technique in order to provide a sound basis for using such sections in the design of complex structures. The results of this analysis are presented as a set of equations expressing the stress concentration factor as a function of the relevant geometric parameters for various loading conditions. A comparison is made between the results obtained for square-to-square and square-to-round tubular joints and those obtained for round-to-round tubular joints by other researchers. In general, the stress concentration factors for square-to-square tubular joints are the highest, followed by those of the corresponding round-to-round joints, with those of the corresponding square-to-round joints the lowest when the joints are subject to axial loads. In the case of in-plane bending moment, the stress concentration factors for square-to-square joints are generally still the highest, but followed by those of the corresponding square-to-round joints, with those of the corresponding round-to-round joints the lowest. However, the stress concentration factors for the three types of joint are comparable when they are subject to out-of-plane bending moments.

Studies in Three-Dimensional Photoelasticity: Stresses in Bent Circular Shafts With Transverse Holes—Correlation With Results From Fatigue and Strain Measurements

1944 ◽  
Vol 11 (1) ◽  
pp. A10-A16
Author(s):  
M. M. Frocht
Keyword(s):  
Stress Concentration ◽  
Three Dimensional ◽  
Fatigue Tests ◽  
Pure Bending ◽  
Simple Method ◽  
Strain Measurements ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Considerable Work ◽  
Maximum Stresses

Abstract Bent circular shafts with holes in the plane of bending are of frequent occurrence in modern machines. They often form a part of the lubricating system as, for example, in the crankshafts of aircraft engines. Considerable work has been done to determine the maximum stresses and the factors of stress concentration in such shafts. The author presents a simple method of calculating such stresses for transverse holes in pure bending. Experimental photoelastic evidence that led to this method is given. A comparison of the stress-concentration factors obtained by it is made with the published results from fatigue tests and strain measurements from large steel shafts, which were performed a number of years ago at the Westinghouse Research Laboratories.

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.

Stress Concentration Effects in Short Cylindrical Vessels With Holes Subjected to Tension: A Complete Account

2005 ◽  
Vol 127 (2) ◽  
pp. 184-189 ◽  
Author(s):  
Nando Troyani ◽  
Nelson Jaimes ◽  
Gaetano Sterlacci ◽  
Carlos J. Gomes
Keyword(s):  
Stress Concentration ◽  
Elastic Shell ◽  
Critical Factor ◽  
Circular Cylinders ◽  
Stress Concentrations ◽  
Concentration Effects ◽  
Analysis And Design ◽  
Circular Holes ◽  
Concentration Factors ◽  
Stress Concentration Factors

Whenever regular geometric discontinuities are present the so called stress concentration factors concept is widely used in both analysis and design of loaded components especially when subjected to fatigue, frequently the working condition of vessels. However, recent observations suggest that the influence of member length on the magnitude of the stated factors was not considered in previous analyses. In this work, this observation was studied in the context of cylindrical vessels and it was found that in this case, as well, length could be a critical factor when computing stresses developed as a result of externally applied loads. Accordingly, the values of the finite element calculated theoretical stress concentration factors are computed, for the case of short circular cylinders with circular holes subjected to axial tension, in the context of elastic shell theory, and are presented in a fashion similar to existing published results. It is shown that significantly larger stress concentrations appear for shorter members. The transition length concept defining the threshold between long cylinders and short cylinders is discussed in the context of this study and reported as well.

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