Contact Stress Between Two-Dimensional Finite Elastic Bodies

1969 ◽  
Vol 36 (3) ◽  
pp. 397-402 ◽  
Author(s):  
D. O. Blackketter ◽  
H. D. Christensen
Keyword(s):  
Trigonometric Series ◽  
Contact Stress ◽  
Surface Load ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Rectangular Shape ◽  
Elastic Bodies ◽  
Theoretical Stress ◽  
Contact Stress Distribution ◽  
Good Agreement

A method is presented for determining the contact stress distribution between two two-dimensional finite elastic bodies with general surface configurations. The bodies treated are nearly rectangular with surfaces which deviate from the rectangular shape by a small amount. The approximate method used involves a solution to the partial differential equations of elasticity for surface load expressed in terms of a trigonometric series. The coefficients of the trigonometric series are evaluated by enforcement of the appropriate constraint conditions. Experimental and theoretical stress distributions are compared and are in good agreement.

Simple Model for Contact Stress of Strands Bent over Circular Saddles

2016 ◽  
Author(s):  
Sherif Mohareb ◽  
Arndt Goldack ◽  
Mike Schlaich
Keyword(s):  
Simple Model ◽  
Stress Distribution ◽  
Contact Force ◽  
Contact Stress ◽  
Flexural Rigidity ◽  
Strong Nonlinearity ◽  
Stress Distributions ◽  
Maximum Contact ◽  
Contact Stress Distribution ◽  
Peak Value

Cable-stayed and extra-dosed bridges are today widely used bridge types. Recently, saddles have been used to deviate strands of cables in the pylons. Up to now the mechanics of strands on saddles are not well understood. It was found, that typical longitudinal contact stress distributions between strand and saddle show a strong nonlinearity and a high peak value around the detachment point, where the strand meets the saddle. This paper presents a procedure to analyse the longitudinal contact stress distribution obtained by FEM calculations: This contact stress can be idealised as a constant contact stress according to the Barlow's formula and a contact force at the detachment point due to the flexural rigidity of the bent tension elements. An analytical model is provided to verify this contact force. Finally, a formula is presented to calculate the maximum contact stress. This study provides the basis for further research on saddle design and fatigue of strands.

An Analysis of Circular Bolted Flanged Joints on Solid Round Bars Subjected to External Bending Moments

2000 ◽  
Author(s):  
Toshiyuki Sawa ◽  
Tsuneshi Morohoshi ◽  
Akihiro Shimizu
Keyword(s):  
Stress Distribution ◽  
Contact Stress ◽  
Three Dimensional ◽  
Bending Moment ◽  
Theory Of Elasticity ◽  
Load Factor ◽  
Bending Moments ◽  
Sealing Performance ◽  
Contact Stress Distribution ◽  
Good Agreement

Abstract In designing bolted joints, it is important to know the contact stress distribution which governs the clamping effect or the sealing performance and to estimate the load factor (the ratio of an increment in axial bolt force to an external load) from bolt design standpoint. The clamping force by bolts and the external bending moment are axi-asymmetrical loads and not many investigations have seen reported which treat axi-asymmetrical. In this paper, the clamping effect, and the load factor for the case of solid round bars with circular flanges, subjected to external bending moments, are analyzed as an axi-asymmetrical problem using the three-dimensional theory of elasticity. Experiments were carried out concerning the contact stress distribution, and the load factor for the external bending moment (a relationship between an increment in axial bolt force, and external bending moment). The analytical results were in fairly good agreement with the experimental ones.

FEM Stress Analyses of the Contact Stress Distributions at the Bearing Surfaces in Bolted Joints Using Hexagon Bolts With Flanges

2010 ◽  
Author(s):  
Yukio Morozumi ◽  
Masahiko Okumura ◽  
Toshiyuki Sawa ◽  
Kengo Kuwaki
Keyword(s):  
Stress Distribution ◽  
Contact Stress ◽  
Slope Angle ◽  
Bolted Joints ◽  
Stress Distributions ◽  
Bearing Surface ◽  
Permanent Set ◽  
Flange Thickness ◽  
The Difference ◽  
Contact Stress Distribution

In designing bolted joints, it is important to understand the contact stress distribution and permanent set at the bearing surface in the case of high initial axial tension. They are investigated using elasto-plastic FEM for hexagon bolts with flange. It is found that the difference in the contact stress distribution is large between elastic FEM and elasto-plastic FEM. Effects of the flange thickness and the flange slope angle on the contact stress distribution and permanent set are examined, and it is shown that they are substantially influential. In the experiments, hollow cylindrical specimens are compressed by the bolts with flange and permanent sets are measured at the bearing surface. The permanent sets are compared with permanent sets obtained from the elasto-plastic FEM and they are in a fairly good agreement. In addition, the equivalent length for the hexagon bolt with flange is proposed.

Two-Dimensional Stress Analysis and the Strength Estimation of Adhesive Butt Joints Under Static Tensile Loadings and Bending Moments

2005 ◽  
Author(s):  
Toshiyuki Sawa ◽  
Yosuke Akita
Keyword(s):  
Stress Analysis ◽  
Stress Singularity ◽  
Adhesive Bond ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Bending Moments ◽  
Stress Distributions ◽  
Butt Joints ◽  
Static Tensile ◽  
Good Agreement

This paper deals with a two-dimensional stress analysis of adhesive butt joints under static tensile loading and bending moments in order to contribute to an establishment of the fracture criteria of joints. Similar adherends and an adhesive bond are replaced with finite strips in the analyses. Stress distributions in adhesive joints are analyzed strictly by using the two-dimensional theory of elasticity. The effects of stiffness and thickness of adhesive bonds on the stress distributions at the interfaces are shown by numerical computations. It is found that the stress singularity occurs at the ends of the interfaces. For verification, experiments to measure the strains and the strength were carried out. The analytical results are in fairly good agreement with the experimental ones. In addition, the analytical result is also compared with the result obtained by F.E.M in order to verify the stress distributions at the interfaces. It is shown that are in a fairly good agreement.

An Analytical Model for Predicting Contact Stress and Sliding Wear of a Three-Dimensional Textured Surface

2009 ◽  
Author(s):  
Elon J. Terrell ◽  
C. Fred Higgs
Keyword(s):  
Stress Distribution ◽  
Stress Analysis ◽  
Analytical Model ◽  
Contact Stress ◽  
Sliding Wear ◽  
Flat Surface ◽  
Three Dimensional ◽  
Textured Surface ◽  
Two Dimensional ◽  
Contact Stress Distribution

In this paper, an analytical model for predicting the contact stress and wear distribution between a textured surface and a compliant flat is presented. The modeling formulation is based upon a two-dimensional stress analysis of the flat, and it allows the contact stress distribution to be found from the distribution of the sample deflection into the flat surface. The wear evolution was calculated from the contact stress.

Stress Distribution in Rotating Discs with Non-Central Holes

1964 ◽  
Vol 15 (2) ◽  
pp. 107-121 ◽  
Author(s):  
W. A. Green ◽  
G. T. J. Hooper ◽  
R. Hetherington
Keyword(s):  
Stress Distribution ◽  
Numerical Solution ◽  
Plane Stress ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Uniform Thickness ◽  
Dimensional Model ◽  
One Dimensional ◽  
Rotating Discs ◽  
Good Agreement

SummaryThe stress distribution in rotating circular discs containing a central hole and a symmetrical array of non-central holes is determined by numerical solution of the equations of generalised plane stress. Particular attention is given to an annulus containing the holes and of width approximately eight hole diameters, in which the full two-dimensional equations are solved. The region outside this annulus is treated as radially symmetric and the stresses there are determined from a simpler one-dimensional model. Stress distributions are reported for uniform discs of fixed geometry containing 10, 20 and 45 holes. Results are also obtained for 20-hole discs of non-uniform thickness comprising a uniformly tapered disc, a disc with a thickened annulus containing the holes, and a uniform disc with each hole surrounded by thickened bosses. As a check on the numerical method, calculations have been carried out on a disc of identical geometry to one examined photoelastically bv Leist and Weber with good agreement. The effect of changing Poisson's ratio for this particular disc is also examined.

Variations in Contact Stress Distribution of Real Rough Surfaces During Running-In

1993 ◽  
Vol 115 (4) ◽  
pp. 602-606 ◽  
Author(s):  
Xian Liang ◽  
Ji Kaiyuan ◽  
Ju Yongqing ◽  
Chen Darong
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Contact Stress ◽  
Dimensionless Parameter ◽  
Gradual Increase ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Stress Distributions ◽  
Exponential Form ◽  
Contact Stress Distribution

A numerical model for the elastic contact of three-dimensional real rough surfaces has been developed and applied to the study of the variations in contact stress distribution in running-in process. The specimens for calculation and experiment are washers with nominally flat grinding surfaces. The stresses of real contact between specimens at each stage of running-in are calculated and the contact stress distributions are given. It is shown that the contact stress distribution is in an exponential form which could be characterized by one dimensionless parameter: λ, the index of contact stress distribution. The proportion of plastic deformation β may be expressed as a function of λ. The results of the present work confirm the reasonableness of the early opinion that the running-in process can be considered as a gradual increase in the elastic component of deformation of the contact area and a decrease in the proportion of plastic deformation.

Contact stress variations near the insulated rail joints

2002 ◽  
Vol 216 (4) ◽  
pp. 265-273 ◽  
Author(s):  
Y. C. Chen ◽  
J. H. Kuang
Keyword(s):  
Contact Stress ◽  
Three Dimensional ◽  
Hertzian Contact ◽  
Stress Distributions ◽  
Linear Elastic ◽  
Contact Points ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Stress Variations ◽  
Contact Stress Distribution

The effect of an insulated rail joint (IRJ) on the contact stress variation near wheel-rail contact zones was simulated by employing three-dimensional finite element models. Three linear elastic IRJ materials, i.e. epoxy-fibreglass, polytetrafluoroethylene (PTFE) and Nylon-66, were investigated. Contact elements were used to simulate the interaction between the wheel and rail contact points. Numerical results showed that the presence of IRJ might significantly affect the wheel-rail contact stress distributions. Results also indicated that the traditional Hertzian contact theory is no longer available to predict the contact stress distribution around the rail joints.

Two-Dimensional Dynamic Stress Behavior of Sheet Glass Caused by a Continuous Step Input from a Cylindrical Loader

2016 ◽  
Vol 10 (3) ◽  
pp. 401-410 ◽  
Author(s):  
Akira Chiba ◽  
◽  
Hirofumi Hidai ◽  
Souta Matsusaka ◽  
Noboru Morita ◽  
...  
Keyword(s):  
Stress Distribution ◽  
Sheet Glass ◽  
Contact Stress ◽  
Glass Surface ◽  
Dynamic Stress ◽  
Stress Component ◽  
Stress Model ◽  
Two Dimensional ◽  
Stress Behavior ◽  
Contact Stress Distribution

The distribution of dynamic stress in sheet glass, stress which is caused by a continuous step input from a cylindrical loader, was estimated by considering elastic wave propagation. In modeling the dynamic stress behavior, we used a two-dimensional dynamic stress model combining a plane stress model and the equations of motion. A finite-difference method was used in the numerical calculation. Under damped vibration mode conditions, the dynamic stress behavior in the sheet glass was investigated in both the depth (Z) and horizontal (X) directions. The stress component in the Z direction changed from tensile to compressive near the outside glass surface of the contact stress distribution. The stress component in the X direction changed from compressive to tensile in the Z direction under the glass surface at the center of the contact stress distribution. The overshoot of the dynamic stress in the Z direction was 1.8 times that of the steady stress during an elapsed time of less than 1 ns from the beginning of loading.

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