Stress Distributions Around Hydrostatically Loaded Circular Holes in the Neighborhood of Corners

1958 ◽  
Vol 25 (2) ◽  
pp. 178-183
Author(s):  
A. J. Durelli ◽  
A. S. Kobayashi
Keyword(s):  
Shear Stress ◽  
Maximum Shear Stress ◽  
Applied Pressure ◽  
Infinite Plate ◽  
Maximum Principal Stress ◽  
Stress Distributions ◽  
Principal Stresses ◽  
Exterior Boundary ◽  
Hole Radius ◽  
Circular Holes

Abstract The stress distributions around hydrostatically loaded circular holes in the neighborhood of corners was determined by using photoelasticity and brittle coatings. Photoelasticity (by means of a diffused-light polariscope) was used to determine the maximum shear lines (isochromatics), and brittle coatings were used to determine the directions of the principal stresses (isostatics). Tests were conducted for six plates with different ratios of hole radius to hole distance to the exterior boundary of plate (R/L). The results of these tests are presented in the form of curves. These curves show the distribution of the maximum shear stress along the diagonal of the plate, the maximum principal stress along the edges of the plate and of the hole, and the maximum shear stress along a perpendicular line to the exterior boundary drawn from the center of the hole. All these values are given as a function of R/L. Curves also are presented which compare the stresses on the diagonal of the plate at the boundary of the hole with the stresses computed using Lamé’s equation for a thick-walled cylinder. Comparisons also are made with the results obtained by Jeffery for a semi-infinite plate with a circular hole subjected to a hydrostatic pressure. All results are given in dimensionless form with the applied pressure as reference. The results published in this paper are new, but the techniques used have been described previously in papers by researchers from the Armour Research Foundation.

Internal Stresses in Elastohydrodynamic Lubrication of Rolling/Sliding Contacts

1989 ◽  
Vol 111 (1) ◽  
pp. 180-187 ◽  
Author(s):  
Farshid Sadeghi ◽  
Ping C. Sui
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Internal Stress ◽  
Maximum Shear Stress ◽  
Elastohydrodynamic Lubrication ◽  
Normal Pressure ◽  
Internal Stresses ◽  
Stress Distributions ◽  
Principal Stresses ◽  
Dimensionless Velocity

The internal stress distribution in elastohydrodynamic lubrication of rolling/sliding line contact was obtained. The technique involves the full EHD solution and the use of Lagrangian quadrature to obtain the internal stress distributions in the x, y, z-directions and the shear stress distribution as a function of the normal pressure and the friction force. The principal stresses and the maximum shear stress were calculated for dimensionless loads ranging from (2.0452 × 10−5) to (1.3 × 10−4) and dimensionless velocity of 10−10 to 10−11 for slip ratios ranging from 0 to pure sliding condition.

Stress Distribution in Square Plates With Hydrostatically Loaded Central Circular Holes

1955 ◽  
Vol 22 (4) ◽  
pp. 539-544
Author(s):  
A. J. Durelli ◽  
J. Barriage
Keyword(s):  
Stress Distribution ◽  
Maximum Shear Stress ◽  
Maximum Principal Stress ◽  
Thick Wall ◽  
Principal Stresses ◽  
Interior Boundary ◽  
Circular Holes ◽  
Square Plate ◽  
Stress Ratios ◽  
Diffused Light

Abstract The stress distribution in square plates with hydrostatically loaded central circular holes was determined using photoelasticity and brittle coatings. Photoelasticity was used to determine the maximum shear lines (isochromatics) and a brittle coating was used to determine the directions of the principal stresses (isostatics). The investigation was conducted for plates with holes producing seven ratios of the diameter to the square side (D/a). Curves are presented which show the distribution of the maximum shear stress along the axis and along the diagonal of the square plate, as a function of D/a, Figs. 3 and 4. The maximum principal stress along the exterior and interior boundaries as a function of D/a, Figs. 5 and 6, has also been given. A comparison is made of the stress ratios (σ1/P) at a point on the axis of the square at the interior boundary with that calculated for a thick-wall cylinder using Lamé’s equation, Fig. 1. Stress ratios (σ1/P) also are determined for a point on the diagonal of the square plate at the interior boundary, Fig. 8. A diffused-light polariscope was used. The loading jig consisted of rubber tubing in a grooved block. The photoelastic material (CR39) was calibrated automatically. No new methods are developed in the paper but it is felt that the use of the presently available methods has been simplified appreciably.

Off-Axis Torsion Tests on Tubular Specimens of Steel

2001 ◽  
Vol 123 (3) ◽  
pp. 268-273 ◽  
Author(s):  
Takenobu Takeda ◽  
Zhongchun Chen
Keyword(s):  
Shear Stress ◽  
Yield Stress ◽  
Maximum Shear Stress ◽  
Torsion Test ◽  
Combined Loading ◽  
Anisotropic Hardening ◽  
Principal Stresses ◽  
Maximum Value ◽  
The Difference ◽  
Tubular Specimens

In order to analyze the anisotropic hardening behavior of metals, an off-axis torsion test by combined loading is developed. In this test, the maximum shear stress direction φ can be changed from 0 deg to 90 deg while the ratio of maximum and minimum principal stresses is kept at −1. With increasing angle φ, the yield stress of the torsional-prestrained steel decreases; the difference between the directions of the maximum shear stress and principal shear strain increment rises to a maximum value and then decreases. It is experimentally verified that anisotropy is more severe when a smaller offset strain is used in defining the yield stress.

A Stress Analysis and Strength Evaluation of Scarf Adhesive Joints Subjected to Static Tensile Loading

2006 ◽  
Author(s):  
Toshiyuki Sawa ◽  
Masahiro Sasaki ◽  
Yuya Hirayama
Keyword(s):  
Joint Strength ◽  
Three Dimensional ◽  
Maximum Principal Stress ◽  
Adhesive Joints ◽  
Stress Distributions ◽  
Principal Stresses ◽  
Adhesive Properties ◽  
Maximum Value ◽  
Static Tensile ◽  
Three Dimensional Finite Element

Scarf adhesive joints used in practice. However, the stress distributions and the joints strengths have not yet been fully elucidate. Important issues are how to determine the scarf angle in adherend and how to determine the adhesive properties. In this study, the stress distributions in scarf adhesive joints under static tensile loadings are analyzed using three-dimensional finite-element calculations. In the FEM calculations, the effects of Young's modulus of the adhesive, adhesive thickness, scarf angle of the adherend on the stress distributions at the adhesive interfaces are examined. The maximum principal stresses were calculated at every element at the interfaces. As the results, it is found that the maximum value of the maximum principal stress occurs at the edge of the adhesive interfaces (z=0, 1/s=1). It is also observed that the maximum value of the stress is the smallest, when the scarf angle is 60 degree. In addition, the joint strength is estimated using the interface stress. For the verification of the FEM calculations, the experiments were carried out to measure the strengths and the strains in the joints under static tensile loadings using strain gauges. Fairly good agreements are observed between the numerical and the measured results concerning the joint strength and the strains.

scholarly journals Numerical Investigation of a Hydrosplitting Fracture and Weak Plane Interaction Using Discrete Element Modeling

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 535
Author(s):  
Shuaiqi Liu ◽  
Fengshan Ma ◽  
Haijun Zhao ◽  
Jie Guo ◽  
Xueliang Duan ◽  
...  
Keyword(s):  
Shear Stress ◽  
Principal Stress ◽  
Stress Ratio ◽  
Water Pressure ◽  
Maximum Shear Stress ◽  
Water Inrush ◽  
Discrete Element ◽  
Maximum Principal Stress ◽  
In Situ Stress

Water inrush caused by hydrosplitting is an extremely common disaster in the engineering of underground tunnels. In this study, the propagation of fluid-driven fractures based on an improved discrete element fluid-solid coupling method was modeled. First, the interactions between hydrosplitting fractures (HFs) and preexisting weak planes (WPs) with different angles were simulated considering water pressure in the initial fracture. Second, the influence of the in situ stress ratio and the property of WPs were analyzed, and corresponding critical pressure values of different interactions were calculated. Lastly, the maximum principal stress and maximum shear stress variation inside the pieces were reproduced. The following conclusions can be drawn: (1) Five different types of interaction modes between HFs and natural WPs were obtained, prone to crossing the WPs under inclination of 90°. (2) The initiation pressure value decreased with an increased in situ stress ratio, and the confining stress status had an effect on the internal principal stress. (3) During HFs stretching in WPs with a high elastic modulus, the value of the maximum principal stress was low and rose slowly, and the maximum shear stress value was smaller. Through comprehensive analysis, the diversity of the principal stress curves is fundamentally determined by the interaction mode between HFs and WPs, which are influenced by the variants mentioned in the paper. The analysis provides a better guideline for understanding the failure mechanism of water gushing out of deep buried tunnel construction and cracking seepage of high head tunnels.

Mechanics of Cell Mechanosensing on Patterned Substrate

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
Chenglin Liu ◽  
Shijie He ◽  
Xiaojun Li ◽  
Bo Huo ◽  
Baohua Ji
Keyword(s):  
Shear Stress ◽  
Principal Stress ◽  
Maximum Shear Stress ◽  
Cell Monolayer ◽  
Maximum Principal Stress ◽  
Mechanical Force ◽  
Shear Stresses ◽  
Plane Shear ◽  
Cell Behaviors ◽  
Mechanical Signals

It has been recognized that cells are able to actively sense and respond to the mechanical signals through an orchestration of many subcellular processes, such as cytoskeleton remodeling, nucleus reorientation, and polarization. However, the underlying mechanisms that regulate these behaviors are largely elusive; in particular, the quantitative understanding of these mechanical responses is lacking. In this study, combining experimental measurement and theoretical modeling, we studied the effects of rigidity and pattern geometry of substrate on collective cell behaviors. We showed that the mechanical force took pivotal roles in regulating the alignment and polarization of cells and subcellular structures. The cell, cytoskeleton, and nucleus preferred to align and polarize along the direction of maximum principal stress in cell monolayer, and the driving force is the in-plane maximum shear stress. The higher the maximum shear stress, the more the cells and their subcellular structures preferred to align and polarize along the direction of maximum principal stress. In addition, we proved that in response to the change of in-plane shear stresses, the actin cytoskeleton is more sensitive than the nucleus. This work provides important insights into the mechanisms of cellular and subcellular responses to mechanical signals. And it also suggests that the mechanical force does matter in cell behaviors, and quantitative studies through mechanical modeling are indispensable in biomedical and tissue engineering applications.

scholarly journals Simulation of knee implants made of Ti6Al4V material during walking

2018 ◽  
Vol 204 ◽  
pp. 07015
Author(s):  
Djoko Kustono ◽  
Retno Wulandari ◽  
Andoko ◽  
Poppy Puspitasari ◽  
Galih Adhi Kurniawan ◽  
...  
Keyword(s):  
Extracellular Matrix ◽  
Shear Stress ◽  
Human Body ◽  
Maximum Shear Stress ◽  
Bone Matrix ◽  
Maximum Principal Stress ◽  
Total Deformation ◽  
Body Frame ◽  
The Matrix ◽  
Simulation Results

Bone is the connective tissue in the human body which consists of cells, fibers, and extracellular matrix. The bone matrix is the hardest part located in the outer layer of the bone, which is caused by the deposition of minerals in the matrix, so that the bone undergoes classification. The bone functions as a hard, rigid body frame, and provides a place or space for attachment of muscles and organs found in the human body. The simulation results using FEM showed that knee implants made with Ti6Al4V material had a total deformation of 0.15 mm, maximum principal stress of 17.012 MPa, and a maximum shear stress of 15.841 MPa. The analysis was performed using a variation of time 0 to 1.01 seconds.

Variably Reinforced Circular Holes in Stressed Plates

1958 ◽  
Vol 9 (3) ◽  
pp. 213-231 ◽  
Author(s):  
Raymond Hicks
Keyword(s):  
Infinite Plate ◽  
Shear Stresses ◽  
List Type ◽  
Principal Stresses ◽  
Cross Sectional ◽  
Uniform Shear ◽  
Uniform Tension ◽  
Wide Range ◽  
Circular Holes ◽  
Applied Stresses

SummaryExpressions are obtained for the radial, tangential, and shear stresses in an infinite plate containing a variably reinforced circular hole. The variation in the cross-sectional area of the reinforcement is chosen so that the maximum tensile resistance of the reinforcement occurs at points around the hole where the stresses in the plate tend to be high. It is shown that when the reinforcement has a given weight, the effect of varying its cross section is to reduce the stress concentration in the plate.The following particular applied stress systems are considered:— (i)Uniform tension or compression in one direction.(ii)Uniform shear.(iii)Unequal principal stresses.For the particular cases of uniform end loading and unequal applied stresses in the ratio 2:1, data have been obtained which enable the designer to determine the stress distribution in plates with reinforcements having a reasonably wide range of practical dimensions.

On the Analysis of Asymmetric Stress

1972 ◽  
Vol 39 (4) ◽  
pp. 1133-1136 ◽  
Author(s):  
V. K. Stokes
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Stress Tensor ◽  
Maximum Shear Stress ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Symmetric Part ◽  
Principal Stresses ◽  
Asymmetric Stress

An attempt has been made to analyze asymmetric stress. Bounds for the principal stresses have been established in terms of the principal stresses corresponding to the symmetric part of the stress tensor. Sufficient conditions for the existence of one or three principal stresses have been established. Bounds have also been established for the maximum shear stress. Detailed results have been given for the case of a quasi two-dimensional stress distribution.

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