A Simple Nomogram for the Ratios of Octahedral to Maximum Shearing Stresses and Its Physical Interpretation

1954 ◽  
Vol 21 (3) ◽  
pp. 291-293
Author(s):  
G. A. Zizicas
Keyword(s):  
Physical Interpretation ◽  
Recent Observation ◽  
Stress Distributions ◽  
Shearing Stress ◽  
Constant Ratio ◽  
Principal Stresses ◽  
Absolute Value ◽  
The One ◽  
Straight Lines

Abstract A nomogram constructed exclusively by means of straight lines is presented, giving the ratio of the octahedral to the maximum shearing stresses for all possible stress distributions in terms of the nondimensional ratios of the two principal stresses to the one of maximum absolute value. The physical interpretation of the nomogram is discussed. It is shown that states of stress with constant ratio of octahedral to maximum shearing stress are represented by straight lines. To such lines are found to correspond fixed values of the deviatoric parameter μ = 2 S 2 - S 1 - S 3 S 1 - S 3 in agreement with a recent observation by Novozhilov. The values of μ are given directly by the nomogram.

Representation of Three-Dimensional Stress Distributions by Mohr Circles

1955 ◽  
Vol 22 (2) ◽  
pp. 273-275
Author(s):  
G. A. Zizicas
Keyword(s):  
Normal Stress ◽  
Stress Component ◽  
Three Dimensional ◽  
Stress Distributions ◽  
Shearing Stress ◽  
Principal Stresses ◽  
Normal Stress Component

Abstract O. Mohr has developed a diagram representing the normal stress component snn = σn and the total shearing stress component τn on an element of surface of any prescribed orientation with respect to the directions of the principal stresses. His procedure, however, does not give the orientation of the shearing stress τn within the element or, which is equivalent, the components of this shearing stress in a plane co-ordinate system within the element under consideration. An extension of the Mohr method that overcomes this limitation is presented in this note.

scholarly journals Prosthetic Correction of Proclined Maxillary Incisors: A Biomechanical Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Yiting He ◽  
Yung-Chung Chen ◽  
Wei Teng ◽  
Alex S. L. Fok ◽  
Hooi Pin Chew
Keyword(s):  
Alveolar Bone ◽  
Biomechanical Analysis ◽  
Maxillary Incisor ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Principal Stresses ◽  
Fixed Prosthesis ◽  
Maxillary Incisors ◽  
The One ◽  
Surrounding Bone

In some cases of proclined maxillary incisors, the proclination can be corrected by a fixed prosthesis. The aim of this study was to investigate the magnitude and distribution of (i) principal stresses in the adjacent alveolar bone and (ii) direct and shear stresses that are normal and parallel, respectively, to the bone-tooth interface of a normal angulated maxillary incisor, a proclined one, and a proclined one corrected with an angled prosthetic crown. 2D finite-element models were constructed, and a static load of 200 N on the palatal surface of the maxillary incisor at different load angles was applied. Load angles (complementary angle to interincisal angle) ranging from 20° to 90° were applied. The results indicate that the load angle could have a more significant impact on the overall stress distributions in the surrounding alveolar bone and along the bone-tooth interface than the proclination of the maxillary incisor. Provided that the resulting interincisal angle is 150° or smaller, the stresses in the surrounding bone and at the bone-tooth interface are similar between a proclined maxillary incisor and the one with prosthodontic correction. Hence, such a correction, when deemed appropriate clinically, can be undertaken with confidence that there is little risk of incurring additional stresses over that already in existence, in the supporting bone and at the tooth-bone interface.

scholarly journals Dipolar stability in spherical simulations: The impact of an inner stable zone

2019 ◽  
Vol 15 (S354) ◽  
pp. 185-188
Author(s):  
Bonnie Zaire ◽  
Laurène Jouve
Keyword(s):  
Magnetic Fields ◽  
Rossby Number ◽  
Constant Ratio ◽  
Stellar Rotation ◽  
Convective Motions ◽  
The Stability ◽  
The One ◽  
The Impact ◽  
The Magnetic Field ◽  
Stable Zone

AbstractMagnetic fields vary in complexity for different stars. The stability of dipolar magnetic fields is known to depend on different quantities, e.g., the stellar rotation, the stratification, and the intensity of convective motions. Here, we study the dipolar stability in a system with an inner stable zone. We present preliminary results of dynamo simulations using the Rayleigh number as a control parameter. The stiffness of the stable zone is accordingly varied to keep a constant ratio of the Brunt-Väisälä frequency to the angular velocity. Similarly to the completely convective spherical shell, we find that a transition exists between a regime where the magnetic field is dipolar to a multipolar regime when the Rossby number is increased. The value of the Rossby number at the transition is very close to the one of the fully convective case.

Stress Distributions in an Elastic Body due to Molecular Interactions Considering One-Dimensional Periodic Material Distribution Based on Mindlin Solution

2018 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Toshiki Otani ◽  
Shigehisa Fukui
Keyword(s):  
Stress Distribution ◽  
Elastic Body ◽  
Molecular Interactions ◽  
Material Distribution ◽  
Stress Distributions ◽  
One Dimensional ◽  
Calculation Results ◽  
Basic Characteristics ◽  
The One

A method to calculate the stress distributions in the elastic body caused by the molecular interactions has been established. The stress distribution was calculated based on the Mindlin’s solution considering the one-dimensional periodic material distribution. The calculation results for a distribution of two materials were presented. The basic characteristics of the stress distribution in the elastic body were quantitatively clarified.

scholarly journals Equations with powers of singular moduli

2019 ◽  
Vol 15 (03) ◽  
pp. 445-468 ◽  
Author(s):  
Antonin Riffaut
Keyword(s):  
Rational Number ◽  
The Other ◽  
Other Hand ◽  
Singular Moduli ◽  
Cm Points ◽  
The One ◽  
Straight Lines ◽  
Positive Integers

We treat two different equations involving powers of singular moduli. On the one hand, we show that, with two possible (explicitly specified) exceptions, two distinct singular moduli [Formula: see text] such that the numbers [Formula: see text], [Formula: see text] and [Formula: see text] are linearly dependent over [Formula: see text] for some positive integers [Formula: see text], must be of degree at most [Formula: see text]. This partially generalizes a result of Allombert, Bilu and Pizarro-Madariaga, who studied CM-points belonging to straight lines in [Formula: see text] defined over [Formula: see text]. On the other hand, we show that, with obvious exceptions, the product of any two powers of singular moduli cannot be a non-zero rational number. This generalizes a result of Bilu, Luca and Pizarro-Madariaga, who studied CM-points belonging to a hyperbola [Formula: see text], where [Formula: see text].

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.

Fitting straight lines to experimental data

1977 ◽  
Vol 233 (3) ◽  
pp. R94-R99 ◽  
Author(s):  
R. A. Brace
Keyword(s):  
Standard Error ◽  
Least Squares Regression ◽  
Simple Method ◽  
Mean Values ◽  
Absolute Value ◽  
Best Value ◽  
The Mean ◽  
Straight Lines ◽  
Relationship Of ◽  
Conventional Regression

The problem associated with use of statistical methods for determining a best linear relationship of the form Y = AX +B have been examined for a condition quite prevalent with experimental research, i.e., when the values of both variables are subject to essentially unknown errors. Under this condition standard least-squares regression analysis underestimates the value of the slope A. A very simple method for determining the best value of the slope and intercept has been introduced which can be used when errors are present in both variables. With this proposed method, the calculated slope is equal to the standard error of Y divided by the standard error of X (with the appropriate sign) and the intercept is found from the mean values of X and Y, i.e., B = Y - AX. The best estimate of the slope is also equal to the slope found with the conventional regression method divided by the absolute value of the correlation coefficient. The line determined with the suggested method can be considered to be a line of symmetry through the data.

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.

scholarly journals Traveltime calculations from frequency‐domain downward‐continuation algorithms

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1380-1388 ◽  
Author(s):  
Changsoo Shin ◽  
Seungwon Ko ◽  
Wonsik Kim ◽  
Dong‐Joo Min ◽  
Dongwoo Yang ◽  
...  
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Downward Continuation ◽  
Calculation Algorithm ◽  
Near Surface ◽  
Absolute Value ◽  
Head Waves ◽  
First Arrival ◽  
The One ◽  
Derivatives Of

We present a new, fast 3D traveltime calculation algorithm that employs existing frequency‐domain wave‐equation downward‐continuation software. By modifying such software to solve for a few complex (rather than real) frequencies, we are able to calculate not only the first arrival and the approximately most energetic traveltimes at each depth point but also their corresponding amplitudes. We compute traveltimes by either taking the logarithm of displacements obtained by the one‐way wave equation at a frequency or calculating derivatives of displacements numerically. Amplitudes are estimated from absolute value of the displacement at a frequency. By using the one‐way downgoing wave equation, we also circumvent generating traveltimes corresponding to near‐surface upcoming head waves not often needed in migration. We compare the traveltimes computed by our algorithm with those obtained by picking the most energetic arrivals from finite‐difference solutions of the one‐way wave equation, and show that our traveltime calculation method yields traveltimes comparable to solutions of the one‐way wave equation. We illustrate the accuracy of our traveltime algorithm by migrating the 2D IFP Marmousi and the 3D SEG/EAGE salt models.

scholarly journals Methods for evaluation of mechanical stress condition of materials

2018 ◽  
Vol 145 ◽  
pp. 05008 ◽  
Author(s):  
Yordan Mirchev ◽  
Pavel Chukachev ◽  
Mitko Mihovski
Keyword(s):  
Surface Waves ◽  
Mechanical Stress ◽  
Ultrasonic Method ◽  
Mechanical Stresses ◽  
Principal Stresses ◽  
Small Depth ◽  
Type Size ◽  
Cylindrical Holes ◽  
The One ◽  
First Time

Primary attention is given to the following methods: method by drilling cylindrical holes (drill method) and integrated ultrasonic method using volume (longitudinal and transverse), surface, and sub-surface waves. Drill method allows determination of residual mechanical stress in small depth of material surfaces, assessing type, size, and orientation of principal stresses. For the first time, parallel studies are carried out of mechanical stress in materials using the electroacoustic effect of volume, surface and sub-surface waves on the one hand, and effective mechanical stresses on the other. The experimental results present electroacoustic coefficients for different types of waves in the material of gas pipeline tube of 243 mm diameter and 14 mm thickness. These are used to evaluate mechanical stresses in pipelines, according to active GOST standards.

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