Stress distribution for a rigid fractal embedded in a two-dimensional elastic medium

1987 ◽  
Vol 36 (1) ◽  
pp. 325-331 ◽  
Author(s):  
Paul Meakin
Keyword(s):  
Stress Distribution ◽  
Elastic Medium ◽  
Two Dimensional

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

scholarly journals Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

2021 ◽  
Author(s):  
Tuoya Sun ◽  
Junhong Guo ◽  
E. Pan
Keyword(s):  
Elastic Medium ◽  
Vibration Frequency ◽  
Surrounding Medium ◽  
Nonlocal Parameter ◽  
Buckling Load ◽  
Width Ratio ◽  
Two Dimensional ◽  
Coating Materials ◽  
Decagonal Quasicrystal ◽  
Critical Buckling Load

AbstractA mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

A Mixed Boundary-Value Problem of Elasticity With Parabolic Boundary

1957 ◽  
Vol 24 (1) ◽  
pp. 122-124
Author(s):  
Gunadhar Paria
Keyword(s):  
Stress Distribution ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Complex Variable ◽  
Hilbert Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Parabolic Boundary

Abstract The problem of finding the stress distribution in a two-dimensional elastic body with parabolic boundary, subject to mixed boundary conditions, has been reduced to the solution of the nonhomogeneous Hilbert problem following the method of complex variable. The result has been compared with that for a straight boundary.

Photoelasticity and Aircraft Design

1951 ◽  
Vol 3 (3) ◽  
pp. 161-172 ◽  
Author(s):  
H.T. Jessop ◽  
C. Snell
Keyword(s):  
Stress Distribution ◽  
Aircraft Design ◽  
Two Dimensional ◽  
Laboratory Technique ◽  
Fringe Patterns ◽  
Practicable Method

It is now more than 25 years since Coker and Filon first developed photoelasticity as a practicable method of exploring the stress distribution in certain types of engineering components. All engineers must be familiar with the striking photographs of fringe patterns obtained by their method in stressed plates of various shapes viewed in a polariscope. In those early days observations were made on Xylonite models and the method was only applicable to components in which stress distribution was of a two-dimensional type. Moreover, with the apparatus then available investigations were somewhat difficult and many engineers at that time were very distrustful of the results obtained from what was, to them, a little understood laboratory technique.

A Simplified Method for Calculating Crack Opening Area

2002 ◽  
Author(s):  
E. Smith
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Crack Opening ◽  
Two Dimensional ◽  
Simple Method ◽  
Tensile Stresses ◽  
Normal Operating ◽  
General Stress ◽  
Simplified Method ◽  
Leak Before Break

In the context of the formulation of a leak-before-break case for a component in a pressurized system, this paper is concerned with the quantification of the crack opening area associated with a two-dimensional crack that is subjected to tensile stresses. We present a simple method, based on the strip yield representation of plastic deformation, for calculating the area. The method is validated against the known result for the ease of an isolated crack in a uniformly stressed infinite solid. It is then used for a general stress distribution, as might arise from a combination of pressure induced and weld residual tensile stresses, with the considerations being focussed on the case where plastic deformation is limited, as is usually appropriate for normal operating situations; application of the method is then especially simple.

Elastic Stresses in Layered Snow Packs

1972 ◽  
Vol 11 (63) ◽  
pp. 407-414 ◽  
Author(s):  
F. W. Smith
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Computer Program ◽  
Elastic Stress ◽  
Two Dimensional ◽  
Strength Data ◽  
Elastic Stresses ◽  
Stress Levels ◽  
Dimensional Finite Element

Abstract A two-dimensional finite element computer program has been used to compute the elastic stress distribution in realistic multi-layered snow packs. Computations have been done on three-layered and five-layered snow packs intended to simulate conditions on the Lift Gully at Berthoud Pass, Colorado. Calculations have been performed to determine the effect of a layer of new snow and the effect of a weak sub-layer. Stress levels were obtained which are reasonable compared with available snow strength data.

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