On steady plane flows in classical elasticity

1985 ◽  
Vol 33 (3) ◽  
pp. 315-322 ◽  
Author(s):  
R. Hill
Keyword(s):  
Classical Elasticity ◽  
Steady Plane

New Exact Solutions of Steady Plane Flows of an In Compressible Fluid of Variable Viscosity

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Sobia Younus
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Compressible Fluid ◽  
Variable Viscosity ◽  
Plane Motion ◽  
Transformation Technique ◽  
Vorticity Distribution ◽  
New Exact Solutions ◽  
Steady Plane ◽  
Uniform Stream

<span>Some new exact solutions to the equations governing the steady plane motion of an in compressible<span> fluid of variable viscosity for the chosen form of the vorticity distribution are determined by using<span> transformation technique. In this case the vorticity distribution is proportional to the stream function<span> perturbed by the product of a uniform stream and an exponential stream<br /><br class="Apple-interchange-newline" /></span></span></span></span>

Hodograph transformation in steady plane rotating MHD flows

1987 ◽  
Vol 43 (4) ◽  
pp. 347-353 ◽  
Author(s):  
S. N. Singh ◽  
D. D. Tripathi
Keyword(s):  
Mhd Flows ◽  
Hodograph Transformation ◽  
Steady Plane

Analytical treatment of two-dimensional supersonic flow. II. Flow with weak shocks

1956 ◽  
Vol 248 (952) ◽  
pp. 499-515 ◽  
Keyword(s):  
Solution Process ◽  
Wave Interaction ◽  
Analytical Treatment ◽  
Plane Flow ◽  
Flow Equations ◽  
Interaction Regions ◽  
Steady Plane ◽  
Set Up ◽  
Downstream Flow ◽  
Weak Shocks

A scheme of approximate solution is presented for the treatment of shock waves in the steady, plane flow of a perfect gas. It is based on the neglect of any entropy variations produced by the shocks and hence is applicable only when the shocks are weak. The method provides an extension of Friedrichs’s (1948) results for simple waves to wave-interaction regions. By an examination of the solution of the continuous-flow equations in the neighbourhood of a known shock wave it is shown how the downstream flow may be calculated without reference to the particular shock shape (§2). There are certain cases in which this approach fails and they are discussed by means of a typical example in §3.3. Once the downstream flow has been calculated, it is possible to set up general equations for the determination of the shock (§ 2). Examples of the solution of these equations for typical problems are given in §3. In §4 there is a brief discussion of the validity of using homentropic theory and estimates of the errors involved in the solution process are obtained.

A force-based coupling scheme for peridynamics and classical elasticity

2013 ◽  
Vol 66 ◽  
pp. 34-49 ◽  
Author(s):  
Pablo Seleson ◽  
Samir Beneddine ◽  
Serge Prudhomme
Keyword(s):  
Coupling Scheme ◽  
Classical Elasticity

Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems

2003 ◽  
Vol 10 (2) ◽  
pp. 257-270
Author(s):  
N. Khomasuridze
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Cognitive Significance ◽  
Cylindrical Coordinates ◽  
Classical Elasticity ◽  
Representation Of Solutions ◽  
Elasticity Problems ◽  
Lamé Coefficients

Abstract Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < ∞} in generalized cylindrical coordinates ρ, α, 𝑧 with Lamé coefficients ℎ ρ = ℎ α = ℎ(ρ, α), ℎ𝑧 = 1. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.

scholarly journals Modeling of Size Effects in Bending of Perforated Cosserat Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Roman Kvasov ◽  
Lev Steinberg
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Numerical Study ◽  
The Finite Element Method ◽  
Classical Elasticity ◽  
Element Analysis ◽  
Plate Deformation ◽  
The Finite Element Analysis ◽  
Circular Holes ◽  
Different Shapes

This paper presents the numerical study of Cosserat elastic plate deformation based on the parametric theory of Cosserat plates, recently developed by the authors. The numerical results are obtained using the Finite Element Method used to solve the parametric system of 9 kinematic equations. We discuss the existence and uniqueness of the weak solution and the convergence of the proposed FEM. The Finite Element analysis of clamped Cosserat plates of different shapes under different loads is provided. We present the numerical validation of the proposed FEM by estimating the order of convergence, when comparing the main kinematic variables with an analytical solution. We also consider the numerical analysis of plates with circular holes. We show that the stress concentration factor around the hole is less than the classical value, and smaller holes exhibit less stress concentration as would be expected on the basis of the classical elasticity.

Steady plane-parallel flow of a magnetic fluid

1984 ◽  
Vol 19 (6) ◽  
pp. 907-914 ◽  
Author(s):  
D. V. Lyubimov ◽  
T. P. Lyubimova
Keyword(s):  
Magnetic Fluid ◽  
Parallel Flow ◽  
Plane Parallel ◽  
Steady Plane

Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems

2019 ◽  
Vol 344 ◽  
pp. 251-275 ◽  
Author(s):  
Xiaonan Wang ◽  
Shank S. Kulkarni ◽  
Alireza Tabarraei
Keyword(s):  
Classical Elasticity

scholarly journals The Steady Profile of an Axisymmetric Ice Sheet

1981 ◽  
Vol 27 (95) ◽  
pp. 25-37 ◽  
Author(s):  
I. R. Johnson
Keyword(s):  
Aspect Ratio ◽  
Power Law ◽  
Viscous Incompressible Fluid ◽  
Ice Sheet ◽  
Plane Flow ◽  
The Third ◽  
Basal Sliding ◽  
Steady Plane ◽  
Third Dimension ◽  
Special Case

AbstractSteady plane flow under gravity of an axisymmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding is treated according to a power law between shear traction and velocity. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, and temperature variation through the ice sheet is neglected. Illustrations are presented for Glen’s power law (including the special case of a Newtonian fluid), and the polynomial law of Colbeck and Evans. The analysis follows that of Morland and Johnson (1980) where the analogous problem for an ice sheet deforming under plane flow was considered. Comparisons are made between the two models and it is found that the effect of the third dimension is to reduce (or leave unchanged) the aspect ratio for the cases considered, although no general formula can be obtained. This reduction is seen to depend on both the surface accumulation and the sliding law.

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