The Singularity Strength at the Apex of a Wedge Undergoing Finite Deformations

1990 ◽  
Vol 57 (3) ◽  
pp. 577-580 ◽  
Author(s):  
J. M. Duva
Keyword(s):  
Boundary Conditions ◽  
Plane Strain ◽  
Finite Deformation ◽  
Finite Deformations ◽  
The Other ◽  
Nonlinear Material ◽  
Singular Behavior ◽  
Arbitrary Size

Herein we establish general formulae for characterizing the singular behavior at the apex of a wedge of nonlinear material of arbitrary size undergoing plane-strain finite deformation. Two sets of boundary conditions are considered: (a) both wedge flanks are clamped, and (b) one flank is clamped and the other free. The mode of deformation is obtained in one simple case for illustration.

The Singularity at the Apex of a Rigid Wedge Embedded in a Nonlinear Material

1988 ◽  
Vol 55 (2) ◽  
pp. 361-364 ◽  
Author(s):  
J. M. Duva
Keyword(s):  
Plane Strain ◽  
Power Law ◽  
Nonlinear Material ◽  
Stress And Strain ◽  
Singular Behavior ◽  
Strain Fields

The singular behavior of the stress and strain fields at the apex of a square rigid wedge embedded in a nonlinear material under plane-strain conditions is described. Both a power law and a bilinear law for the nonlinear material are considered.

Velocity field and strain-rates in plastic deformation

1967 ◽  
Vol 2 (3) ◽  
pp. 196-206 ◽  
Author(s):  
T C Hsu
Keyword(s):  
Plastic Deformation ◽  
Steady State ◽  
Velocity Field ◽  
Finite Deformation ◽  
Finite Deformations ◽  
The Other ◽  
Strain Rates ◽  
Steady State Flow ◽  
Quantitative Results ◽  
The One

Grid lines have often been scribed, printed or photographed on metal surfaces for studying plastic deformation. Hitherto, most of them have been used only for qualitative results. It has been shown in a previous paper (2)∗ how quantitative results on finite deformations can be derived from a deformed grid. As a sequel to that paper, a method is presented here for deriving the rates of deformation from deformed grids. The relation between the velocity field on the one hand and the strain-rates and rotations on the other is first discussed. The theory thus developed is then applied to the cases of steady-state and non-steady-state flow, with practical example for the former. The connection between finite deformation and rate of deformation is also explained.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

scholarly journals Some Non-Simple–Equilibrium Aspects in Axisymmetric Turbomachine Flow Theory

1969 ◽  
Author(s):  
H. J. Schroder
Keyword(s):  
Boundary Conditions ◽  
Axisymmetric Flow ◽  
Flow Theory ◽  
Flow Fields ◽  
The Other ◽  
Equilibrium Flow ◽  
Free Vortex ◽  
Difference Methods ◽  
Definite Difference ◽  
Insight Into

In turbomachines of non-free-vortex design the axisymmetric flow is mostly in a state of “disturbed equilibrium.” Methods of calculating flow fields of this kind were developed nearly 20 years ago. The examples chosen for their demonstration were rather intricate. Here, on the other hand, two very simple examples are produced which provide some insight into the — anything but self-evident — behavior of disturbed equilibrium flow. The examples serve to give some indication as to the use of definite difference methods, including the choice of boundary conditions, and a first attempt at taking incidence at the leading edges of the blades into account.

Tensorial Deformation Measures for Flexible Joints

2010 ◽  
Vol 6 (3) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Leihong Li ◽  
Pierangelo Masarati ◽  
Marco Morandini
Keyword(s):  
Finite Deformation ◽  
Nonlinear Behavior ◽  
Critical Issue ◽  
Finite Deformations ◽  
Flexible Joints ◽  
Elastic Bodies ◽  
Infinitesimal Deformations ◽  
Stiffness Characteristics ◽  
Definition Of

Flexible joints, sometimes called bushing elements or force elements, are found in all multibody dynamics codes. In their simplest form, flexible joints simply consist of sets of three linear and three torsional springs placed between two nodes of a multibody system. For infinitesimal deformations, the selection of the lumped spring constants is an easy task, which can be based on a numerical simulation of the joint or on experimental measurements. If the joint undergoes finite deformations, the identification of its stiffness characteristics is not so simple, especially if the joint itself is a complex system. When finite deformations occur, the definition of deformation measures becomes a critical issue. Indeed, for finite deformation, the observed nonlinear behavior of materials is partly due to material characteristics and partly due to kinematics. This paper focuses on the determination of the proper finite deformation measures for elastic bodies of finite dimension. In contrast, classical strain measures, such as the Green–Lagrange or Almansi strains, among many others, characterize finite deformations of infinitesimal elements of a body. It is argued that proper finite deformation measures must be of a tensorial nature, i.e., must present specific invariance characteristics. This requirement is satisfied if and only if the deformation measures are parallel to the eigenvector of the motion tensor.

CHIRAL ZEROMODES ON VORTEX-TYPE INTERSECTING FIVE-BRANE IN HETEROTIC STRING

2013 ◽  
Vol 21 ◽  
pp. 191-192
Author(s):  
MASAYA YATA
Keyword(s):  
Dirac Equation ◽  
String Theory ◽  
Boundary Conditions ◽  
Heterotic String ◽  
The Other ◽  
Two Dimensional ◽  
Complete Spectrum ◽  
Heterotic String Theory ◽  
Brane Solution ◽  
Opposite Chirality

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8 × E8 heterotic string theory to search for localized chiral zeromodes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zeromodes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zeromodes, one of which has opposite chirality to the other two.

Equilibrium equations and boundary conditions of strain gradient theory in arbitrary curvilinear coordinates

2014 ◽  
Vol 23 (5-6) ◽  
pp. 169-176
Author(s):  
Mikhail Guzev ◽  
Chengzhi Qi ◽  
Jiping Bai ◽  
Kairui Li
Keyword(s):  
Boundary Conditions ◽  
Plane Strain ◽  
Strain Gradient ◽  
Special Form ◽  
Curvilinear Coordinates ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Equilibrium Equations ◽  
Plane Strain Problem

AbstractEquilibrium equations and boundary conditions of the strain gradient theory in arbitrary curvilinear coordinates have been obtained. Their special form for an axisymmetric plane strain problem is also given.

Computational Study of Streamfunction-Vorticity Formulation of Incompressible Flow and Heat Transfer Problems

2011 ◽  
Vol 52-54 ◽  
pp. 511-516 ◽  
Author(s):  
Arup Kumar Borah
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Boundary Conditions ◽  
Incompressible Flow ◽  
Computational Study ◽  
The Other ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Continuity Constraint ◽  
Transfer Problems

In this paper we have studied the streamfunction-vorticity formulation can be advantageously used to analyse steady as well as unsteady incompressible flow and heat transfer problems, since it allows the elimination of pressure from the governing equations and automatically satisfies the continuity constraint. On the other hand, the specification of boundary conditions for the streamfunction-vorticity is not easy and a poor evaluation of these conditions may lead to serious difficulties in obtaining a converged solution. The main issue addressed in this paper is the specification in the boundary conditions in the context of finite element of discretization, but approach utilized can be easily extended to finite volume computations.

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