Torsion of a Rigid Cylinder Embedded in an Elastic Half Space

1976 ◽  
Vol 43 (3) ◽  
pp. 419-423 ◽  
Author(s):  
J. E. Luco
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Constants ◽  
Elastic Half Space ◽  
Integral Representations ◽  
Axially Symmetric ◽  
Stress Singularities ◽  
Rigid Cylinder ◽  
Perfect Bonding

A study is made of the axially symmetric torsion of a rigid cylinder partially embedded into a layered elastic half space. The problem is formulated on the basis of perfect bonding between the cylinder and the surrounding material. Integral representations are used to reduce the problem to the solution of two integral equations. Stress singularities of fractional order are obtained along the perimeter of the base of the cylinder. A numerical solution of the integral equations is used to obtain the torque-twist relationship for different embedment depths and for different values of the elastic constants.

THREE-DIMENSIONAL SURFACE CRACK ANALYSIS OF ELASTIC HALF-SPACE UNDER ROLLING CONTACT LOAD

2009 ◽  
Vol 06 (02) ◽  
pp. 317-332 ◽  
Author(s):  
MENG-CHENG CHEN ◽  
HUI-QIN YU
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Rolling Contact ◽  
Contact Load ◽  
Hypersingular Integral ◽  
Space Body ◽  
Planar Crack

In this work a three-dimensional planar crack on the surface of elastic half-space was analyzed under rolling contact load. The stresses interior to an elastic half-space body under rolling contact load and those produced by an infinitesimal displacement jump loop for the elastic half-space body were used to reduce the planar crack problem to the solution of a system of two-dimensional hypersingular integral equations with unknown displacement jump. The ideas of finite element discretization were employed to construct numerical solution schemes for solving the integral equations. An appropriate treatment of the associated hypersingular integral in the numerical solution to the integral equations was proposed in Hadamard's finite-part integral sense. The numerical results showed that the present procedure yields solutions with high accuracies. The stress intensity factors near the crack front edge under rolling contact load were indicated in graphical form with varying the crack shape, the radius of rolling contact zone and the friction coefficients, respectively. In addition, the influence of the lubricant infiltrating the crack surfaces on the crack propagation was also discussed in the paper.

The Singularity at the Apex of a Bonded Wedge-Shaped Stamp

1979 ◽  
Vol 46 (3) ◽  
pp. 577-580 ◽  
Author(s):  
K. S. Parihar ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Singular Integral ◽  
Green's Functions ◽  
Green’S Functions ◽  
Singular Integral Equations ◽  
Elastic Half Space

The problem of determining the singularity at the apex of a rigid wedge bonded to an elastic half space is formulated by considerations of Green’s functions for the loaded half space. The eigenvalue problem is reduced to finding the solution of a coupled pair of singular integral equations. A numerical solution for small wedge angles is given.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

Plane Strain Sliding Contact Between a Rigid Cylinder and a Pseudoelastic Shape Memory Alloy Half-Space

2018 ◽  
Author(s):  
Ralston Fernandes ◽  
James G. Boyd ◽  
Dimitris C. Lagoudas ◽  
Sami El-Borgi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Half Space ◽  
Maximum Stress ◽  
Transformation Strain ◽  
Elastic Half Space ◽  
Sliding Contact ◽  
Temperature Dependent ◽  
Rigid Cylinder ◽  
Parametric Studies

This study uses the finite element method to analyze the sliding contact behavior between a rigid cylinder and a shape memory alloy (SMA) semi-infinite half-space. An experimentally validated constitutive model is used to capture the pseudoelastic effect exhibited by these alloys. Parametric studies involving the maximum recoverable transformation strain and the transformation temperatures are performed to analyze the effects that these parameters have on the stress fields during indentation and sliding contact. It is shown that, depending on the amount of recoverable transformation strain possessed by the alloy, a reduction of almost 40 % of the maximum stress in the pseudoelastic half-space is achieved when compared to the maximum stress in a purely elastic half-space. The studies also reveal that the sliding response is strongly temperature dependent, with significant residual stress present in the half-space at temperatures below the austenitic finish temperature.

Numerical Solution of Prestressed Foundation - Subsoil Interaction Using FEM

2020 ◽  
Vol 832 ◽  
pp. 81-88 ◽  
Author(s):  
Radim Čajka ◽  
Jaroslav Navrátil
Keyword(s):  
Numerical Solution ◽  
Numerical Integration ◽  
Half Space ◽  
Structural Strength ◽  
Elastic Half Space ◽  
Isoparametric Element ◽  
Foundation Soil ◽  
Fem Model ◽  
Interaction Task ◽  
Internal Forces

This paper deals with prestressed foundation - soil interaction. For interaction task is used FEM model of thick slab with shear influence which is supported by structural strength modified elastic half-space. The calculation of deformations, internal forces and contact stresses in subsoil is performed iteratively by means of isoparametric element and numerical integration. The results of settlement and stress of non-prestressed/prestressed slab - subsoil interaction are compared on example.

The motion excited by an impulsive source in an elastic half-space with a surface obstacle

1971 ◽  
Vol 61 (3) ◽  
pp. 747-763
Author(s):  
Jacob Aboudi
Keyword(s):  
Finite Difference ◽  
Perturbation Method ◽  
Half Space ◽  
Elastic Constants ◽  
Elastic Waves ◽  
Elastic Half Space ◽  
Reflected Waves ◽  
Finite Difference Solution ◽  
Impulsive Source ◽  
Difference Solution

abstract An elastic half-space having a surface obstacle of slightly different elastic constants whose deviation and shape of boundaries are small is considered. By combining a perturbation method and a finite difference solution, the motion of the half-space due to an impulsive source is given. Results show that Rayleigh and reflected waves are highly influenced by the existence of the obstacle and could give some indications for screening purposes of elastic waves.

The In-Plane Loading of a Rigid Disk Inclusion Embedded in an Elastic Half-Space

1991 ◽  
Vol 58 (2) ◽  
pp. 362-369 ◽  
Author(s):  
A. P. S. Selvadurai ◽  
B. M. Singh ◽  
M. C. Au
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Space Region ◽  
Rigid Disk ◽  
Lateral Translation

The paper examines the problem of the in-plane loading of a rigid disk inclusion which is embedded in bonded contact with an isotropic elastic half-space region. The governing coupled integral equations, derived via a Hankel transform technique, are evaluated numerically to generate results for the in-plane stiffness of the rigid disk inclusion and the rotation which accompanies the lateral translation.

Sign in / Sign up

Export Citation Format

Share Document