Stress Interference in Three-Dimensional Torsion

1965 ◽  
Vol 32 (1) ◽  
pp. 21-25 ◽  
Author(s):  
R. A. Eubanks
Keyword(s):  
Stress Concentration ◽  
Displacement Field ◽  
Series Solution ◽  
Three Dimensional ◽  
Pure Torsion ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Spherical Cavities ◽  
Infinite Extent ◽  
Axis Of Symmetry

An explicit series solution is presented for the stress and displacement fields in an elastic body of infinite extent containing two equidiameter spherical cavities. At large distances from the cavities the displacement field coincides with that which arises from pure torsion about the axis of symmetry. Numerical results are presented in graphs which demonstrate the interference of the two sources of stress concentration.

On the Axisymmetric Problem of the Theory of Elasticity for an Infinite Region Containing Two Spherical Cavities

1952 ◽  
Vol 19 (1) ◽  
pp. 19-27
Author(s):  
E. Sternberg ◽  
M. A. Sadowsky
Keyword(s):  
Axisymmetric Problem ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Uniform Field ◽  
Dimensional Problem ◽  
Spherical Cavities ◽  
Infinite Region ◽  
In Series ◽  
The Common ◽  
Axis Of Symmetry

Abstract This paper contains a solution in series form for the stress distribution in an infinite elastic medium which possesses two spherical cavities of the same size. The loading consists of tractions applied to the cavities, as well as of a uniform field of tractions at infinity, and both are assumed to be symmetric with respect to the common axis of symmetry of the cavities and with respect to the plane of geometric symmetry perpendicular to this axis. The loading is otherwise unrestricted. The solution is based upon the Boussinesq stress-function approach and apparently constitutes the first application of spherical dipolar co-ordinates in the theory of elasticity. Numerical evaluations are given for the case in which the surfaces of the cavities are free from tractions and the stress field at infinity is hydrostatic. The results illustrate the interference of two sources of stress concentration in a three-dimensional problem. The approach used here may be extended to cope with the general equilibrium problem for a region bounded by two nonconcentric spheres.

Shrink Fit of a Thick-Walled Cylinder With Contact Shear

1968 ◽  
Vol 35 (4) ◽  
pp. 729-736 ◽  
Author(s):  
L. R. Hill ◽  
A. S. Cakmak ◽  
R. Mark
Keyword(s):  
Coefficient Of Thermal Expansion ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Displacement Fields ◽  
Dual Integral Equations ◽  
Two Phase ◽  
Stress And Displacement Fields ◽  
Shrink Fit ◽  
Finite Band ◽  
Shear Condition

The shrink fit of a finite band on an infinite elastic thick-walled circular cylinder is formulated in terms of inhomogeneous dual integral equations. The solution is obtained by the series method for the case of a prescribed uniform radial displacement and an arbitrary contact shear. A three dimensional photoelastic experiment was performed to provide a realistic contact shear condition and to confirm the analytical solution. The model loading fixture was based on the high coefficient of thermal expansion and the two-phase character of epoxy. The resulting stress and displacement fields are compared with those of a similar mixed boundary value problem neglecting the contact shear.

Three-dimensional elasticity problems for the prismatic bar

2006 ◽  
Vol 462 (2070) ◽  
pp. 1877-1896 ◽  
Author(s):  
J.R Barber
Keyword(s):  
Three Dimensional ◽  
Elastic Problem ◽  
Displacement Fields ◽  
Recursive Procedure ◽  
Axial Coordinate ◽  
Linear Elastic ◽  
Stress And Displacement Fields ◽  
Elasticity Problems ◽  
Finite Power ◽  
Three Dimensional Elasticity

A general solution is given to the three-dimensional linear elastic problem of a prismatic bar subjected to arbitrary tractions on its lateral surfaces, subject only to the restriction that they can be expanded as finite power series in the axial coordinate z . The solution is obtained by repeated differentiation of the tractions with respect to z , establishing a set of sub-problems . A recursive procedure is then developed for generating the solution to from that for . This procedure involves three steps: integration of the stress and displacement fields with respect to z , using an appropriate Papkovich–Neuber (P–N) representation; solution of two-dimensional in-plane and antiplane corrective problems for the tractions in that are independent of z ; and expression of these corrective solutions in P–N form. The method is illustrated by an example.

Analytical Solutions for Stress and Displacement Fields in Disks under Arbitrarily Distributed Loads

2017 ◽  
Vol 14 (06) ◽  
pp. 1750060
Author(s):  
Dexuan Qi ◽  
Yongshu Jiao ◽  
Lingling Pan
Keyword(s):  
Series Solution ◽  
Industrial Applications ◽  
Mining Engineering ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
General Series ◽  
In Series ◽  
Normal And Tangential Loads ◽  
Stress Boundary Conditions ◽  
Stress Boundary

The general series solution (GSS) approach is presented, in order to determine the stress and displacement fields in disks under arbitrarily distributed normal and tangential loads. An Airy stress function in series form is selected. Stresses are expressed by infinite coefficients. Thus displacements are expressed by the infinite stress coefficients. And self-equilibrated loads acting on the side edge are extended to Fourier series. Stress coefficients are related to loading coefficients by stress boundary conditions. Then five examples show the validity of this approach. The GSS approach might lead to industrial applications in rock mechanics, petroleum and mining engineering, etc.

Numerical Modeling of Partial Slip Contact Involving Inhomogeneous Materials

2012 ◽  
Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Partial Slip ◽  
Inhomogeneous Materials ◽  
Displacement Fields ◽  
Homogeneous Solutions ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Stress And Displacement Fields

When solving the problems involving inhomogeneous materials, the influence of the inhomogeneity upon contact behavior should be properly considered. This research proposes a fast and novel method, based on the equivalent inclusion method where inhomogeneity is replaced by an inclusion with properly chosen eigenstrains, to simulate contact partial slip of the interface involving inhomogeneous materials. The total stress and displacement fields represent the superposition of homogeneous solutions and perturbed solutions due to the chosen eigenstrains. In the present numerical simulation, the half space is meshed into a number of cuboids of the same size, where each cuboid is has a uniform eigenstrain. The stress and displacement fields due to eigenstrains are formulated by employing the recent half-space inclusion solutions derived by the authors and solved using a three-dimensional fast Fourier transform algorithm. The partial slip contact between an elastic ball and an elastic half space containing a cuboidal inhomogeneity was investigated.

scholarly journals Stress and Strain Analysis of Functionally Graded Rectangular Plate with Exponentially Varying Properties

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Amin Hadi ◽  
Abbas Rastgoo ◽  
A. R. Daneshmehr ◽  
Farshad Ehsani
Keyword(s):  
Rectangular Plate ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Functionally Graded ◽  
Stress And Strain ◽  
Governing Equations ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Graded Material ◽  
Three Dimensional Elasticity

The bending of rectangular plate made of functionally graded material (FGM) is investigated by using three-dimensional elasticity theory. The governing equations obtained here are solved with static analysis considering the types of plates, which properties varying exponentially along direction. The value of Poisson’s ratio has been taken as a constant. The influence of different functionally graded variation on the stress and displacement fields was studied through a numerical example. The exact solution shows that the graded material properties have significant effects on the mechanical behavior of the plate.

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