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.

Asymmetric Mixed Boundary-Value Problems of the Elastic Half-Space

1965 ◽  
Vol 32 (2) ◽  
pp. 411-417 ◽  
Author(s):  
R. A. Westmann
Keyword(s):  
Boundary Value Problems ◽  
Half Space ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Elastic Half Space ◽  
Integral Solution ◽  
Displacement Fields ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Stress And Displacement Fields

Solutions are presented, within the scope of classical elastostatics, for a class of asymmetric mixed boundary-value problems of the elastic half-space. The boundary conditions considered are prescribed interior and exterior to a circle and are mixed with respect to shears and tangential displacements. Using an established integral-solution form, the problem is reduced to two pairs of simultaneous dual integral equations for which the solution is known. Two illustrative examples, motivated by problems in fracture mechanics, are presented; the resulting stress and displacement fields are given in closed form.

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.

Stress Behavior at the Interface Junction of an Elastic Inclusion

2002 ◽  
Vol 69 (6) ◽  
pp. 844-852 ◽  
Author(s):  
Z. Q. Qian ◽  
A. R. Akisanya ◽  
D. S. Thompson
Keyword(s):  
Finite Element ◽  
Elastic Inclusion ◽  
Symmetric Mode ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Two Phase ◽  
Stress And Displacement Fields ◽  
Higher Order Terms ◽  
The Matrix ◽  
Finite Element Prediction

The stress distribution at the interface junction of an elastic inclusion embedded in a brittle matrix is examined. Solutions are derived for the stress and displacement fields near the junction formed by the intersection of the interfaces between the inclusion and the matrix. The stress field consists of symmetric (mode I) and skew-symmetric (mode II) components. The magnitude of the intensity factor associated with each mode of deformation is determined using a combination of the finite element method and a contour integral. The numerical results of the stresses near the interface junction of two different inclusion geometries show that the asymptotic solutions of the stresses are in agreement with those from the finite element prediction when higher-order terms are considered. The implications of the results for the failure of particle-reinforced and two-phase brittle materials are discussed.

scholarly journals Width-Wise Variation of Magnetic Tape Pack Stresses

2002 ◽  
Vol 69 (3) ◽  
pp. 358-369 ◽  
Author(s):  
Y. M. Lee ◽  
J. A. Wickert
Keyword(s):  
Magnetic Tape ◽  
Mixed Boundary ◽  
Element Model ◽  
Order Model ◽  
Displacement Fields ◽  
Reduced Order ◽  
One Dimensional ◽  
Stress And Displacement Fields ◽  
The Media ◽  
Winding Tension

A model is developed for predicting the stress and displacement fields within a magnetic tape pack, where those quantities are allowed to vary in both the pack’s radial and transverse (cross-tape) directions. As has been the case in previous analyses based upon one-dimensional wound roll models, the present approach accounts for the anisotropic and nonlinear constitutive properties of the layered tape, and the incremental manner in which the pack is wound. Further, such widthwise variation effects as differential hub compliance and nonuniform winding tension, which can be significant in data cartridge design, are also treated in the model. The pack is analyzed through a two-dimensional axisymmetric finite element model that couples individual representations of the hub/flange and layered tape substructures. The bulk radial elastic modulus of the tape, which depends on the in-pack radial stress, is measured for a variety of media samples, and a reduced-order model is developed to capture the nonlinear modulus-stress correlation. The stiffness matrix of the hub/flange at its interface with the media provides a mixed boundary condition to the tape substructure. In this manner, design-specific hubs can be readily analyzed, and criteria for their optimization explored. Simulations of several cartridge designs are presented, and the roles of hub compliance and wound-in tension gradient in setting the pack’s stress field and cross-tape width change are discussed.

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.

THREE-DIMENSIONAL ANALYSIS OF THICK PLATES BY MLS-RITZ METHOD

2008 ◽  
Vol 08 (01) ◽  
pp. 77-101 ◽  
Author(s):  
L. ZHOU ◽  
W. X. ZHENG
Keyword(s):  
Mixed Boundary ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Least Square ◽  
3D Analysis ◽  
Displacement Fields ◽  
Linear Elasticity Theory ◽  
Thick Plates ◽  
Moving Least Square

This paper presents a three-dimensional (3D) moving least-square Ritz (MLS-Ritz) formulation for the free vibration analysis of homogeneous elastic thick plates with mixed boundary constraints. The analysis is based on the linear elasticity theory. The Ritz trial functions are established through the moving least-square technique for the displacement fields of the plates. Vibration frequencies for thick square plates and right-angled isosceles triangular plates are obtained by the MLS-Ritz method. The reliability and accuracy of the presented method are examined by extensive convergence and comparison studies and it is established herein that the MLS-Ritz method is a powerful and effective numerical method for the 3D analysis of thick plates.

Shrink fit of an elastic half-space with a cylindrical cavity

1995 ◽  
Vol 448 (1932) ◽  
pp. 81-88 ◽  
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elastic Half Space ◽  
Series Method ◽  
Dual Integral Equations ◽  
Axisymmetric Contact Problem ◽  
Shrink Fit

This paper deals with the axisymmetric contact problem for an elastic half-space with a cylindrical cavity when mixed boundary conditions are prescribed on the surface of the cavity. The problem is simplified to that of finding the solution of dual integral equations arising from the mixed boundary conditions. The solution is obtained by the series method, and quantities of physical interest are calculated.

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.

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