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Research Papers

Vertical Action of a Concentric Multi-Annular Punch on a Transversely Isotropic Elastic Half-Space

[+] Author and Article Information
Morteza Eskandari-Ghadi1

 Faculty of Engineering Department of Engineering Science, University of Tehran, P.O. Box 11155-4563, Tehran, Iranghadi@ut.ac.ir

Ronald Y. S. Pak

 Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO 80309-0428,pak@colorado.edu

Azizollah Ardeshir-Behrestaghi

 Department of Civil Engineering, Mazandaran University of Science and Technology, P.O. Box 737, Babol, Irana_ardeshir@ustmb.ac.ir

1

Corresponding author.

J. Appl. Mech 79(4), 041008 (May 09, 2012) (9 pages) doi:10.1115/1.4005546 History: Received June 29, 2010; Revised April 03, 2011; Posted January 30, 2012; Published May 09, 2012; Online May 09, 2012

In this paper, the response of a transversely isotropic half-space under the punch action of a set of rigid concentric annuli frictionless contacts is considered. By virtue of a compact potential representation and Hankel transforms, a set of ring-load Green’s functions for the axisymmetric equations of equilibrium are derived and shown to be expressible in terms of standard elliptic integrals. With the aid of a rigorous yet highly efficient numerical method, the integral equation is solved for the multi-interval singular mixed boundary value problem. Detailed solutions to illustrate the performance of the computational approach and the influence of the degree of anisotropy and contact conditions on the mechanics problem are presented.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Half-space containing transversely isotropic material under an axisymmetric surface vertical ring-load

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Figure 2

Geometry of a multiring rigid foundation on a transversely isotropic half-space

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Figure 3

Vertical displacement for different materials at the surface due to vertical ring load with r¯ equals unity

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Figure 4

Radial displacement for different materials at z=0.1 r¯ due to vertical ring load with r¯ equals unity

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Figure 5

Convergence of contact stress at z=0 for material II by AG element method to exact solution

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Figure 6

Comparison of contact stress per unit prescribed displacement at z=0 for a range of transversely isotropic materials

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Figure 7

The stress σzz per unit load under the effect of rigid punch at different depths for a range of transversely isotropic materials

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Figure 8

Vertical displacement variation under the action of rigid punch at different depth for a range of transversely isotropic materials

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Figure 9

Convergence of contact stress per unit prescribed displacement at z=0 for materials I and III by AG element method

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Figure 10

Contact stress per unit prescribed displacement at z=0 for materials I and III determined with different number of standard three-node elements

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Figure 11

The contact stress per unit displacement at z=0 for a rigid bi-annular punch with a1,1=0,  a2,2=a, and a2,1=0.50a, on material I as a1,2→a2,1

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Figure 12

The stress σzz at z = 0.25a per unit rigid displacement of a bi-annular foundation for different transversely isotropic materials

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Figure 13

The stress σzz at z = a per unit rigid displacement of a bi-annular foundation for different transversely isotropic materials

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Figure 14

Vertical displacement at z = 0 under the action of a bi-annular foundation for different transversely isotropic materials

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Figure 15

Vertical stiffness of an annulus rigid foundation as a function of Δa for materials I, III, and V

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Figure 16

Vertical stiffness of a bi-annular rigid foundation as a function of Δa1=Δa2 for materials I, III, and V: (a1,2,a2,2)=(0.5a,a)

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