Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm

[+] Author and Article Information
Shuangbiao Liu, Qian Wang

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208

J. Tribol 124(1), 36-45 (Jun 19, 2001) (10 pages) doi:10.1115/1.1401017 History: Received February 14, 2001; Revised June 19, 2001
Copyright © 2002 by ASME
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Elastic bodies and notations: (a) a halfspace; and (b) a halfspace with a single coating layer
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Discretization for computation: (a) in the z or zr direction; and (b) N1×N2 grid points on the x-y plane with z=zl or z=zrl
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The aliasing phenomenon in the frequency domain: (a) a spatial function with its discrete series; and (b) FT,FFT, the aliasing phenomenon, and the wrap-around order
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The aliasing phenomenon in the spatial domain (L=4,N=64; function f̃(m)=2/(1+m2) is illustrated, whose values outside the region [−201,201] are small enough to be neglected): (a) the function, its discrete series, and wrap-around order in the frequency domain; and (b) the spatial function f(x)=e−|x| and the aliasing phenomenon
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The Gibbs phenomenon shown by a rectangular pulse: (Dashed line: By conversion with AL=0,N=256; Solid line: By a Fourier series with 256 terms; and Bold solid line: By conversion with AL=8,N=256)
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The von Mises stress J2/P0 (x-z plane with y=0): (a) pressure loading; and (b) shear loading
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Relative errors of the Von Mises stress by comparing the solutions from the DC-FFT algorithm with those from Ref. 17: (a) x-z plane at y=0, pressure loading; (b) x-z plane at y=0, shear loading; (c) x-y plane at z=2/63 aH, pressure loading; and (d) x-y plane at z=2/63 aH, shear loading
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The von Mises stress J2/P0 (x-z plane at y=0): (a) μf=0.25; and (b) μf=0.5
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A halfspace with a rough surface in contact (RMS roughness=0.21 μm): (a) pressures distribution (H=1.8 GPa); and (b) the von Mises stress in the halfspace, μf=0.25
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A layered halfspace with a smooth surface in contact: (a) contact pressure profiles for different layers; (b) the von Mises stress J2/P0f=0.25,E1=2E2; and (c) the Von Mises stress J2/P0f=0.5,E1=E2/2
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The von Mises stress distribution in a layered halfspace (the loading is given in Fig. 9(a))




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