Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space |
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2-3 boundary Abramowitz and Stegun annular indenter Appendix approximation axisymmetric dashed axisymmetric geometry axisymmetric problem behavior Bessel function boundary conditions boundary in figure calculated Cauchy singularity coefficient method dot-dashed components contact dimensions contact pressure contact problem contact region solution coordinate corner curve defined determined elliptic integral Erdogan and Gupta evaluated figure 14 geometry parameter space given by equation Gladwell and Gupta Green's function Gupta moment method h₁ h₂ half-space solution Hankel transform inner radius integrand interface stresses kernel linear equations load equation logarithmic singularity method dashed method of solution nondimensional normal stress obtained orthogonal polynomials parameter space divisions plane-strain geometry plane-strain problem plane-strain solid Poisson's ratio present solution solid shear stress single layer singular integral equation solu solve stress intensity factor substrate surface displacement three contact region tion TOP LAYER MODULUS transfer matrix values variable vector zero