An analytical method for solving the two-dimensional frictionless continuous contact
problem of an orthotropic layer pressed by a rigid stamp is presented in this paper.
The orthotropic layer lies on a rigid foundation, and plane-strain orthotropy prevails
in the layer, which is not bonded to the rigid foundation. An external load
was applied to the orthotropic layer through a rigid stamp. The profiles of
flat and cylindrical stamps as stamp shapes were handled separately. The
orthotropic layer was assumed to be subjected to uniform vertical body forces
owing to the effect of gravity. For values of the resultant compressive force
acting on the stamp vertically that were lesser than a critical value, the continuous
contact along the orthotropic layer–rigid foundation interface was maintained. By
assuming plane-strain conditions, the governing equations corresponding to the
mentioned contact problem were extracted separately in the presence and absence of
the body force of the orthotropic layer using the theory of elasticity and the Fourier
integral transformation technique. Subsequently, the mixed boundary value problem
was reduced to a singular integral equation, and the numerical solution of this
singular integral equation was obtained by applying the Gauss–Chebyshev
integration formulas. Numerical results reveal the effect of the orthotropic material
parameters, stamp length (in the case of a flat stamp), stamp radius (in the case of a
cylindrical stamp), applied load on the contact stress distributions, contact length,
initial separation load and initial separation distance. The results of this
study may provide insights for engineers in fields closely related to contact
mechanics.
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