Abstract
The paper addresses a contact problem of the theory of elasticity, i.e., the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer. The elastic properties of a functionally graded layer arbitrarily vary with depth, and the foundation is assumed to be elastic, yet much harder than a layer. Approximated analytical solution is constructed, and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem. Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties. Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation.
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