Contact Problems for Spherical Lens
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In this chapter the method for reducing a problem in the theory of elasticity to a generalized, in the sense of I.N.Vekua, Hilbert boundary-value problem, is extended to a mixed 3-D problem for a truncated sphere with a rigidly fixed spherical surface. The normal stresses at the cut are specified. The problems for a half-space with a spherical hollow or jut are treated similarly. The systems of functional equations of these problems are transformed to systems of singular integral equations. Then contact problems of a circular and annular punch punch are considered. Integral equations of these problems are reduced, supposing a geometric symmetry of contact regions, to Fredholm integral equations of the second kind with help of the method of paired equations.
KeywordsStress Intensity Factor Contact Pressure Contact Problem Contact Stress Contact Region
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