A generalization of a Hertz problem and that of a Mindlin problem were found for fourth-order paraboloids in contact. In particular, microslips and annulus of slip were sought. To this end an inverse method was devised. Moreover, an optimization procedure is described for finding the geometry for a given loading condition and set of material properties, within the family of paraboloids, which gives minimum slip. It has been shown in an example that the annulus of slip may be reduced by 60 percent while the maximum slip may be reduced by 90 percent.

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