The contact problem of a plate pressed between two spheres

The elastic contact of a plate with two axisymmetric bodies, generally of dissimilar elastic properties and curvatures, is considered. The solution of the resulting two integral equations is given as a truncated- series of Legendre polynomials of even order whose coefficients may be determined from a system of linear algebraic equations. The relationships between the total load, radii of curvature of the bodies, contact radii, approach, radial displacements, maximum contact stress, and the plate thickness can then be computed in terms of these coefficients. Numerical compulations have been carried out for the contact of a plate with two identical spheres. © 1964 by ASME.