Many authors attempted to establish a direct correlation between the equation of the surface of an equivalent rigid punch and the pressure distribution arising when this punch is pressed against a corresponding elastic half-space. The results are encouraging, but they have a limited applicability and the involved calculations are still complicated. This paper advances a simple correlation based on a new interpretation of integral condition of deformation of a contact and on the dependence of pressure or pressure gradient on singularities in surface gradient or curvature. Based on this correlation, a method to find the pressure distribution for contacts bound by surfaces described by up to second order polynomials is advanced. The new method is applied in several classical contact problems and a very good agreement is found with existing solutions.

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