A boundary element solution is developed for the unilateral contact problem of a thin elastic plate resting on elastic homogeneous or nonhomogeneous subgrade. The reaction of the subgrade may depend linearly, or nonlinearly, on the deflection of the plate. The contact between the plate and the subgrade is unbonded. The subgrade surface is not necessarily plane, and miscontact between plate and subgrade due to initial gaps is also encountered. The solution procedure is based on the integral representation of the deflection for the biharmonic equation in which the unknown subgrade reaction is treated as loading term. The effectiveness of the proposed method is illustrated by several examples.

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