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The existence of a "variational" solution to the system of nonlinear equations, governing the equilibrium of a thin elastic plate is proved. The boundary conditions correspond with a plate, the edge of which is partially clamped, supported and elastically supported or clamped, being loaded by moments, transversal loads and by forces in the plane of the plate. In Part I only "fixed" plates are studied, i.e. such that any deflection of a rigid plate on rigid supports and clampings is eliminated by the kinematic constraints.
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