Initial Compressive Buckling of Clamped Plates Resting on Tensionless Elastic or Rigid Foundations

Abstract

The unilateral contact buckling problem of thin plates resting on tensionless foundations is investigated. Three different plate models are considered. For a plate of limited length on a tensionless elastic foundation, the plate is first simplified to a one-dimensional mechanical model by assuming a buckling mode in terms of transverse coordinates, after which a new method is employed to determine the initially unknown boundaries of the areas in contact. Based on the continuity condition on the borderline between contact and noncontact regions, the buckling mode displacements of the whole plate may be expressed through the critical load coefficient and the first half-wavelength, reducing the buckling problem to two nonlinear algebraic equations with two unknowns. This procedure has been named the transfer function method. For a very long plate with a symmetric buckling mode, an infinite plate model with two half-waves is presented. For a plate on a rigid foundation, a single half-wave buckling model is shown to be appropriate. Comparison of limiting cases with exact solutions and with ABAQUS results showed good agreement. Finally, the influences of aspect ratio and foundation stiffness are presented.