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Summary A method is given for the treatment of plates, portions of which are constrained by two smooth, rigid, plane, clamping sur faces. By employing the E. Reissner plate theor}^, expressions for the stresses and displacements, valid for the region constrained within the clamp, are obtained and appropriate continuity condi tions are satisfied at the edge of that region. The numerical re sults of a specific axisymmetric example illustrate the sub stantial improvement of the present treatment. HE PRESENT paper is concerned with the bending of uniform, isotropic, elastic plates, portions of which are clamped between two smooth rigid plane surfaces. In particular, the analysis of the present paper is con cerned with axisymmetric circular plates, having an nular portions constrained by smooth, rigid, clamping members. Consistent with the assumption that the transverse normal component of the displacement of the plate is independent of the thickness coordinate, to gether with the usual assumptions associated with smooth rigid surfaces, it will be assumed that those por tions of the plate contained within the smooth clamp will satisfy the following conditions: (1) The deflection is constant; and (2) the top and bottom surfaces of the plate are free from shearing tractions. Such assumed conditions serve as an idealization for the clamped edge conditions for the particular case where the interior sur faces of the clamping members are relatively smooth and where the rigidity of the plate is small in compari son to the rigidity of the clamping member. While the usual clamped or built-in edge conditions1 are physi cally consistent (as well as experimentall y verified) for the case where the surface of the clamp is sufficiently rough to prevent slippage, it should be noted that al though they imply the application of stress couples and resultants at the edge of the clamp, no information is given regarding the displacement and stress fields in that portion of the plate contained within the clamp. For the case of a smooth clamp, the method of the present paper is to obtain expressions for the stresses and displacements, valid for the plate region contained |
