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National Advisory Committee for Aeronautics, Report - Square Plate with Clamped Edges Under Normal Pressure Producing Large Deflections

A theoretical analysis is given for the stresses and
deflections of a square plate with clamped edges under
normal pressure producing large deflections. Values of
the bending stress and membrane stress at the center of the
plate and at the midpoint of the edge are given for center
deflections up to 1.9 times the plate thickness. The shape
of the deflected suzface is given for low pressures and for
the highest pressure considered. Convergence of the
solution is considered and it is estimated that the possible
error is less than 2 percent. The results are compared
with the only previous approximate analysis lmoum to
the author and agree within 5 percent. They are also.
shown to compare favorably with the known exact solutions
for the long rectangular plate and the circular plate.

An exact solution for the small deflections of a plate
with clamped edges was given by Hencky in reference 1
and an approximate solution for large deflections was
presented by Way in reference 2. In a previous paper
(reference 3) there is presented a solution of the
fundamental von Karmzin large-deflection equations for
a simply supported rectangular plate under combined
edge compression and lateral loading.

In the present paper a theoretical analysis is given
for the stresses and deflections of a square plate under
normal pressure producinglarge deflections. The edge
supports are assumed to clamp the plate rigidly against
rotations and displacements normal to the edge'but to
permit displacements parallel to the edge. . The analysis
replaces the edge bending moments by an equivalent
pressure distribution and then applies the general
solution for the simply supported rectangular plate.

The results for small deflections obtained by the.
analysis agree exactly with those of Hencky and for
large deflections differ by less than 5 percent from the
approximate solution of Way.