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 surface is given for low pressures and for the highest pressure considered. Convergence of the solution is considered, and it sis estimated that the possible error is less than 2 percent. The results are compared with the only previous approximate analysis known to the author and agree with 5 percent. They are also shown to compare favorably with the known exact solutions for the long rectangular plate and the circular plate.