Nonlinear Asymptotic Solution of the Reissner Plate Equations

Abstract

Based on the Reissner plate equations for large displacements and rotations within the limits of small strain, asymptotic solutions are developed for circular plates under uniform pressure. With the boundary layer solution assumed in exponential form, the boundary conditions are applied directly at the plate edge without the need for matched asymptotic expansions. Results are presented for plates with clamped edges. When compared to the solution for the special case of von Kármán plate theory, stresses generally deviate by less than 10 percent for rotation angles up to about 30 deg.