Abstract
The present analysis examines the behavior of thin, circular, isotropic plates considering geometric nonlinear behavior but not material nonlinearity. The circular plates examined were solid with a fully clamped outer boundary. An approximate solution was determined with the aid of MACSYMA, a symbolic manipulation computer program, using the energy method. The loading cases examined were: a uniform pressure load and a central point load. The solution was based upon a two-term trial function for the plate deflection, with the coefficients written in a new way. This type of trial function allows the dimensionless deflection profile to vary with the loading. This is an improvement over many existing solutions. Results are given for dimensionless plate center deflection and dimensionless radial bending stress at the plate center. Comparisons between the present results and several existing analytical and finite-element solutions are presented. Also, comparisons of the present results and experimental analyses are given, with good agreement. Nomenclature a = plate radius D = plate flexural stiffness E — Young's modulus h = plate thickness k,kl,k2 = general undetermined coefficients K — kh = dimensionless form of constant k p =
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