A finite element procedure for large deflection analysis of plates with initial deflections

Abstract

The concepts of the matrix displacement approach to finite element structural analysis are extended to analyze the large deflection behavior of plates with initial deflections. The initial deflections are considered to be of the order of magnitude of the plate thickness. The large deflection phenomena are accounted for by considering the influence of the element membrane forces due to initial deflection and large bending on element flexure stiffness matrices. The effects of element membrane forces due to initial deflection and large bending are characterized in the nonlinear stiffness formulations by the zero, first, and second order incremental stiffness matrices. Representations of the nonlinear effects are formulated for a conforming rectangular plate finite element. The formulations are appropriate for both the iterative and incremental approaches. Large deflection behaviors are predicted for rectangular plates with different length-width ratios and various boundary conditions. Comparisons with some available alternative analytic solutions are provided. Examples are performed by a piecewise linear incremental approach. A reduction scheme which removes certain degrees of freedom from the problem statement is incorporated into the numerical procedure.