Finite-Element Large Deflection Analysis of Plates

A finite element formulation for the analysis of thin elastic plates subjected to transverse loading and including nonlinear geometric effects associated with large deflections is presented. The analysis utilizes local co-ordinate axes which translate and rotate with the individual elements so that the small deflection Kirchhoff formulation remains valid, with respect to these axes, and may be applied to determine element stiffness and resisting forces. Nonlinear terms in the strain displacement equations are included in the coordinate transformation and change of plate configuration is included in the equilibrium equations. The formulation is applied, using an iterative technique and an approximate incremental stiffness, to obtain solutions to a number of typical large deflection plate problems. Results include an inextensional plate problem, cylindrical bending, and a square plate with simple edge condition. Deflection and stress results are compared with solutions available in the literature.