The performance of Mindlin plate finite strips in geometrically nonlinear analysis

Abstract

The finite strip method is used in the geometrically nonlinear analysis of laterally loaded isotropic plates within the context of Mindlin plate theory wherein the effects of transverse shear deformation are included. The analysis is of the Lagrangian type with the nonlinearity introduced by the inclusion of certain nonlinear terms in the strain-displacement equations. Following on from a related earlier investigation which dealt with a particular finite strip model, the performance of a range of different models is investigated. Linear, quadratic, cubic, and quartic polynomial interpolation is used in the different models in representing the variation of the five relevant displacement type quantities across a strip: also, both analytical (exact) and numerical (reduced, selective) schemes of integration are used in the crosswise direction in evaluating the stiffness properties of the various models. The ends of the finite strips are simply supported for out-of-plane behaviour and immovable for inplane behaviour. Detailed results are presented of the application of seven types of finite strip model to a range of plate problems, all involving uniformly loaded, square plates but with thin or moderately thick geometry and with simply supported or clamped longitudinal edges.