Geometrically nonlinear analysis of rectangular mindlin plates using the finite strip method

A general finite strip method of analysis is presented for the geometrically nonlinear analysis of laterally loaded, rectangular, isotropic plates. The analysis is based on the use of Mindlin plate theory and therefore includes the effects of transverse shear deformation. The nonlinearity is introduced via the strain-displacement equations and correspondingly the analysis pertains to problems involving moderate displacements but small rotations. The principle of minimum potential energy is used in the development of the strip and the complete plate stiffness equations and the latter equations are solved using the Newton-Raphson method. In numerical applications a particular type of finite strip is used in which all five reference quantities (three displacements and two rotations) are represented by cubic polynomial interpolation across the strip whilst the ends of the strip are simply supported for bending/shearing behaviour and immovable for membrane behaviour. These applications are concerned with uniformly loaded plates of both thin and moderately-thick geometry and detailed presentation is given of both displacement- and force-type quantities.