Predictor-corrector procedures for stress and free vibration analyses of multilayered composite plates and shells

Abstract

A study is made of two predictor-corrector procedures for the accurate determination of the global, as well as detailed, static and vibrational response characteristics of plates and shells. Both procedures use first-order shear deformation theory in the predictor phase, but differ in the elements of the computational model being adjusted in the corrector phase. The first procedure calculates a posteriori estimates of the composite correction factors and uses them to adjust the transverse shear stiffnesses of the plate (or shell). The second procedure calculates a posteriori the functional dependence of the displacement components on the thickness coordinate. The corrected quantities are then used in conjunction with the three-dimensional equations to obtain better estimates for the different response quantities. Extensive numerical results are presented showing the effects of variation in the geometric and lamination parameters for antisymmetrically laminated anisotropic plates, and simply supported multilayered orthotropic cylinders, on the accuracy of the linear static and free vibrational responses obtained by the predictor-corrector procedures. Comparison is also made with the solutions obtained by other computational models based on two-dimensional shear deformation theories. For each problem the standard of comparison is taken to be the analytic three-dimensional elasticity solution. The numerical examples clearly demonstrate the accuracy and effectiveness of the predictor-corrector procedures.