Stochastic behavior of Mindlin plate with uncertain geometric and material parameters

The Mindlin assumption in the plate bending allows the shear deformation together with the bending one. The constitutive relation for shear behavior, however, has different order of contribution from the plate thickness t than that in bending. Therefore, when we have concern on the stochastic behavior of Mindlin plate taking into account the uncertain plate thickness, the bending and shear parts have to be handled in different ways. Furthermore, if the concern is put on the multiple uncertain parameters such as between elastic modulus and plate thickness, the influence of correlation between these parameters also has to be resolved. In this study, a formulation for stochastic analysis is given in the context of the weighted integral method for Mindlin plate with uncertainties in elastic modulus and plate thickness. The effects of correlation between these parameters on the structural behavior are examined. In addition, the stability of response variability in terms of the aspect ratio of a plate is investigated. Several square plates with various boundary conditions subjected to uniformly distributed or concentrated loads are taken as examples, and the results are compared with those of precedent works as well as those of classical Monte Carlo simulation.