Chapter 16 - Global plate equations for large transverse displacements

Abstract

Here, we will now derive the global plate equations by integrating the non-linear equations of motion that the Kirchhoff stress tensor satisfies, for the case where the absolute value of u 3 is not small in comparison with the plate thickness. This configuration allows the buckling of plates to be studied. In addition, the absolute values of uI and u2 are small in comparison with the plate thickness, and the absolute values of partially derived functions of u I and u 2 with respect to xl, x 2 and x 3 are less than 1. We will clarify these relations in both Reissner–Mindlin and Kirchhoff–Love type analyses. First, in detail we look at the local plate equations, then the global plate equations are seen, the global plate moment equation for static, vibration, and buckling cases are covered. Reissner–Mindlin equations and Kirchoff–Love equations are studied.