DYNAMICS OF PRESTRESSED ROTATING ANISOTROPIC PLATES SUBJECT TO TRANSVERSE LOADS AND HEAT SOURCES, PART I: MODELLING AND SOLUTION METHOD

This paper considers the application of the finite element method for the analysis of translating or rotating plates, based on Mindlin plate theory and the von Kلrmلn strain expression, in the context of linear thermoelasticity. The existence of convective terms generates gyroscopic terms, unstabilizing effects in the stiffness matrix, and radial in-plane tension. Homogenization theory, applicable to not only determining the global material properties for composite materials like laminate or fiber-reinforced matrix, but also computing microscopic stress levels, was applied to obtain orthotropic material properties. The quasi-static stretching assumption was used to simplify the governing equations. A second order implicit time-integration scheme, applicable for both the linear and non-linear governing equations, was presented, which allows a time increment sufficiently large (without numerical stability problems) based on the accuracy needed. This paper (Part I) presents the problem formulation and solution methods, while a companion paper (Part II) presents and discusses results for specially orthotropic rotating disks.