This paper considers the application of the "nite element method for the analysis of translating or rotating plates, based on Mindlin plate theory and the von KaH rmaH n strain expression, in the context of linear thermoelasticity. The existence of convective terms generates gyroscopic terms, unstabilizing e!ects in the sti!ness matrix, and radial in-plane tension. Homogenization theory, applicable to not only determining the global material properties for composite materials like laminate or "ber-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 su$ciently 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.
2000 Academic Press
1. Introduction
This paper considers a general two-dimensional coupled thermal and plate bending problem for a rotating anisotropic plate subject to transverse forces and heat sources, including transverse shear stresses and rotary inertia. Such problems arise in a variety of technologies, including subsidiary memory devices such as #oppy disks, hard disks, CD-ROMs, and optical disks. Many researchers have studied the behavior of disks or circular plates in such applications as circular saws, turbines, and more recently, computer memory devices. Recently, laminated composite media are e!ectively utilized in some of these applications. It is, thus, important to consider anisotropic material properties in the study of the dynamic behavior of disks. In a computer disk this anisotropy*special orthotropy*comes from two sources. One is that, the disk has di!erent geometric shapes in the radial and circumferential directions, because the disks used for data storage store their data along tracks in the circumferential direction. These tracks are actually circumferentially aligned