A Derivation of Perturbed Equations of Motion and Heat Conduction of a Thermoelastic Solid.
ARMY MISSILE COMMAND REDSTONE ARSENAL ALA GROUND EQUIPMENT AND MATERIALS DIRECTORATE
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The report presents a brief discussion of the finite element method and the derivation of the perturbed equations of motion and heat conduction for an element. The general equations are first derived then nodal values of displacement, force, stress, entropy, temperature, heat flux, and heat flow are perturbed. Next, the material is assumed to follow anisotropic linear thermoelastic theory throughout its behavioral history. Alternatively, it is allowed to follow an unspecified theory in the gross behavior and anisotropic thermoelasticity only during the perturbations. No geometrical assumptions are made at this point concerning the finite element therefore, the equations derived in Section II can be adapted to a wide class of finite element approximations. In Section III various aspects of structural stability are considered. First, a number of fundamental definitions and theorems are presented. This is followed by a discussion of the stability of the behavioral expressions formulated in Section II for specific types of systems. Author