A simplified, nonlinear thermodynamic theory of beamshells

Abstract

Abstract.This paper develops a nonlinear thermodynamical theory for arbitrary elastic beamshells (infinite cylindrical shells in plane strain) in which approximations are made only in the First Law of Thermodynamics (Conservation of Energy) and in the associated constitutive relations. The basic approach is straightforward:the threedimensional equations of motion and the Second Law of Thermodynamics (ClausiusDuhem Inequality) for an infinite cylindrical body subject to external loads and heating are written in integral-impulse form and then specialized to beamshells.

A Simple Nonlinear Thermodynamic Theory of Arbitrary Elastic Beams

“…First, a beam in some ways is more complicated than a shell, having two lateral dimensions small compared to its length, although no assumption of slenderness is made herein. Second, T and G, as defined herein, are different from the definitions in [2] and [3] and lead to a cleaner form of a beamlike Second Law.…”

“…Much of the development follows [1] and [2]; however, there are important differences. First, a beam in some ways is more complicated than a shell, having two lateral dimensions small compared to its length, although no assumption of slenderness is made herein.…”

Heat conduction and radiative heat exchange in cellular structures using flat shell elements

“…In this context, the geometrical aspects are largely simpliÿed and contrary to some recent works on the subject (e.g. Reference [2]), we develop a much more e cient form. In taking into account for thermo-mechanical coupling e ects in such a model, we introduce average temperature T and through-the-thickness gradient G, supplemented by generalized dual uxes Q and R. The resulting discrete approximation and implementation employ a at quadrilateral shell element (see Reference [3]) which furnishes a useful tool in structural analysis.…”