Nonlinear Behavior of Nonhomogeneous Beam due to Unsteady Heat Supply.

Abstract

In this paper, nonlinear behaviors such as large deflection, prebuckling and postbuckling are developed for a nonhomogeneous beam. Assuming that the beam is composed of a medium with nonhomogeneous thermal and mechanical material properties in the transverse direction, the one-dimensional transient heat conduction problem for such a nonhomogeneous beam is solved under the condition that the upper and lower surfaces of the beam are kept at constant temperature by the surrounding media. Thereafter, the associated nonlinear thermal deformation fields are analyzed theoretically making use of von Karman's deformation theory under the assumption of Bernoulli-Euler's hypothesis. As for the nonlinear response of the beam, the stationary principle of total potential energy is employed, and the numerical calculations are carried out for the thermal buckling behavior of a simply supported beam, making use of the calculating program for the nonlinear search procedure. The results for the thermal pre- and postbuckling behaviors are shown in the figures, and the influences of the nonhomogeneous material properties are discussed briefly.