Nonlinear Thermal Bending Problem of Nonhomogeneous Beam due to Unsteady Heat Supply.

Abstract

In this study, the nonlinear thermal bending problem is developed for a nonhomogeneous beam. Assuming that the beam is composed of the medium with nonhomogeneous thermal and mechanical material properties in the transverse direction, the transient heat conduction problem for such a nonhomogeneous beam is analyzed making use of the methods of finite sine transform and Laplace transform, and the analytical results are obtained under the condition that heat transfer between the surrounding media occurs at the upper and lower surfaces of the beam. Thereafter, the associated nonlinear thermal deformation fields are analyzed theoretically making use of the von Karman deformation theory under the assumption of the Bernoulli-Euler hypothesis. As for the nonlinear response of the beam, the stationary principle of total potential energy is employed, and the numerical simulations are carried out to elucidate the nonlinear thermal bending behaviors of the beam under the clamped edge condition, making use of the calculation program for the nonlinear search procedure. The results are shown in the figures, and the influences of geometrical nonlinearty, the nonhomogeneous material properties, and condition of heat transfer at surfaces of beam are discussed briefly.