The energy method for solving a nonlinear problem of thermoelasticity for arod of variable cross section

Abstract

A horizontal rod of limited length is considered. Radius of the rod varies linearly along its length. The cross - sectional area of the left end is larger than the cross - sectional area of the right end. The lateral surface of the test rod is completely insulated. The heat flow is fed to the cross - sectional area of the left end. Through the cross - sectional area of the right end of the rod, heat exchange takes place with the surrounding medium. The field of distribution of temperature, displacement, three components of deformation and stresses are determined in the work, provided that both ends of the rod are rigidly fixed. And also, the magnitude of the elongation of the rod is determined when one end of the rod is fixed and when the other is free.In the case of fixing the two ends of the rod, the magnitude of the resulting axial compressive force is also calculated. When studying the rod, the fundamental laws of conservation of energy were used.