Thermotropic yield characteristic of the ceramic–alloy composite beam induced by a unilateral heat source

Abstract

Thermotropic yield characteristic of the ceramic–alloy composite beam induced by a unilateral heat source is investigated by using the Hamilton principle and the variation method based on the first‐order shear deformation theory. The mathematical essence of the yield problem of the composite beam is that the variation of the Lagrange function of the system to the space coordinates equals zero. The Tamura–Tomota–Ozawa model and the linear rule of mixtures are used to simulate the composite material properties of functionally graded material (FGM), and the constitutive equations are established with the linear hybrid hardening model. The von‐Mises yield condition is introduced to judge whether the beam enters the yield state. The governing equations are established by using the Hamilton principle and variation method. The thermotropic yield surfaces, the yield stresses, and the critical temperature rises of the yield functionally graded beam are obtained, and the deflections of the beam are calculated by analytical method. The results reveal that the yield interfaces, the yield stresses, the critical temperature rises, and the deflections of the beam vary with material parameters, geometric parameters, and so on.