Nonlinear analysis of thermal-mechanical coupling bending of clamped FG porous curved micro-tubes

A nonlinear analysis on the thermal-mechanical coupling bending behavior of functionally graded porous curved micro-tubes is performed in this research. The case of curved micro-tubes with doubly-clamped boundary conditions resting on nonlinear elastic foundation is considered. Based on the modified couple stress theory, curved micro-tubes under uniformly distributed transverse pressure and uniform temperature rise are analyzed. It is assumed that the material properties of the curved micro-tube are temperature-dependent and graded across the radius of cross-section. The governing equations of the curved micro-tube are established within the framework of higher-order shear deformation theory and the von Karman kinematic assumptions. These equations are reformulated for the case of curved micro-tubes with even distributed porosities based on the uncoupled thermoelasticity theory. The system of nonlinear differential equations governing the equilibrium position of curved micro-tubes is solved using the two-step perturbation technique. The analytical solutions are given in this study to obtain the large deflection in curved micro-tubes as an explicit function of the thermal/mechanical load. The influences of porosity volume fraction, power law index, microstructural length scale parameter, foundation stiffness, and geometrical parameters on the thermomechanical deflection of curved micro-tubes are investigated.