Material gradation effects on twisting statics of bi-directional functionally graded micro-tubes

Abstract

This study aims to characterize the twisting behavior of bi-directional functionally graded (FG) micro-tubes under torsional loads within the modified couple stress theory framework. The two material properties involved in the torsional static model of FG small-scale tubes, i.e., shear modulus and material length scale parameter, are assumed to possess smooth spatial variations in both radial and axial directions. Through the utilization of Hamilton’s principle, the governing equations and boundary conditions are derived, and then, the system of partial differential equations is numerically solved by using the differential quadrature method. A verification study is conducted by comparing limiting cases with the analytical results available in the literature to check the validity of the developed procedures. A detailed study is carried out on the influences of the phase distribution profile and geometric parameters upon twist angles and shear stresses developed in FG micro-tubes undergoing external distributed torques.