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Torsional statics of two-dimensionally functionally graded microtubes

ABSTRACT A size-dependent governing equation is derived to investigate the torsional static behaviors of two-dimensionally functionally graded microtubes based on the modified couple stress theory. The shear modulus is assumed to vary along the tube’s length direction according to an exponential distribute function, and varies along the tube’s radius direction according to a power-law function. A generalized differential quadrature method is developed to determine the rotational angle and shear stresses. Some illustrative examples are given to investigate the effects of applied torques, the length scale parameter and various material compositions on the torsional angle and shear stresses.