It is well known from the classical torsion theory that the cross section of aprismatic beam subjected to end torsional moments will rotate and warp inthe longitudinal direction. Rotation is depicted through the angle of twist perunit length and depends in general on the position along the length of thebeam, while the warping function addresses the longitudinal distortion of theunrotated cross sections. In the present study, we consider a prismatic beamthat possesses an initial twist which is constant along its length. A thermalfield is present along the beam and its ends are loaded with axial forcesand torsional moments. The governing equilibrium equations and the correspondingboundary conditions were obtained using an energy variationalstatement. A one-dimensional gradient thermoelastic analogue is developed.The advantageous aspect of the present study is that the additional (andpeculiar) boundary conditions required by the gradient elasticity theory andthe related microstructural lengths, analogous to micromechanical lengths,emerge in a natural way from the geometrical characteristics of the beam crosssection and the material properties. We have examined various examples withdifferent cross sections and loads to demonstrate the applicability of the modelto the design of special yarns useful in smart textiles and thermally activatedmicrodrilling actuators.
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