Pretwisted beam subjected to thermal loads: A gradient thermoelastic analogue

Abstract

It is well known from the classical torsion theory that the cross section of a prismatic beam subjected to end torsional moments will rotate and warp in the longitudinal direction. Rotation is depicted through the angle of twist per unit length and depends in general on the position along the length of the beam, while the warping function addresses the longitudinal distortion of the unrotated cross sections. In the present study, we consider a prismatic beam that possesses an initial twist which is constant along its length. A thermal field is present along the beam and its ends are loaded with axial forces and torsional moments. The governing equilibrium equations and the corresponding boundary conditions were obtained using an energy variational statement. A one-dimensional gradient thermoelastic analogue is developed. The advantageous aspect of the present study is that the additional (and peculiar) boundary conditions required by the gradient elasticity theory and the related microstructural lengths, analogous to micromechanical lengths, emerge in a natural way from the geometrical characteristics of the beam cross section and the material properties. We have examined various examples with different cross sections and loads to demonstrate the applicability of the model to the design of special yarns useful in smart textiles and thermally activated microdrilling actuators. © 2017 Taylor & Francis.