Pretwisted Beams in Axial Tension and Torsion: Analogy with Dipolar Gradient Elasticity and Applications to Textile Materials

AbstractA technical theory for pretwisted beams that accounts for variable twist (constrained warping) is based on an approximate displacement field that is defined completely in terms of two unknown functions: the axial displacement w1(z) and the rotation ϕ(z) of the cross section about the centroidal axis of the beam, z being the coordinate along the axis of the beam. The primary unknowns are determined by minimizing the potential energy of the beam. The problem is then formulated in terms of w1(z), and an analogue between the technical theory and a one-dimensional dipolar gradient elasticity model is presented. The application of the theory to textile materials is discussed.