HOMOGENEOUS SOLUTIONS AND SAINT-VENANT PROBLEMS FOR A NATURALLY TWISTED ROD

The method of homogeneous solutions is used to investigate a three-dim ensional problem for a naturally twisted rod. A group of elementary so lutions is established, enabling an applied theory of naturally twiste d rods to be developed without involving any hypotheses, by rigorous m athematical methods, as done previously [1] for prismatic rods. It is shown that in the general case (arbitrary twist and arbitrary position of the cross-sectional centre of gravity relative to the screw axis) the construction of elementary solutions reduces to solving two types of boundary-value problem in the cross-section, which in turn reduces to variational problems far non-negative operators. A stiffness matrix is obtained which relates the components of the principal vector and principal momentum of the external stresses to the coefficients of exp ansions in series of elementary solutions (the latter may be considere d as generalized displacements). The Saint-Venant principle is substan tiated. Copyright (C) 1996 Elsevier Science Ltd.