Crystal Lattice Theory of Torsion of a Rectangular Bar of Simple Cubic Structure

摘要

In this paper, there is described an exact, closed solution of the Gazis-Herman-Wallis difference equations of a simple cubic crystal lattice for the case of torsion of an elastic bar of rectangular cross section. Examples are worked out for increasing numbers of particles in the cross section and various ratios of width to depth of cross section until the pattern of the warping function from de St. Venant's continuum solution is established. The displacement of each particle, characterizing the warping function, is given as a simple ratio of integers times the product of the angle of twist per unit length and the square of the distance between nearest neighbor particles. (Author)