Projective transformations of structural equilibrium

Direct methods that transform the geometry of a structure and conserve its static equilibrium are of particular interest for designers. They allow the exploration of alternative solutions at minimum computational cost. While parallel transformations (stretch, contraction, and skew) are easily understood and have been in use since long, nonparallel transformations that maintain static equilibrium have not been studied in detail. The contributions of this article are as follows. First, an extensive review of transformation methods maintaining static equilibrium of planar and spatial structures is carried out. Second, an alternative construction of projective transformation is developed as an original set of graphical operations. Third, the benefits and limitations of use of projective transformations are discussed for the first time. This article concludes that (1) projective transformations are of practical interest only for a restricted range of structural applications but (2) can significantly simplify the computational problem of geometric exploration of spatial networks in equilibrium with few or no external forces.