On the duality of space-trusses and plate structures of rigid plates and elastic edges

Abstract

Dualities have been known to map space trusses and plate structures to each other since the 1980-s. Yet the computational similarity of the two has not been used to solve the unfamiliar plate structure with the methods of the well known truss. This paper gives a method to find the forces and displacements of a plate structure with rigid plates and elastic edges, using a dual truss. It is applicable for both statically determinate and indeterminate structures, subjected to both statical and kinematical loads.

On transformations and graphic methods of algebraically 3 dimensional force, velocity and displacement systems

“…The relevant forces can be either coplanar (F p ) or orthogonal to the plane (F c ), which is concurrent in the projective sense: the lines of action of the forces meet at infinity. (In certain cases the orthogonality is not a criterion and sometimes it is more convenient to consider different concurrent systems, see [11].) The same can be said for relevant velocities (E) and infinitesimal displacements (D).…”