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

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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.

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I.—On Reciprocal Figures, Frames, and Diagrams of Forces

J. Maxwell (1870)

Two figures are reciprocal when the properties of the first relative to the second are the same as those of the second relative to the first. Several kinds of reciprocity are known to mathematicians, and the theories of Inverse Figures and of Polar Reciprocals have been developed at great length, and have led to remarkable results. I propose to investigate a different kind of geometrical reciprocity, which is also capable of considerable development, and can be applied to the solution of mechanical problems.