From a Weightless Bent Wire Coat Hanger to Shell Structures Via the Beltrami Stress Tensor

Abstract

A weightless wire coat hanger bent out of its plane is one of the simplest possible structures. All it does is transfer a force and moment around a closed space curve. Assembling a family of coat hangers enables us to build up trusses and frames and if we allow an infinite number of coat hangers which overlap we can assemble plates, shells and fully three dimensional structures. We can apply loads to these structures via a loading frame and wires, also made from coat hangers. A wire carrying an electric current produces a magnetic field in the space surrounding the wire. For the bent coat hanger we can imagine that there is a vector field surrounding the wire as a result of the force and moment in the wire. We can use this vector field to obtain expressions for the forces and moments in a shell in equilibrium with applied loads.