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Form-finding method of cable-net structures using Grassmann algebra and mass-points

In the paper, an application of Grassmann algebra and weighted points, called mass- points, to the Force Density Method (FDM) for cable-net structures is described. In classical mechanics, point represents location in space, and vector represents a force acting on that point with added mass. In this way, it is possible to study geometry using fundamental principles of mechanics. Procedure for determining the centre of mass-points is closely related to finding the position of a free node of cable-net structure based on FDM. The method presented in this paper is iterative, based on mass-points, where points represent fixed nodes, their masses represent force densities in cables of structure, and centre of the mass-points represents the position of a free node, whose coordinates are unknown. The procedure is presented through an example of a simple cable-net structure consisting of only one free node. Since the form-finding in the form diagram is studied using principles of mechanics, it is possible to construct the reciprocal force polygon using obtained centres of the given mass-points. Applying the method described in this paper, an example of a cable-net structure is shown in the form diagram whereas force polygons are assembled in the force diagram.

graphic statics, reciprocal diagrams, form diagram, force diagram, mass-points, Grassmann algebra, Plücker coordinates, form-finding, equilibrium-finding

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