Adaptive Structures Optimization by means of the Virtual Force Density Method

The Virtual Force Density Method (VFDM) represents an extension of the well known Force Density Method (FDM) through a re-interpretation of the concept of connectivity matrix and a more general vector generation rule which no longer needs for an applied force field but only requires geometry. The method, already applied to geometrical optimization problems in architecture, such as the frames standardization of free form grid-shells and the approximation of complex shapes by planar quad meshes (PQ meshes), is proposed in this paper as an optimization tool in the field of Variable Geometry Structures (VGS). In particular, two novel possible applications of the VFDM are presented concerning, the first one, the study of the so-called origami structures and, the second one, Mutually Supported Elements (MSE). Both the studies aim to demonstrate the high flexibility of the method and its aptitude to face architectural/structural/geometrical problems since the only requirements are a set of nodes and a law to connect them, as available in most of the structures. Other than the method, the discussion aims to underline the feasibility of the proposed solutions in view of their application to the field of adaptive structures in architecture, that’s to say those structures belonging to the overall framework of ‘bionic’ building skin systems able to dynamically respond to or interact with various design drivers.