Algebraic 3D Graphic Statics: Constrained Areas

This research is a continuation of the Algebraic 3D Graphic Statics Methods that addressed reciprocal constructions in an earlier publication (Hablicsek et al. 2019). It provides algorithms and (numerical) methods to geometrically control magnitude internal external forces diagrams 3D/Polyhedral statics. graphic statics (3DGS) recently rediscovered method structural form-finding based on 150-year old proposition by Rankine Maxwell Philosophical Magazine. In 3DGS, form structure its equilibrium are represented two polyhedral topologically related. The areas faces force diagram represent members diagram. proposed allows user constrain edge lengths general polyhedrons can be convex, self-intersecting, or concave group aggregated cells. this method, quadratic formulation introduced compute area face only. function then turned into linear facilitate non-trivial computation diagrams. approach applied diagrams, including cells, manipulating geometry with predefined lengths. implemented as multi-step algorithm where each step includes computing single target updating geometry. One remarkable results framework construction zero-area McRobie (2017b). member zero shows how self-intersecting faces, constructed additional constraints cells without breaking reciprocity Thus, it more hints generalization principle frames. also suggests design boundary conditions compression-only systems manipulated both compression tensile no change faces’ planarity • Proposed algebraic controls system defined precise achieved. computes updates zero-bar elements controlled.