![]() ![]() This quadratic function is then turned into a linear formulation to facilitate the non-trivial computation of reciprocal polyhedral diagrams. In this method, a quadratic formulation is introduced to compute the area of a face based on its edge lengths only. The proposed method allows the user to control and constrain the areas and edge lengths of the faces of general polyhedrons that can be convex, self-intersecting, or concave in a group of aggregated polyhedral cells. The areas of the faces of the force diagram represent the magnitude of the internal and external forces in the members of the form diagram. In 3DGS, the form of the structure and its equilibrium of forces is represented by two polyhedral diagrams that are geometrically and topologically related. 3D graphic statics (3DGS) is a recently rediscovered method of structural form-finding based on a 150-year old proposition by Rankine and Maxwell in Philosophical Magazine. It provides algorithms and (numerical) methods to geometrically control the magnitude of the internal and external forces in the reciprocal diagrams of 3D/Polyhedral Graphic statics. This research is a continuation of the Algebraic 3D Graphic Statics Methods that addressed the reciprocal constructions in an earlier publication Hablicsek et al. This method facilitates the initial design and form generation of hollow-rope tensegrity optimized nodal geometry in a fully parametric interface. Then, by introducing an adaptive problem-solving algorithm, the correct functioning of the defined plugin for creating new and optimized tensegrity forms is investigated in several case studies. It is developed as an innovative workflow for design exploration, performance evaluation, and structural optimization of the tensegrity hollow-rope systems. ![]() In this research, using a modified force density algorithm, a fully parametric approach is developed for tensegrity design and form-finding. Although some research is conducted based on tensegrity form-finding and structural analysis, finding the optimal form of these systems is a complicated task in terms of its geometrical complexity and nonlinear behavior. ![]() The tensegrity hollow-rope modules can be implemented in the Architecture–Engineering–Construction (AEC) field, such as in the design of towers and bridges. Tensegrity is a stable self-equilibrated spatial structure composed of isolated members in compression inside contiguous tensioned components. ![]()
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