2021/11/04 by Rafael Pastrana, Patrick Ole Ohlbrock, Pastrana, Rafael +7
Engineering · #Architecture and Computational Design #Computational Engineering #Design Education and Practice #FOS: Computer and information sciences #FOS: Mathematics #Finance #J.2 #J.6 #Manufacturing Process and Optimization #Optimization and Control (math.OC) #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2111.02607
openalex publication_date 2021/11/04 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
This paper proposes a computational approach to form-find pin-jointed, bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet force and geometric constraints via gradient-based optimization. We achieve this by extending the combinatorial equilibrium modeling (CEM) framework in three important ways. First, we introduce a new topological object, the auxiliary trail, to expand the range of structures that can be form-found with the framework. Then, we leverage automatic differentiation (AD) to obtain an exact value of the gradient of the sequential and iterative calculations of the CEM form-finding algorithm, instead of a numerical approximation. Finally, we encapsulate our research developments into an open-source design tool written in Python that is usable across different CAD platforms and operating systems. After studying four different structures -- a self-stressed planar tensegrity, a tree canopy, a curved bridge, and a spiral staircase -- we demonstrate that our approach enables the solution of constrained form-finding problems on a diverse range of structures more efficiently than in previous work.