Constrained Form-Finding of Tension–Compression Structures using Automatic Differentiation. (February 2023) - Pastrana, Rafael; Ohlbrock, Patrick Ole; Oberbichler, Thomas; D'Acunto, Pierluigi; Parascho, Stefana
Abstract: 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 structural and geometrical 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 in 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 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. Highlights: A numerical form-finding method is extended to compute optimal shapes for 3D bar structures. The form-found shapes meet design constraints via automatic differentiation (AD) and gradient descent. AD leads to computational performance gains when solving constrained form-finding problems. A new topological object simplifies the modeling of a structure for form-finding. An open-source design tool for constrained form-finding written in Python is developed.