@article{PASTRANA2023103435,
title = {Constrained Form-Finding of Tension–Compression Structures using Automatic Differentiation},
journal = {Computer-Aided Design},
volume = {155},
pages = {103435},
year = {2023},
issn = {0010-4485},
doi = {https://doi.org/10.1016/j.cad.2022.103435},
url = {https://www.sciencedirect.com/science/article/pii/S0010448522001683},
author = {Rafael Pastrana and Patrick Ole Ohlbrock and Thomas Oberbichler and Pierluigi D’Acunto and Stefana Parascho},
keywords = {Form-finding, Shape optimization, Automatic differentiation, Structural design, Design tool, Combinatorial equilibrium modeling},
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.}
}