%0 Generic %1 pastrana2021constrained %A Pastrana, Rafael %A Ohlbrock, Patrick Ole %A Oberbichler, Thomas %A D'Acunto, Pierluigi %A Parascho, Stefana %D 2021 %K automatic_differentiation design_tool generative-models inverse-problems numerical-methods optimization %T Constrained Form-Finding of Tension-Compression Structures using Automatic Differentiation %U http://arxiv.org/abs/2111.02607 %X 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.

@misc{pastrana2021constrained, 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 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.}, added-at = {2023-09-29T15:10:44.000+0200}, author = {Pastrana, Rafael and Ohlbrock, Patrick Ole and Oberbichler, Thomas and D'Acunto, Pierluigi and Parascho, Stefana}, biburl = {https://www.bibsonomy.org/bibtex/22e179b887082121b7bd4a3fa978714f3/tabularii}, description = {[2111.02607] Constrained Form-Finding of Tension-Compression Structures using Automatic Differentiation}, interhash = {4043eed7857e96ef710069f6dc820d75}, intrahash = {2e179b887082121b7bd4a3fa978714f3}, keywords = {automatic_differentiation design_tool generative-models inverse-problems numerical-methods optimization}, note = {cite arxiv:2111.02607}, timestamp = {2023-09-29T15:10:44.000+0200}, title = {Constrained Form-Finding of Tension-Compression Structures using Automatic Differentiation}, url = {http://arxiv.org/abs/2111.02607}, year = 2021 }