Constrained Form-Finding of Tension–Compression Structures using Automatic Differentiation

This paper proposes a computational approach to form-find pin-jointed bar structures subjected combinations of tension and compression forces. The generated equilibrium states can meet additional structural geometrical constraints via gradient-based optimization. We achieve this by extending the combinatorial modeling (CEM) framework in three important ways. First, we introduce new topological object, auxiliary trail, expand range that be form-found with framework. Then, leverage automatic differentiation (AD) obtain an exact value gradient sequential iterative calculations CEM form-finding algorithm, instead numerical approximation. Finally, encapsulate our research developments into open-source design tool written Python is usable across different CAD platforms operating systems. After studying four –a self-stressed tensegrity, tree canopy, curved bridge, spiral staircase– demonstrate enables solution constrained problems on diverse more efficiently than previous work. • A method extended enhance form generation spatial static output forms satisfy force geometric presented which simplifies representation structure as valid input herein extended. Automatic leveraged algorithm marginal human intervention. application AD leads significant performance gains, especially when solving large problems. standalone, developed formulation plain simple code. readily systems distinct 3D software environments.