![]() ![]() Adriaenssens S., Ney L., Bodarwe E., Williams C., Finding the form of an irregular meshed steel and glass shell based on construction constraints, J Archit Eng 18 ( 3) ( 2012) 206– 213, 10.1061/(asce)ae.1943-5568.0000074. ![]() Kilian A., Ochsendorf J., Particle-Spring Systems for Structural Form Finding, J Int Assoc Shell Spat Struct 46 ( 2) ( 2005) 77– 84.Argyris J.H., Angelopoulos T., Bichat B., A general method for the shape finding of lightweight tension structures, Comput Methods Appl Mech Engrg 3 ( 1) ( 1974) 135– 149, 10.1016/0045-7825(74)90046-2.Bletzinger K., Fifty years of progress for shell and spatial structures : in celebration of the 50th anniversary jubilee of the IASS (1959-2009), International Association for Shell and Spatial Structures, Madrid, 2011.Lewis W.J., Tension structures: form and behaviour, Thomas Telford Distributors, ASCE Press, London, 2003. ![]() 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. 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. 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. First, we introduce a new topological object, the auxiliary trail, to expand the range of structures that can be form-found with the framework. We achieve this by extending the combinatorial equilibrium modeling (CEM) framework in three important ways. The generated equilibrium states can meet structural and geometrical constraints via gradient-based optimization. This paper proposes a computational approach to form-find pin-jointed bar structures subjected to combinations of tension and compression forces. ![]()
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