  In the design of tensegrity structures, traditional form-finding methods
utilize kinematic and static approaches to identify geometric configurations
that achieve equilibrium. However, these methods often fall short when applied
to actual physical models due to imperfections in the manufacturing of
structural elements, assembly errors, and material non-linearities. In this
work, we develop a deep neural network (DNN) approach to predict the geometric
configurations and physical properties-such as nodal coordinates, member
forces, and natural frequencies-of any tensegrity structures in equilibrium
states. First, we outline the analytical governing equations for tensegrity
structures, covering statics involving nodal coordinates and member forces, as
well as modal information. Next, we propose a data-driven framework for
training an appropriate DNN model capable of simultaneously predicting
tensegrity forms and physical properties, thereby circumventing the need to
solve equilibrium equations. For validation, we analyze three tensegrity
structures, including a tensegrity D-bar, prism, and lander, demonstrating that
our approach can identify approximation systems with relatively very small
output errors. This technique is applicable to a wide range of tensegrity
structures, particularly in real-world construction, and can be extended to
address additional challenges in identifying structural physics information.
