Efficient generation of the cartesian coordinates of truncated icosahedron and related polyhedra

Deep Neural Networks for Form-Finding of Tensegrity Structures

Analytical paradigms have limited conventional form-finding methods of tensegrities; therefore, an innovative approach is urgently needed. This paper proposes a new form-finding method based on state-of-the-art deep learning techniques. One of the statical paradigms, a force density method, is substituted for trained deep neural networks to obtain necessary information of tensegrities. It is based on the differential evolution algorithm, where the eigenvalue decomposition process of the force density matrix and the process of the equilibrium matrix are not needed to find the feasible sets of nodal coordinates. Three well-known tensegrity examples including a 2D two-strut, a 3D-truncated tetrahedron and an icosahedron tensegrity are presented for numerical verifications. The cases of the ReLU and Leaky ReLU activation functions show better results than those of the ELU and SELU. Moreover, the results of the proposed method are in good agreement with the analytical super-stable lines. Three examples show that the proposed method exhibits more uniform final shapes of tensegrity, and much faster convergence history than those of the conventional one.