A self-equilibrated load method to locate singular configurations of symmetric foldable structures

Because of the geometric specialization, a foldable structure could be singular during folding along its ideal motion path. Singularity tends to result in undesired geometric configurations, and thus, it is necessary to locate singular configurations of foldable structures and to study their kinematic bifurcations. Using the steepest descent method and the nonlinear prediction-correction algorithm, we will present a self-equilibrated load method to locate singular configurations of foldable structures holding certain symmetries. The change of symmetry representation of internal mechanisms can reveal the singularity. The increment size for each iteration step depends on the product of the self-equilibrated load and the internal mechanisms. The singularity of both foldable pin-jointed structures and over-constrained structures is studied. Numerical results show that the method is effective and has a good convergence. Given certain load patterns, the proposed load method is capable of detecting the exact singular configurations in a small number of iteration steps. Independent mechanism modes associated with low-order symmetry representations will be induced, if a symmetric foldable structure reaches the singular configuration.