Numerical approach for detecting bifurcation points of the compatibility paths of symmetric deployable structures

Abstract

New internal mechanisms of a deployable structure could be generated, when the structure undergoes significant transformations along its compatibility path. Because of such kind of kinematic bifurcation, the structure might not transform into the desired configuration. To design novel deployable structures, it is necessary to detect all possible bifurcation points of the compatibility paths and study the bifurcation behavior. Here, on the basis of the nonlinear prediction–correction algorithm with variable increment size, we will propose an efficient approach to detect all the possible bifurcation points of the compatibility path for a symmetric deployable structure. Null space of the Jacobian matrix is studied iteratively, to follow the complete compatibility path. The variable increment size at each step is determined by evaluating whether the configuration is close to the singular configuration. Numerical examples of several 2D and 3D symmetric deployable structures are presented, to verify the feasibility and computational complexity of the proposed approach. The results show that the proposed method is computationally efficient, and could detect different bifurcation points of the compatibility path. Further, it turns out that all the analyzed symmetric structures experience kinematic bifurcation on certain conditions.