Contact Analysis of Cable Networks by Using Second-Order Cone Programming

A method based on mathematical programming is proposed for large deformation and contact analysis of cable networks. By explicitly considering these nonsmooth behaviors, we formulate the linear complementarity problems over symmetric cones under some practically acceptable assumptions. We also present the equivalent second-order cone programming (SOCP) problems, which can be regarded as the minimization problem of total potential energy and complementary energy with the subsidiary constraints on the displacements and contact forces, respectively. By solving the presented SOCP problems by using the primal-dual interior-point method, the equilibrium configurations and internal forces of several cable networks are obtained without any assumptions on stress states and contact conditions.