3-Node Sptial Saddle Element for Finite Element Calculation of Suspension Bridge

In order to solve the computational problem of nonlinear contact between main cable and saddle on tower top, a new 3-node spatial saddle element, including the saddle on tower top and both sides of the main cable, was produced. Based on the spatial catenary theory and the geometric relationship between main cable and saddle, the location of the tangent points and the cable force at the tangent points were obtained by solving the element state determination problem with known conditions. The accurate nodal force of the element was derived according to the static equilibrium. The elements of the tangent stiffness matrix were calculated based on its definition by replacing the differential with the increment. The new element could automatically satisfy the condition that the main cable is always tangent to the saddle, and thus the saddle jacking could be conveniently realized by modifying a parameter. Calculation shows that the new element has high calculation accuracy and convergence rate. The calculation results are the same with the numerical analytical solutions. The number of iterations is generally less than 12 in each element state solution.