Stability analysis of cable–bar structures by inverse-power method for eigenvalue analysis with penalization

A numerical method is presented for stability analysis of cable–bar structures. An optimization problem is formulated to find the minimum value of the incremental total potential energy that depends on the direction of the incremental displacements. The penalty method with slack variables is used for representing the discontinuity in member stiffness. The tangent stiffness matrix is shifted to be positive definite so that the minimum of its quadratic form is found by the inverse-power method. It is shown in the numerical examples that the minimum value of the incremental potential energy and the associated displacement increments can be found with good accuracy in about 10 steps of iteration.