Direct calculation of critical points in parameter sensitive systems

At critical points along the equilibrium path, sudden and sometimes catastrophic changes in the structural behaviour are observed. The equilibrium path, load-bearing capacity and locations of critical points can be sensitive to variations in parameters, such as geometrical imperfections, multi-parameter loadings, temperature and material properties. This paper introduces an incremental-iterative procedure to directly calculate the critical load for parameterized elastic structures. A modified Newton’s method is proposed to simultaneously set the residual force and the minimum eigenvalue of the tangent stiffness matrix to zero by using an iterative algorithm. To demonstrate the performance of this method, numerical examples are presented.

► A method to calculate the critical load for parameter sensitive elastic structures is introduced.
► Stability boundaries with limit, simple or multi-bifurcation points can be traced.
► A formula to update the arc length constraint for better convergence is introduced.