Stabilization Techniques for the Nonlinear Analytic Nodal Method

The nonlinear analytic nodal method, which is formulated by combining the nonlinear iteration technique and the analytic nodal method (ANM), requires analytic solutions of the two-node problems. When the method is applied to problems that contain near-critical nodes in which there is essentially no net leakage, the two-node ANM solution for such nodes results in highly ill-conditioned matrices and potential numerical instabilities, especially in single precision arithmetic. Two stabilization techniques are introduced to resolve the instability problem by employing alternate basis functions for near-critical nodes. The first uses the exact ANM solution for a critical node, and the second employs the nodal expansion method. Both techniques are shown to perform well; however, the solution accuracy can be mildly sensitive to the criterion used to invoke the stabilized coupling kernel.