Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems

In computational contact mechanics problems, local searching requires calculation of the closest point projection of a contactor point onto a given target segment. It is generally supposed that the contact boundary is locally described by a convex region. However, because this assumption is not valid for a general curved segment of a three-dimensional quadratic serendipity element, an iterative numerical procedure may not converge to the nearest local minimum. To this end, several unconstrained optimization methods are tested: the Newton-Raphson method, the least square projection, the sphere and torus approximation method, the steepest descent method, the Broyden method, the Broyden-Fletcher-Goldfarb-Shanno method, and the simplex method. The effectiveness and robustness of these methods are tested by means of a proposed benchmark problem. It is concluded that the Newton-Raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods, whereas the torus approximation method can be recommended for contact searching algorithms, which employ the Lagrange method or the augmented Lagrangian method. Copyright (c) 2015 John Wiley & Sons, Ltd.