Solving 2D rolling problems using the NORM–TANG iteration and mathematical programming

In this paper, an approach to steady-state rolling, based on the boundary element method and mathematical programming techniques is presented. The algorithm solves the problem by an enchained iteration with the NORM and TANG parts of the problem. These two parts are solved by different methods because of the different nature of the non-linearities inside each one of them. The normal part has a weak non-linearity and can be solved as a linear complementary problem by the Lemke method, but the tangential part, with a stronger non-linearity, needs other methods. This work presents three different ways to solve this part by using mathematical programming techniques, showing their flexibility and reliability by solving various classic problems.