Mixed linear complementary formulation of lateral contacts among a system of parallel beams

摘要

A novel linear complementary formulation is developed in this paper to deal with multiple lateral contacts at a number of cross sections for a structure consisting of many parallel beams and having rigid body displacements. The proposed method can be used to handle a challenging situation where the number of potential contact pairs exceeds the total number of available lateral displacements at a cross section. The traditional displacement-based contact algorithms cannot be employed to solve this type of contact problem. In this paper, a mixed force-displacement scheme is developed. This scheme removes the restriction on the number of contact pairs at a cross section and is suitable for handling contacts among many parallel beams. It is proven that a unique solution to the linear complementary equations obtained using the mixed force-displacement scheme exists and can be obtained using the Lemke algorithm. Numerical results for an example application show that the scheme is indeed convergent and accurate.