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

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.