Advantages of a semi-analytical approach for the analysis of an evolving structure with contacts

This paper presents a semi-analytical approach for the evolution analysis of a beam into given boundaries. The analytical description of contact locations, contact forces and beam deflections results in an exact modelling of the phenomenon (no penetration allowed). Despite the apparent complexity of the problem, the analytical relations leading to two-point boundary and integro-restrained differential equations are formally written. An iterative resolution of these equations is adopted by converting the problem into a single-point boundary value one. Due to a proper selection of the global unknowns, namely the contact forces and their locations, the proposed method is particularly efficient in the context of evolving structures. The resolution is illustrated on a simple example and comparisons with the finite element method are given as persuasive arguments.