A general formulation of the contact interaction between a circle surface and a convex-concave-convex surface

Abstract

Representation of contact/impact mechanics in the context of multibody dynamics still poses a big challenge. The main problem lies in finding a balance between results accuracy and computational efficiency. With the purpose of describing this complex phenomenon, there exist different modelling techniques. A widespread approach consists of reducing the contact problem to a geometrically determined contact point and normal direction. Under this assumption, two different procedures can be generally utilized to model collisions in the framework of multibody systems formulations, namely the non-smooth approaches and the continuous methods. The first type of solution considers contact interactions as additional geometrical constraints, whereas the latter implements these phenomena in the form of contact forces. This work will focus on the use of continuous methods to propose a methodology that allows the characterization of the contact kinematics of planar bodies with both concave and convex surfaces. The results obtained will be compared with those provided by Finite Element Analysis (FEA) software. Subsequently, the presented solution will be applied to the modelling of a complex mechanical system, in which multiple contacts of different natures take place simultaneously. Continuous approaches have proved to deal with multiple-simultaneous contact scenarios successfully while containing the computational cost.