Comparison between the discrete and finite element methods for modelling an agricultural spray boom—Part 1: Theoretical derivation

The paper develops a systematic procedure for modelling linear flexible multibody structures of which the flexible parts are a composition of beams. The theory of mechanics of solids is fit into a general expression of virtual work, linking rigid-body motions with flexible deformations of the different bodies. A comparison is made with the finite element method for approximating the behaviour of the flexible bodies. It turns out that the discrete element method boils down to a particular selection of shape functions of which the mass matrix is inconsistent with the flexibility matrix. Furthermore, contrary to the finite element method, only point forces can be applied.