Coupling 1D Beams to 3D Bodies

A new technique for coupling one dimensional beam elements to three dimensional bodies is described. The essence of the problem is to ensure compatibility of the displacements at the interface. This is achieved by equating the work done at the dimensional interface by the 3D nodes with the work done at the 1D node. This is carried out in a manner similar to that used in the development of Reissner plate theory and leads to 6 multipoint constraint equations, one for each degree of freedom of the node in the 1D element. The methods used to achieve the coupling for axial force, bending moment, shear force and torsion are discussed and it is shown that the proposed technique does not introduce any spurious stresses at the dimensional interface.