A variable-offset joint formulation for beams with arbitrary cross-sections using a null space method

Abstract

In this paper, we present a variational formulation of local configurational constraints that couple multiple beams with arbitrarily shaped cross-sections. Since this formulation requires no explicit interface to rotational degrees-of-freedom, it applies to any beam kinematics and finite element discretization. Here, we define the offset coordinates in a moving frame to constrain or release the relative position between connected beams. The present method is based on a first-order approximation of the Lagrange multiplier field in the cross-section, which limits the transferability of the joint to the resultant force and moment only. The multipliers are eliminated using a discrete null space method, which provides size reduction and improved conditioning of the system matrix. Further, we apply the developed formulation to a beam element based on extensible directors and to a brick element in nonlinear elastostatics. Several numerical examples are presented.