Abstract
Abstract. In this paper, we develop two alternative formulations for the rotational constraint between the tangents to connected beams with large deformations in 3-D space. Such a formulation is useful for modeling bonded/welded connections between beams. The first formulation is derived by consistently linearizing the variation of the strain energy and by assuming linear shape functions for the beam elements. This formulation can be used with both the Lagrange multiplier and the penalty stiffness method. The second non-consistent formulation assumes that the contact normal is independent of the nodal displacements at each iteration, and is updated consistently between iterations. In other words, we ignore the contribution due to the change of the contact normal in the linearization of the contact gap function. This assumption yields simpler equations and requires no specific assumption regarding the shape functions for the underlying beam elements. However, it is limited to the penalty method. We demonstrate the performance of the presented formulations in solving problems using implicit time integration. We also present a case showing the implications of ignoring this rotational constraint in modeling a network of beams.
Highlights
The beam-to-beam contact formulation was originally discussed by Wriggers and Zavarise (1997) for the case of normal contact between 3-D beams
Litewka used the formulations with the Lagrange and penalty stiffness methods (Litewka, 2005) and used smoothing procedures to solve the divergence problem that can occur when the contact point moves from one element to another (Litewka, 2006, 2007, 2010)
Θ2 ·n where θ 1 and θ 2 are the incremental changes in the rotation vectors of Beams 1 and 2 evaluated at the contact point and n is the current contact normal which is updated at each iteration. θ 1 and θ 2 can be related to the nodal incremental displacements of Beams 1 and 2, u1 and u2, through the rotational shape functions of the beam elements, HR1 and HR2 : θ 1 = HR1 u1 (44)
Summary
The beam-to-beam contact formulation was originally discussed by Wriggers and Zavarise (1997) for the case of normal contact between 3-D beams. Motamedian (2018) suggested a robust algorithm with a penalty method and the assumption that the contact point, normal, and tangent vectors are constant (independent of deformations) at each iteration. This assumption made it possible to derive an easy-toimplement formulation for the normal and tangential contact of beams suitable for any appropriate shape function. We assume that the contact normal is independent of the deformation at each iteration We present this simpler formulation with the penalty stiffness method. We show the efficiency of both formulations by solving several examples and demonstrate the effect of including the rotational constraint in the simulation of a network of randomly oriented, interconnected fibers
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
