Coupling 2D continuum and beam elements: a mixed formulation for avoiding spurious stresses

This paper presents a novel approach to coupling beam and solid elements. Connecting standard beam elements with solid elements results in a situation where the solid part of the model covers the cross-sectional deformation, while at the beam part assumptions only consider the rigid body movement of the cross-section. Therefore, kinematic assumptions do not include cross-section deformations such as warping and contraction. Due to this restriction, spurious stresses occur at the transition zone. To circumvent this problem, this contribution introduces a mixed hybrid transition element based on an extended Hu–Washizu functional. The extension allows the cross-section to contract and warp. Compared with other approaches that include these phenomena, precomputation of the warping function is unnecessary. The present approach considers the cross-sectional deformation using local variables. On the solid interface, there are only displacement degrees of freedom (depending on the solid discretization), whereas on the beam interface, there are two displacement degrees of freedom and one rotation. This allows beam-like parts of the solid model to be replaced with standard beam elements without affecting the overall accuracy of the model. Besides solid–beam coupling, the proposed formulation can also be used to apply beam-like boundary conditions as well as stress resultants to the solid interface. For the sake of simplicity and without restricting generality, the underlying element formulation is introduced for the 2D linear elastic case. Numerical examples demonstrate that the transition element causes no spurious stress distributions on the solid part. The results of full solid models are compared with mixed beam–solid models.