Weak coupling of nonlinear isogeometric spatial Bernoulli beams

Abstract

This paper proposes a coupling scheme for isogeometric elements, which is valid for large rotations and displacements. Two elements can be coupled not only at interpolated control points but also inside the parametric domain of a NURBS patch. Furthermore, each cross section may be arbitrarily oriented in space. The formulation is applicable for all structural elements, where an orthogonal system of base vectors can be derived. An Euler–Bernoulli beam is used as an example in order to illustrate the demands on the coupling conditions in the proposed approach. Moreover, the conditions are chosen such that different types of joints, e.g. scissor joints, can be modeled and such that they are easy and fast to implement. The coupling is incorporated by an additional term in the Principle of Virtual Work which is here computed using a penalty approach. The Euler–Bernoulli beam is summarized in order to introduce the notations in this contribution. This is followed by the proposed coupling conditions in the weak form. Subsequently, alternatives for the coupling conditions are briefly introduced. Eventually, benchmark and demonstrator examples validate and illustrate the proposed coupling methodology.