Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 403, Issue -, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2022.115722
Keywords
Isogeometric collocation; Spatial curved beams; Timoshenko beams; Bishop frame; Multi -patch formulation; SO(3)
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This paper presents a robust multi-patch formulation based on the isogeometric collocation method for solving linear, spatial Timoshenko beam structures with complex geometry. The proposed approach combines the (local) Bishop frame with the exponential map for SO(3) to compute the beam curvature and its derivative. Unlike existing formulations, which are mostly derived in the local SF frame, the formulation in this paper is consistently derived by linearizing the governing equations in the material setting, allowing for straightforward enforcement of multi-patch coupling.
The present paper presents a robust multi-patch formulation based on the isogeometric collocation (IGA-C) method for the solution of linear, spatial Timoshenko beam structures with complex geometry. The proposed approach is based on the combination of the (local) Bishop frame with the exponential map for SO(3) (Rodrigues formula) to compute the beam curvature and its derivative. This choice permits bypassing known issues related to the Serret-Frenet (SF) frame (in cases where the local beam curvature vanishes) and does not require the Darboux vector and its derivative, which are both affected by limitations of the SF frame. Moreover, in contrast to existing formulations mostly derived in the local SF frame, here the formulation is consistently derived by linearizing the governing equations in the material setting, where the multi-patch coupling can be enforced in a straightforward way. Numerical tests are performed on complex spatial curved beams, including a demanding biomechanical problem of a braided stent, proving the accuracy and the robustness of the formulation.(c) 2022 Elsevier B.V. All rights reserved.
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