Elimination of self-straining in isogeometric formulations of curved Timoshenko beams in curvilinear coordinates.

*(English)*Zbl 1439.74155Summary: Isogeometric formulations of curved Timoshenko beams in curvilinear coordinates often result in self-straining of membrane and shear strains, due to the discretization of the local displacement field. Self-straining means a failure in exact representation of rigid body motions, which consequently deteriorates response quality. To overcome the difficulty of self-straining, we propose an invariant formulation that discretizes the global displacement field. It turns out that the approximated membrane, shear, and bending strain measures are invariant regardless of initial geometry in the proposed formulation. For effective applications to any arbitrarily curved structures and locking-free formulations to alleviate membrane and shear locking, the proposed invariant formulation is combined with selective reduced integration (SRI) and \(\overline{B}\) projection method. Numerical examples demonstrate the effectiveness and applicability of the proposed invariant formulation, which gives much more accurate results together with both SRI and \(\overline{B}\) projection method, in comparison to the existing isogeometric formulations.

##### MSC:

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

74S05 | Finite element methods applied to problems in solid mechanics |

65D07 | Numerical computation using splines |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

##### Keywords:

curvilinear coordinates; self-straining; isogeometric analysis; curved Timoshenko beam; selective reduced integration; \( \overline{B}\) projection method
PDF
BibTeX
XML
Cite

\textit{M.-J. Choi} and \textit{S. Cho}, Comput. Methods Appl. Mech. Eng. 309, 680--692 (2016; Zbl 1439.74155)

Full Text:
DOI

##### References:

[1] | Bouclier, R.; Elguedj, T.; Combescure, A., Locking free isogeometric formulations of curved thick beams, Comput. Methods Appl. Mech. Engrg., 245, 144-162 (2012) · Zbl 1354.74260 |

[2] | Adam, C.; Bouabdallah, S.; Zarroug, M.; Maitournam, H., Improved numerical integration for locking treatment in isogeometric structural elements, part i: Beams, Comput. Methods Appl. Mech. Engrg., 279, 1-28 (2014) |

[3] | Armero, F.; Valverde, J., Invariant hermitian finite elements for thin kirchhoff rods. i: The linear plane case, Comput. Methods Appl. Mech. Engrg., 213, 427-457 (2012) · Zbl 1243.74176 |

[4] | Piegl, L.; Tiller, W., The NURBS Book (2012), Springer Science & Business Media |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.