An iso-parametric \(\pmb {\mathrm {G}^1}\)-conforming finite element for the nonlinear analysis of Kirchhoff rod. Part I: the 2D case

  • L. GrecoEmail author
Original Article


A geometrically exact nonlinear iso-parametric \(\mathrm {G}^1\)-conforming finite element formulation for the analysis of Kirchhoff rods, based on the cubic Bézier curve interpolation, is presented. In this work, the formulation is restricted to the planar 2D case. Introducing the \(\mathrm {G}^1\)-map, the interpolation preserves the continuity requirement during the deformation process of the rod. In this way, the \(\mathrm {G}^1\)-conformity is implicitly accounted at the element formulation level.


Conforming element Kirchhoff rod \(\mathrm {G}^1\) continuity Isogeometric analysis Finite element formulation 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Civile e Architettura (DICAR)Universitá degli Studi di CataniaCataniaItaly

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