A geometrically exact discrete elastic rod model based on improved discrete curvature

Yan, Litan; Song, Kezhi; Meng, Lingfei

doi:10.1016/j.cma.2022.114640

Cited by 4 publications

(2 citation statements)

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“…Alternative approaches for the analysis of slender beams are presented in the previous studies [22–25]. A geometrically exact discrete Kirchhoff rod formulation based on several improved discrete definition for the curvatures has been presented in Liu et al [26]. Isogeometric formulations based on the Timoshenko beam model can be found in Marino [27,28] and Cazzani et al [29–31] for the collocation and the Galerkin schemes, respectively.…”

Section: Introductionmentioning

confidence: 99%

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An updated Lagrangian Bézier finite element formulation for the analysis of slender beams

Greco

Castello

Scrofani

2022

Mathematics and Mechanics of Solids

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A G1-conforming finite element formulation based on the Kirchhoff beam model suitable for the analysis of structures composed by coupling of slender beams is presented. A new set of kinematic parameters is introduced in order to account for the continuity required by the rod model. This new set of kinematic parameters defines the G1-map that guarantees continuity of the rotations at the ends of the beam. The tangent stiffness matrix for the proposed Kirchhoff beam model is derived in a consistent way. It is shown that an additional geometric term, specific for the G1-conforming formulation, appears in the tangent stiffness matrix. In order to avoid the singularities arising with the introduction of the G1-map, an updated Lagrangian formulation is adopted. In this way, a G1-conforming Bézier finite element based on the Kirchhoff beam model able to model large deformations of space rod systems is obtained. Several numerical examples show the high accuracy and the robustness of the proposed conforming formulation.

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Section: Introductionmentioning

confidence: 99%

“…Alternative approaches for the analysis of slender beams are presented in the previous studies [22][23][24][25]. A geometrically exact discrete Kirchhoff rod formulation based on several improved discrete definition for the curvatures has been presented in Liu et al [26].…”

Section: Introductionmentioning

confidence: 99%