Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam

Borković, Aleksandar; Marussig, Benjamin; Radenković, G.

doi:10.1016/j.cma.2021.114447

Cited by 15 publications

(10 citation statements)

References 57 publications

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“…The x -, y - , and z -components of the displacement of the point B are shown in Figure 5(b)–(d), respectively. The computations are in agreement with the literature [7,20,54].…”

Section: Numerical Investigationssupporting

confidence: 90%

“…The benchmark proposed by Yoshiaki et al [54] (and subsequently in [7,13,20,55]) consists in the deployment of a circular ring with initially zero twist. The radius of the centroid curve is R = 20 , the cross-section is rectangular with h n = 1 and h ν = 1 / 3 , the material is linear isotropic with Young’s modulus E = 2 . 1 × 10 − 7 and ν = 0 . 3 while the polar inertia moment is J t = 9 . 753 × 10 − 3 (see Figure 4).…”

Section: Numerical Investigationsmentioning

confidence: 99%

“…Recently, Borkovic´et al [20] presented an invariant non-linear exact Euler-Bernoulli beam formulation accounting for the beam curviness, based on an isogeometric generalization of the invariant formulation proposed in Meier et al [13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…The x -, y - , and z -components of the displacement of the point B are shown in Figure 5(b)–(d), respectively. The computations are in agreement with the literature [7,20,54].…”

Section: Numerical Investigationssupporting

confidence: 90%

Section: Numerical Investigationsmentioning

confidence: 99%

See 1 more Smart Citation

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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“…In future work, more accurate models will be studied, taking into consideration the inertial part of the moving load. In addition, a nonlinear analysis, implicit procedures, and effects of the higher-order metric will be considered as well [14,15].…”

Section: Discussionmentioning

confidence: 99%

Linear Dynamic Analysis of a Spatially Curved Bernoulli-Euler Beam Subjected to a Moving Load

Jočković¹,

Nefovska-Danilović²,

Borković³

2022

AGG+

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This paper considers the dynamic analysis of a spatially curved Bernoulli-Euler beam subjected to a moving load. The isogeometric approach is used for the spatial discretization of the weak form of the equation of motion. Both the reference geometry and the solution space are represented using the same NURBS basis functions that guarantee an accurate description of the beam centerline. The time integration is done by the explicit technique. The presented formulation is validated by the comparison with the existing results from the literature for the curved beam subjected to a constant load moving with a constant velocity. In addition, the influence of the moving load velocity on the dynamic response of a spatially curved beam has been investigated.

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“…Arches of an arbitrary curve are very often analyzed by using the isogeometric approach. This approach is presented in [10,11].…”

mentioning

confidence: 99%

Influence of rotary flexibility of joints on the statics and dynamics of the arch structures

Łasecka-Plura,

Pawlak,

Żak-Sawiak

2023

Bulletin of the Polish Academy of Sciences Technical Sciences

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The paper presents arch structures modeled by finite elements in which the nodes can be flexibly connected. Two-node curved elements with three degrees of freedom at each node were used. Exact shape functions were adopted to obtain stiffness and consistent mass matrices but they were modified by introducing rotational flexibility in the boundary nodes. Calculations of statics and dynamics of arches with different positions of flexible joints and different values of rotational stiffness of the joints were carried out.

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Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam

Cited by 15 publications

References 57 publications

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

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

Linear Dynamic Analysis of a Spatially Curved Bernoulli-Euler Beam Subjected to a Moving Load

Influence of rotary flexibility of joints on the statics and dynamics of the arch structures

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