Geometrically nonlinear multi-patch isogeometric analysis of planar curved Euler–Bernoulli beams

Vo, Duy; Nanakorn, Pruettha

doi:10.1016/j.cma.2020.113078

Cited by 26 publications

(12 citation statements)

References 31 publications

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“…In terms of the Green-Lagrange strain tensor, *, the only non-zero strain component at an arbitrary point of the beam continuum, i.e., + , is expressed as [28] + = 1 2 ⋅ − ⋅ -...../.....0…”

Section: Strain Measurements and Cross-sectional Resultant Forcesmentioning

confidence: 99%

“…It is important to notice that these strain measurements can be considered as the linearized versions of the counterparts derived in [28].…”

Section: Strain Measurements and Cross-sectional Resultant Forcesmentioning

confidence: 99%

“…This is accomplished by presenting a relation between the cross-sectional rotations at the ends and the control variables. The accuracy of this approach has been investigated in [28] with geometrically nonlinear static examples. In this study, this approach is further extended to consider inertia effects, and thus for the first time applied to in-plane dynamic analysis of multi-patch beams.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic multi-patch isogeometric analysis of planar Euler–Bernoulli beams

Borković

Nanakorn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This study presents a novel isogeometric Euler-Bernoulli beam formulation for in-plane dynamic analysis of multi-patch beam structures. The kinematic descriptions involve only displacements of the beam axis, which are approximated by non-uniform rational B-spline (NURBS) curves. Translational displacements of the control points are here considered as control variables. The motivation of this work is to propose a penalty-free method to handle in-plane dynamic analysis of multi-patch beam structures. A simple relation between cross-sectional rotations at the ends of the beams and control variables is derived, allowing the incorporation of the end rotations as degrees of freedom. This improved setting can straightforwardly tackle beam structures with many rigid multi-patch connections, a major challenging issue when using existing isogeometric Euler-Bernoulli beam formulations. Additionally, rotational boundary conditions are conveniently prescribed. Numerical examples with complicated beam structures such as circular arches and frames with kinks are considered to show the accuracy and performance of the developed formulation. The computed results are verified with those derived from the conventional finite element method, and the superior convergence properties of the proposed formulation are illustrated. We additionally discuss about the possible extension of the present approach to spatial beam structures.

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Section: Strain Measurements and Cross-sectional Resultant Forcesmentioning

confidence: 99%

“…It is important to notice that these strain measurements can be considered as the linearized versions of the counterparts derived in [28].…”

Section: Strain Measurements and Cross-sectional Resultant Forcesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic multi-patch isogeometric analysis of planar Euler–Bernoulli beams

Borković

Nanakorn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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“…By another way, Hughes et al [2005] proposed an isogeometric analysis (IGA) utilizing the same basis functions as a B-spline or NURBS in describing the geometry to construct the finite approximation. Literature on the computational application of IGA is extremely vast, especially for the beam and plate problems [Bauer et al 2016;Kiendl et al 2015;Luu et al 2015;Tran et al 2013;Thai et al 2014;Vo and Nanakorn 2020;Greco and Cuomo 2014;Greco et al 2017;Greco 2020]. One of the most salient features of the IGA shown clearly in Niiranen's works is to use a conforming isogeometric C p−1continuous discretization (with order p ≥ 3) to naturally fulfill the required C 2continuity requirement without any additional variables.…”

Section: Loc V Tran and Jarkko Niiranenmentioning

confidence: 99%

Untitled

2020

Math. Mech. Compl. Sys.

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“…Based on [9], the authors in [23] discuss nonlinear applications of a spatial curved BE beam. Planar nonlinear BE beams are analyzed in [24,25,26]. Different approaches to multi-parch modeling are considered in [24,25], while the paper [26] focuses on the weighted residuals and the collocation of strong form.…”

Section: Introductionmentioning

confidence: 99%

Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli-Euler beam

Borković,

Marussig,

Radenković

2021

Preprint

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We present a geometrically exact nonlinear analysis of elastic in-plane beams in the context of finite but small strain theory. The formulation utilizes the full beam metric and obtains the complete analytic elastic constitutive model by employing the exact relation between the reference and equidistant strains. Thus, we account for the nonlinear strain distribution over the thickness of a beam. In addition to the full analytical constitutive model, four simplified ones are presented. Their comparison provides a thorough examination of the influence of a beam's metric on the structural response. We show that the appropriate formulation depends on the curviness of a beam at all configurations. Furthermore, the nonlinear distribution of strain along the thickness of strongly curved beams must be considered to obtain a complete and accurate response.

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Geometrically nonlinear multi-patch isogeometric analysis of planar curved Euler–Bernoulli beams

Cited by 26 publications

References 31 publications

Dynamic multi-patch isogeometric analysis of planar Euler–Bernoulli beams

Dynamic multi-patch isogeometric analysis of planar Euler–Bernoulli beams

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Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli-Euler beam

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