Geometrically nonlinear multi-patch isogeometric analysis of spatial Euler–Bernoulli beam structures

Vo, Duy; Nanakorn, Pruettha; Bui, Tinh Quoc

doi:10.1016/j.cma.2021.113808

Cited by 22 publications

(9 citation statements)

References 45 publications

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“…The SR mapping is commonly used for the modeling of BE beams [42]. The procedure consists of two steps.…”

Section: Smallest Rotationmentioning

confidence: 99%

“…Note that this mapping has a singularity for t * • t = −1 which is of no practical interest if the reference configuration is appropriately defined [42].…”

Section: Smallest Rotationmentioning

confidence: 99%

“…However, for all the other shapes of cross section, this fact does not hold. Instead, the term I 11 is usually replaced with the so-called torsional constant, J, which must be calculated approximately [42]. In the presented research, J is used for the models D 0 and D 1 .…”

Section: The Relation Between Energetically Conjugated Pairsmentioning

confidence: 99%

“…Based on [37], the authors in [41] successfully performed nonlinear applications of a spatial curved BE beam. Recently, a multi-patch approach for the nonlinear analysis of BE beams is suggested [42]. The smallest rotation algorithm is used for an update of the basis.…”

Section: Introductionmentioning

confidence: 99%

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

Borković,

Marussig,

Radenković

2021

Preprint

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The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness on the nonlinear distribution of axial strain over the cross section. The exact constitutive relation between energetically conjugated pairs is employed, along with four reduced relations. The isogeometric approach, which allows smooth connections between finite elements, is used for the spatial discretization of the weak form. Two methods for updating the local basis are applied and discussed in the context of finite rotations. All the requirements of geometrically exact beam theory are satisfied, such as objectivity and path-independence. The accuracy of the formulation is verified by a thorough numerical analysis. The influence of the curviness on the structural response is scrutinized for two classic examples. If the exact response of the structure is sought, the curviness must be considered when choosing the appropriate beam model.

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“…The SR mapping is commonly used for the modeling of BE beams [42]. The procedure consists of two steps.…”

Section: Smallest Rotationmentioning

confidence: 99%

“…Note that this mapping has a singularity for t * • t = −1 which is of no practical interest if the reference configuration is appropriately defined [42].…”

Section: Smallest Rotationmentioning

confidence: 99%

Section: The Relation Between Energetically Conjugated Pairsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Borković,

Marussig,

Radenković

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…To remove these drawbacks, the approach in this study can be generalized, i.e., incorporating the total cross-sectional rotations at the ends of the patch as discrete unknowns. This method has been implemented in [36] for linear analysis and in [37] for geometrically nonlinear analysis. However, applications in dynamic analysis are still not yet examined.…”

Section: Extensibility To Analysis Of Spatial Beamsmentioning

confidence: 99%

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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Isogeometric gradient‐free proportional topology optimization (IGA‐PTO) for compliance problem

Nguyen

Bui

et al. 2023

Numerical Meth Engineering

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This study presents the incorporation of the effective gradient‐free proportional topology optimization algorithm into the framework of isogeometric analysis. The minimization of the compliance is considered, and the solid isotropic material with penalization method is used. The geometry, displacements, and density are all described by non‐uniform rational B‐spline (NURBS) basis functions. The density at an integration point is determined proportionally to its compliance. Then, the NURBS description of the density is constructed elementwise by deriving a relation between densities assigned to integration points and control points. The global NURBS description of the density for the whole domain is a blend of those from elements. Furthermore, a multiresolution scheme is presented by means of ‐refinement technique to enable the efficient performance for large‐scale problems. The accuracy and efficiency of the proposed approach are assessed through six numerical examples, including two‐ and three‐dimensional structures, with several rigorous tests and comparisons with the gradient‐based optimality criteria algorithm.

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Geometrically nonlinear multi-patch isogeometric analysis of spatial Euler–Bernoulli beam structures

Cited by 22 publications

References 45 publications

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

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

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

Isogeometric gradient‐free proportional topology optimization (IGA‐PTO) for compliance problem

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