Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli–Euler beam

Borković, Aleksandar; Kovacevic, Sasa; Radenković, G.; Milovanović, Snježana Z.; Guzijan-Dilber, Matija

doi:10.1016/j.cma.2018.02.002

Cited by 53 publications

(48 citation statements)

References 33 publications

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“…Notice that base vectors 2 3 ( , ) g g remain unit for all configurations. Present derivations are compact version of the ones given in [7] and [5]. …”

Section: Mesh Refinementmentioning

confidence: 99%

“…12b, where excellent correspondence of present and calibrated orthotropic 2D model is noticed, even 118 for high values of curviness . Kh For more detail discussion on influence of curviness on beam models, see [7] and [10]. …”

Section: Figure 5 Clamped Circular Arch Under Concentrated Loadmentioning

confidence: 99%

“…Convergence analysis is performed in such a way that the order of convergence is observed as a function of a number of elements el n , analogously to [10]. Expected values are 1 p + for displacements, p for normal force and 1 p − for bending moment, [11].…”

Section: Numerical Studymentioning

confidence: 99%

“…2D models are created using dense meshes of CPS3 elements in Abaqus. Orthotropic material model is made by multiplication of modulus of elasticity along η direction and shear modulus with an empirically determined factor of 100Kh , [10]. This calibrated orthotropic material model is introduced in order to artificially introduce BE assumptions into general 2D model.…”

Section: Figure 5 Clamped Circular Arch Under Concentrated Loadmentioning

confidence: 99%

“…Aim of this paper is to investigate some numerical aspects of rotation-free IGA of an arbitrarily curved BE beam following recent findings given in [5], [6] and [7]. Detail analysis of influence of NURBS order and continuity on convergence properties is performed.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Some Numerical Aspects of a Linear Static Isogeometric Analysis of an Arbitrarily Curved Plane Bernoulli-Euler Beam

Borković¹

2017

STEPGRAD

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Abstract:Linear static analysis of arbitrarily curved beams is considered. Metric of a BernoulliEuler beam is rigorously defined and the weak form of the corresponding boundary-value problem is solved using isogeometric approach. Driving force behind present research is detail numerical analysis of recently developed model of an arbitrarily curved beam. This is obtained via in-depth analysis of convergence properties, as well as by comparison with other numerical models. Excellent agreement of results is obtained and improved accuracy of the model with the highest continuity is proved to be valid for most cases. Keywords: arbitrarily curved beam; isogeometric analysis; structural modeling НЕКИ НУМЕРИЧКИ АСПЕКТИ ЛИНЕАРНЕ СТАТИЧКЕ ИЗОГЕОМЕТРИЈСКЕ АНАЛИЗЕ ПРОИЗВОЉНО КРИВЕ БЕРНУЛИ-ОЈЛЕРОВЕ ГРЕДЕ Резиме:У раду је размотрена линеарна статичка анализа произвољно кривих греда. Метрика Бернули-Ојлерове греде је строго дефинисана, након чега је, примјеном изогеометријског приступа, ријешена слаба форма одговарајућег граничног проблема. Основни мотив за провођење датог истраживања слиједи из уочене потребе за детаљном нумеричком анализом недавно развијеног модела произвољно криве греде. Ова анализа је извршена пажљивим разматрањем особина конвергенције посматраног модела, као и кроз поређење са другим нумеричким моделима. Добијено је одлично поклапање резултата при чему је потврђена чињеница да модели са највишим континуитетом често имају побољшану тачност. Kључне ријечи: произвољно крива греда, изогеометријска анализа, моделирање конструкција 110

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“…Notice that base vectors 2 3 ( , ) g g remain unit for all configurations. Present derivations are compact version of the ones given in [7] and [5]. …”

Section: Mesh Refinementmentioning

confidence: 99%

Section: Figure 5 Clamped Circular Arch Under Concentrated Loadmentioning

confidence: 99%

Section: Numerical Studymentioning

confidence: 99%

Section: Figure 5 Clamped Circular Arch Under Concentrated Loadmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Some Numerical Aspects of a Linear Static Isogeometric Analysis of an Arbitrarily Curved Plane Bernoulli-Euler Beam

Borković¹

2017

STEPGRAD

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A two‐dimensional corotational curved beam element for dynamic analysis of curved viscoelastic beams with large deformations and rotations

Deng

Niu

Xue

et al. 2022

Numerical Meth Engineering

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This paper presents a two‐dimensional corotational curved beam element for the dynamic analysis of curved viscoelastic beams with large deformations and rotations. In contrast with traditional straight beam elements, the novelty of the presented formulation lies in introducing a curved reference configuration, which follows the rotation and translation of a corotational frame, to measure the pure elastic deformation of the beam and describe the spatial position of an arbitrary material point. A curvilinear coordinate system is fixed on this reference configuration to measure the local deformation of the element. Based on Hamilton's principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. An accurate two‐node curved element and the Kelvin–Voigt model are introduced to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational accuracy, and computational efficiency of the presented formulation. Moreover, the effects of the internal damping and external damping on the dynamic response of a rotating curved beam are investigated.

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Isogeometric analysis for nonlinear planar pantographic lattice: discrete and continuum models

Maurin

Greco

Desmet

2018

Continuum Mech. Thermodyn.

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Pantographic sheets are metamaterials constituted by two interconnected layers of straight fibers. One of the great features of these structures is that they are extremely elastically compliant toward large nonlinear deformations. To model pantographic lattices, Kirchhoff rods based on Euler-Bernoulli assumptions can be used. Otherwise, if the fibers are sufficiently dense, homogenization of the micro-structure results to a two-dimensional second-order gradient continuum model.The discrete and continuum models have in common the fact that their energy terms depend on the second-order derivatives of the displacement field, such that the classical finite element method cannot be directly employed. We propose instead the use of the isogeometric analysis where the basis functions are endowed with a higher inter-element continuity, allowing the rotation-free discretization of these problems. The discrete and continuum models are compared to existing benchmarks and are found in excellent agreement, validating the proposed approach.

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Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli–Euler beam

Cited by 53 publications

References 33 publications

Some Numerical Aspects of a Linear Static Isogeometric Analysis of an Arbitrarily Curved Plane Bernoulli-Euler Beam

Some Numerical Aspects of a Linear Static Isogeometric Analysis of an Arbitrarily Curved Plane Bernoulli-Euler Beam

A two‐dimensional corotational curved beam element for dynamic analysis of curved viscoelastic beams with large deformations and rotations

Isogeometric analysis for nonlinear planar pantographic lattice: discrete and continuum models

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