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

Borković, Aleksandar; Kovacevic, Sasa; Radenković, G.; Milovanović, Snježana Z.; Majstorović, D.

doi:10.1016/j.engstruct.2018.12.003

Cited by 21 publications

(23 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to test this result further, a 2D shell model with Kh=1 is created using a plane stress/strain section in Abaqus with a fine mesh of 125600 CPS3 elements. In order to make a model which is comparable with big-curvature BE beams, the orthotropic material properties are applied, similar as in [4]. The elasticity modulus along the η direction and the shear modulus are amplified with a factor of 100Kh, which is empirically determined in [4].…”

Section: Circular Ringmentioning

confidence: 99%

“…In order to make a model which is comparable with big-curvature BE beams, the orthotropic material properties are applied, similar as in [4]. The elasticity modulus along the η direction and the shear modulus are amplified with a factor of 100Kh, which is empirically determined in [4]. In this way, by setting b=h=E=P=R=1, Abaqus returned displacement of 1.0504 while the present approach gave 1.0441, which is an excellent agreement for this high value of curviness.…”

Section: Circular Ringmentioning

confidence: 99%

“…All the other cases belong to the category of big-curvature beams. The lack of benchmark test results for the recent developments of big-curvature beam model in the frame of isogeometric analysis (IGA), [2], [3], [4], and [5], was one of the main motives for the present research.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the analytical approach to the linear analysis of an arbitrarily curved spatial Bernoulli–Euler beam

Radenković

Borković

2020

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

The equilibrium and kinematic equations of an arbitrarily curved spatial Bernoulli-Euler beam are derived with respect to a parametric coordinate and compared with those of the Timoshenko beam. It is shown that the beam analogy follows from the fact that the left-hand side in all the four sets of those equations are the covariant derivatives of unknown vector. Furthermore, an elegant primal form of the equilibrium equations is composed. No additional assumptions, besides those of the linear Bernoulli-Euler theory, are introduced, which makes the theory ideally suited for the analytical assessment of bigcurvature beams. The curvature change is derived with respect to both convective and material/spatial coordinates, and some aspects of its definition are discussed. Additionally, the stiffness matrix of an arbitrarily curved spatial beam is calculated with the flexibility approach utilizing the relative coordinate system. The numerical analysis of the carefully selected set of examples proved that the present analytical formulation can deliver valid benchmark results for testing of the purely numeric methods.

show abstract

Section: Circular Ringmentioning

confidence: 99%

Section: Circular Ringmentioning

confidence: 99%

See 1 more Smart Citation

On the analytical approach to the linear analysis of an arbitrarily curved spatial Bernoulli–Euler beam

Radenković

Borković

2020

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, several planar rotation-free isogeometric beam formulations have been developed, e.g., see Refs. [19][20][21][22][23][24][25][26], without the need for considering cross-sectional rotations as discrete unknowns, showing its obvious advantage in reduction of the number of degrees of freedom. In [19], a formulation to optimize elastic arches for the maximum fundamental frequency is presented, and then in [20] nonlinear vibration analysis of straight beams with a von Kármán strain-displacement relation is performed.…”

Section: Introductionmentioning

confidence: 99%

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

Borković

Nanakorn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

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.

show abstract

“…Besides, the splines can be directly used to construct the geometric models, so as to solve the data communication problem. IGA has solved many engineering problems, such as solid mechanics, 26,27 fluid mechanics 28 and contact mechanics. 29 The static, [30][31][32] free vibration [33][34][35] and buckling 36,37 analyses of FG plates are also involved.…”

Section: Introductionmentioning

confidence: 99%

Static analysis of FG plates using T-splines based isogeometric approach and a refined plate theory

Liu

Wang

Duan

et al. 2020

Journal of Composite Materials

View full text Add to dashboard Cite

In this study, a novel refined plate theory (RPT) is developed for the geometrically linear static analysis of FG plates, which is a simplification of the higher-order shear deformation theories (HSDTs). It improves the computational efficiency while preserving the accuracy advantage of HSDTs. The C1-continuity problem is overcome by isogeometric analysis (IGA), which shows more advantages than the C0 elements based finite element analysis. By T-splines, the computational cost is effectively reduced, since compared to NURBS based IGA, T-splines can achieve local refinement and improve the utilization of control points. The rule of mixture with power-law and Mori–Tanaka scheme are adopted to calculate the material properties of the plate. Several numerical experiments are given to prove the efficiency of the proposed method

show abstract

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

Cited by 21 publications

References 39 publications

On the analytical approach to the linear analysis of an arbitrarily curved spatial Bernoulli–Euler beam

On the analytical approach to the linear analysis of an arbitrarily curved spatial Bernoulli–Euler beam

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

Static analysis of FG plates using T-splines based isogeometric approach and a refined plate theory

Contact Info

Product

Resources

About