TY  - JOUR
AU  - Borković, A.
AU  - Kovačević, Saša
AU  - Radenković, Gligor
AU  - Milovanović, S.
AU  - Majstorović, D.
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1005
AB  - A novel rotation-free isogeometric formulation of in-plane dynamic analysis of an arbitrarily curved Bernoulli-Euler beam in the convective frame of reference is presented. The driving force behind the present study has been the development of the NURBS-based element which enables an elegant framework of in-plane vibrations of arbitrarily curved Bernoulli-Euler beams, being a function only of the global Cartesian coordinates. Due to the fact that no additional simplifications are made, besides those related to the classic Bernoulli-Euler hypothesis and small strain theory, the formulation is particularly applicable for problems regarding the behavior of strongly curved beams. An excellent agreement of the results is accomplished and efficiency for academic and practical use are shown. The influence of the product of the maximum curvature and the thickness of the beam on the accuracy of the solution is specially treated and debated. The effects of the hpk-refinements are thoroughly checked and a highly nonlinear convergence behavior under the h-refinement is noticed. The well-known fact that models with the highest interelement continuities return superior accuracy per degree of freedom is substantiated by an in-depth numerical analysis of order of convergence. Furthermore, the accuracy of the developed model is analyzed utilizing normalized numerical discrete spectrums. It is remarked that the accuracy per degree of freedom degrades with the complexity of reference geometry of the beam.
PB  - Elsevier Ltd
T2  - Engineering Structures
T1  - Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli-Euler beam
EP  - 215
SP  - 192
VL  - 181
DO  - 10.1016/j.engstruct.2018.12.003
ER  - 

@article{
author = "Borković, A. and Kovačević, Saša and Radenković, Gligor and Milovanović, S. and Majstorović, D.",
year = "2019",
abstract = "A novel rotation-free isogeometric formulation of in-plane dynamic analysis of an arbitrarily curved Bernoulli-Euler beam in the convective frame of reference is presented. The driving force behind the present study has been the development of the NURBS-based element which enables an elegant framework of in-plane vibrations of arbitrarily curved Bernoulli-Euler beams, being a function only of the global Cartesian coordinates. Due to the fact that no additional simplifications are made, besides those related to the classic Bernoulli-Euler hypothesis and small strain theory, the formulation is particularly applicable for problems regarding the behavior of strongly curved beams. An excellent agreement of the results is accomplished and efficiency for academic and practical use are shown. The influence of the product of the maximum curvature and the thickness of the beam on the accuracy of the solution is specially treated and debated. The effects of the hpk-refinements are thoroughly checked and a highly nonlinear convergence behavior under the h-refinement is noticed. The well-known fact that models with the highest interelement continuities return superior accuracy per degree of freedom is substantiated by an in-depth numerical analysis of order of convergence. Furthermore, the accuracy of the developed model is analyzed utilizing normalized numerical discrete spectrums. It is remarked that the accuracy per degree of freedom degrades with the complexity of reference geometry of the beam.",
publisher = "Elsevier Ltd",
journal = "Engineering Structures",
title = "Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli-Euler beam",
pages = "215-192",
volume = "181",
doi = "10.1016/j.engstruct.2018.12.003"
}

Borković, A., Kovačević, S., Radenković, G., Milovanović, S.,& Majstorović, D.. (2019). Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli-Euler beam. in Engineering Structures
Elsevier Ltd., 181, 192-215.
https://doi.org/10.1016/j.engstruct.2018.12.003

Borković A, Kovačević S, Radenković G, Milovanović S, Majstorović D. Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli-Euler beam. in Engineering Structures. 2019;181:192-215.
doi:10.1016/j.engstruct.2018.12.003 .

Borković, A., Kovačević, Saša, Radenković, Gligor, Milovanović, S., Majstorović, D., "Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli-Euler beam" in Engineering Structures, 181 (2019):192-215,
https://doi.org/10.1016/j.engstruct.2018.12.003 . .

TY  - JOUR
AU  - Borković, A.
AU  - Radenković, Gligor
AU  - Milovanović, S.
AU  - Majstorović, D.
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1104
T2  - Savremena teorija i praksa u graditeljstvu
T1  - Some numerical aspects of a linear static isogeometric analysis of an arbitrary curved plane Bernoulli-Euler beam
EP  - 126
IS  - 1
SP  - 110
VL  - 13
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1104
ER  - 

@article{
author = "Borković, A. and Radenković, Gligor and Milovanović, S. and Majstorović, D.",
year = "2018",
journal = "Savremena teorija i praksa u graditeljstvu",
title = "Some numerical aspects of a linear static isogeometric analysis of an arbitrary curved plane Bernoulli-Euler beam",
pages = "126-110",
number = "1",
volume = "13",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1104"
}

Borković, A., Radenković, G., Milovanović, S.,& Majstorović, D.. (2018). Some numerical aspects of a linear static isogeometric analysis of an arbitrary curved plane Bernoulli-Euler beam. in Savremena teorija i praksa u graditeljstvu, 13(1), 110-126.
https://hdl.handle.net/21.15107/rcub_grafar_1104

Borković A, Radenković G, Milovanović S, Majstorović D. Some numerical aspects of a linear static isogeometric analysis of an arbitrary curved plane Bernoulli-Euler beam. in Savremena teorija i praksa u graditeljstvu. 2018;13(1):110-126.
https://hdl.handle.net/21.15107/rcub_grafar_1104 .

Borković, A., Radenković, Gligor, Milovanović, S., Majstorović, D., "Some numerical aspects of a linear static isogeometric analysis of an arbitrary curved plane Bernoulli-Euler beam" in Savremena teorija i praksa u graditeljstvu, 13, no. 1 (2018):110-126,
https://hdl.handle.net/21.15107/rcub_grafar_1104 .

TY  - JOUR
AU  - Radenković, Gligor
AU  - Borković, A.
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/944
AB  - The present research is focused on the linear analysis of a spatial Bernoulli-Euler beam. Metrics of the reference and deformed configurations are rigorously defined with respect to the convective coordinate frame of reference. No higher order terms are neglected which makes the formulation ideally suited for analysis of arbitrarily curved spatial beams in the frame of finite (but small) strain theory. The well-known issue of nonorthogonality of local coordinate system at an arbitrary point of a spatial beam is solved by the introduction of a new coordinate line that is orthogonal to the normal plane of the beam axis at each point. Generalized coordinates of the present model are translations of the beam axis and the angle of twist of a cross section. Two different parameterizations of this angle are discussed and implemented. Both geometry and kinematics are described with the same set of NURBS functions, in line with the isogeometric approach. Numerical analysis proved that the theoretical considerations are correct and some limits of applicability are defined. An in-depth analysis of convergence properties has confirmed the fact that models with the highest interelement continuity have an improved accuracy per DOE, for problems that result in a smooth structural response.
PB  - Elsevier B.V.
T2  - Computer Methods in Applied Mechanics and Engineering
T1  - Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam
EP  - 396
SP  - 360
VL  - 341
DO  - 10.1016/j.cma.2018.07.010
ER  - 

@article{
author = "Radenković, Gligor and Borković, A.",
year = "2018",
abstract = "The present research is focused on the linear analysis of a spatial Bernoulli-Euler beam. Metrics of the reference and deformed configurations are rigorously defined with respect to the convective coordinate frame of reference. No higher order terms are neglected which makes the formulation ideally suited for analysis of arbitrarily curved spatial beams in the frame of finite (but small) strain theory. The well-known issue of nonorthogonality of local coordinate system at an arbitrary point of a spatial beam is solved by the introduction of a new coordinate line that is orthogonal to the normal plane of the beam axis at each point. Generalized coordinates of the present model are translations of the beam axis and the angle of twist of a cross section. Two different parameterizations of this angle are discussed and implemented. Both geometry and kinematics are described with the same set of NURBS functions, in line with the isogeometric approach. Numerical analysis proved that the theoretical considerations are correct and some limits of applicability are defined. An in-depth analysis of convergence properties has confirmed the fact that models with the highest interelement continuity have an improved accuracy per DOE, for problems that result in a smooth structural response.",
publisher = "Elsevier B.V.",
journal = "Computer Methods in Applied Mechanics and Engineering",
title = "Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam",
pages = "396-360",
volume = "341",
doi = "10.1016/j.cma.2018.07.010"
}

Radenković, G.,& Borković, A.. (2018). Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam. in Computer Methods in Applied Mechanics and Engineering
Elsevier B.V.., 341, 360-396.
https://doi.org/10.1016/j.cma.2018.07.010

Radenković G, Borković A. Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam. in Computer Methods in Applied Mechanics and Engineering. 2018;341:360-396.
doi:10.1016/j.cma.2018.07.010 .

Radenković, Gligor, Borković, A., "Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam" in Computer Methods in Applied Mechanics and Engineering, 341 (2018):360-396,
https://doi.org/10.1016/j.cma.2018.07.010 . .

TY  - JOUR
AU  - Borković, A.
AU  - Kovačević, Saša
AU  - Radenković, Gligor
AU  - Milovanović, S.
AU  - Guzijan-Dilber, M.
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/964
AB  - The present study elucidates linear static analysis for plane beam structures using the isogeometric approach. A novel methodology for rotation-free analysis of an arbitrarily curved Bernoulli-Euler beam in the convective frame of reference is derived in detail. The full degeneration of a 3D continuum beam to a 1D line has been presented and a fully applicable isogeometric finite element has been obtained. The driving force behind developing the present research has been the derivation of the NURBS-based isogeometric analysis which will enable an elegant formulation of the plane Bernoulli-Euler beams, being a function only of the global rectangular Cartesian coordinates. The verification and accuracy of the research are obtained via a thorough comparison between theory, finite element analyses and relevant examples from literature. An excellent agreement of results is achieved and usefulness for academic and practical purposes alike are proved. The effects of the hpk-refinements are illuminated and it is observed that the convergences for the most variables and refinement techniques are not monotonic. A special attention is paid to the influence of the product of maximum curvature and thickness of beam on the accuracy of the solution. The limits of applicability of the present approach are defined for a few specific types of analyses. The derived formulation is geometrically exact and appropriate for the analysis of strongly curved Bernoulli-Euler beams.
PB  - Elsevier B.V.
T2  - Computer Methods in Applied Mechanics and Engineering
T1  - Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli-Euler beam
EP  - 267
SP  - 238
VL  - 334
DO  - 10.1016/j.cma.2018.02.002
ER  - 

@article{
author = "Borković, A. and Kovačević, Saša and Radenković, Gligor and Milovanović, S. and Guzijan-Dilber, M.",
year = "2018",
abstract = "The present study elucidates linear static analysis for plane beam structures using the isogeometric approach. A novel methodology for rotation-free analysis of an arbitrarily curved Bernoulli-Euler beam in the convective frame of reference is derived in detail. The full degeneration of a 3D continuum beam to a 1D line has been presented and a fully applicable isogeometric finite element has been obtained. The driving force behind developing the present research has been the derivation of the NURBS-based isogeometric analysis which will enable an elegant formulation of the plane Bernoulli-Euler beams, being a function only of the global rectangular Cartesian coordinates. The verification and accuracy of the research are obtained via a thorough comparison between theory, finite element analyses and relevant examples from literature. An excellent agreement of results is achieved and usefulness for academic and practical purposes alike are proved. The effects of the hpk-refinements are illuminated and it is observed that the convergences for the most variables and refinement techniques are not monotonic. A special attention is paid to the influence of the product of maximum curvature and thickness of beam on the accuracy of the solution. The limits of applicability of the present approach are defined for a few specific types of analyses. The derived formulation is geometrically exact and appropriate for the analysis of strongly curved Bernoulli-Euler beams.",
publisher = "Elsevier B.V.",
journal = "Computer Methods in Applied Mechanics and Engineering",
title = "Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli-Euler beam",
pages = "267-238",
volume = "334",
doi = "10.1016/j.cma.2018.02.002"
}

Borković, A., Kovačević, S., Radenković, G., Milovanović, S.,& Guzijan-Dilber, M.. (2018). Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli-Euler beam. in Computer Methods in Applied Mechanics and Engineering
Elsevier B.V.., 334, 238-267.
https://doi.org/10.1016/j.cma.2018.02.002

Borković A, Kovačević S, Radenković G, Milovanović S, Guzijan-Dilber M. Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli-Euler beam. in Computer Methods in Applied Mechanics and Engineering. 2018;334:238-267.
doi:10.1016/j.cma.2018.02.002 .

Borković, A., Kovačević, Saša, Radenković, Gligor, Milovanović, S., Guzijan-Dilber, M., "Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli-Euler beam" in Computer Methods in Applied Mechanics and Engineering, 334 (2018):238-267,
https://doi.org/10.1016/j.cma.2018.02.002 . .

TY  - JOUR
AU  - Borković, A.
AU  - Kovačević, Saša
AU  - Milasinović, D. D.
AU  - Radenković, Gligor
AU  - Mijatović, O.
AU  - Golubović-Bugarski, V.
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/842
AB  - The present study sheds light on geometric nonlinear static analysis of prismatic shells using the semi-analytical finite strip method. A new computational model, which includes a fully nonlinear compound strip with a longitudinal and transverse stiffener, has been presented. Furthermore, strips with non-uniform characteristics in the longitudinal direction have been used in nonlinear analysis. This has, to the best knowledge of authors, never been reported. Also, this paper describes the design and implementation of eighteen ideal boundary conditions using three different longitudinal and six well-known transverse displacement interpolation functions. The results of the presented study were obtained using an open-source software and multi-purpose software Abaqus. Moreover, the accuracy of the applied computational approach has been verified by comparison with results from the literature. An excellent agreement of displacement fields is achieved for large deflection analyses of plates with a hole and stiffeners as well as for shells with a stepped thickness in the longitudinal direction. Additionally, results from post-buckling analyses of thin-walled structures, a snap-through and snap-back behavior of shallow shells, are matched. The work presented here has profound implications for future studies of the finite strip deployment.
PB  - Elsevier Ltd
T2  - Thin-Walled Structures
T1  - Geometric nonlinear analysis of prismatic shells using the semi-analytical finite strip method
EP  - 88
SP  - 63
VL  - 117
DO  - 10.1016/j.tws.2017.03.033
ER  - 

@article{
author = "Borković, A. and Kovačević, Saša and Milasinović, D. D. and Radenković, Gligor and Mijatović, O. and Golubović-Bugarski, V.",
year = "2017",
abstract = "The present study sheds light on geometric nonlinear static analysis of prismatic shells using the semi-analytical finite strip method. A new computational model, which includes a fully nonlinear compound strip with a longitudinal and transverse stiffener, has been presented. Furthermore, strips with non-uniform characteristics in the longitudinal direction have been used in nonlinear analysis. This has, to the best knowledge of authors, never been reported. Also, this paper describes the design and implementation of eighteen ideal boundary conditions using three different longitudinal and six well-known transverse displacement interpolation functions. The results of the presented study were obtained using an open-source software and multi-purpose software Abaqus. Moreover, the accuracy of the applied computational approach has been verified by comparison with results from the literature. An excellent agreement of displacement fields is achieved for large deflection analyses of plates with a hole and stiffeners as well as for shells with a stepped thickness in the longitudinal direction. Additionally, results from post-buckling analyses of thin-walled structures, a snap-through and snap-back behavior of shallow shells, are matched. The work presented here has profound implications for future studies of the finite strip deployment.",
publisher = "Elsevier Ltd",
journal = "Thin-Walled Structures",
title = "Geometric nonlinear analysis of prismatic shells using the semi-analytical finite strip method",
pages = "88-63",
volume = "117",
doi = "10.1016/j.tws.2017.03.033"
}

Borković, A., Kovačević, S., Milasinović, D. D., Radenković, G., Mijatović, O.,& Golubović-Bugarski, V.. (2017). Geometric nonlinear analysis of prismatic shells using the semi-analytical finite strip method. in Thin-Walled Structures
Elsevier Ltd., 117, 63-88.
https://doi.org/10.1016/j.tws.2017.03.033

Borković A, Kovačević S, Milasinović DD, Radenković G, Mijatović O, Golubović-Bugarski V. Geometric nonlinear analysis of prismatic shells using the semi-analytical finite strip method. in Thin-Walled Structures. 2017;117:63-88.
doi:10.1016/j.tws.2017.03.033 .

Borković, A., Kovačević, Saša, Milasinović, D. D., Radenković, Gligor, Mijatović, O., Golubović-Bugarski, V., "Geometric nonlinear analysis of prismatic shells using the semi-analytical finite strip method" in Thin-Walled Structures, 117 (2017):63-88,
https://doi.org/10.1016/j.tws.2017.03.033 . .