GBT formulation to analyse the buckling behaviour of isotropic conical shells

Nedelcu, Mihai

doi:10.1016/j.tws.2011.02.006

Cited by 31 publications

(12 citation statements)

References 21 publications

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“…The work done on the shell can be written as [22]: (10) Latin American Journal of Solids and Structures 10(2013) 349 -390 where N q is the initial hoop stress due to centrifugal force which is given by: (11) Besides, the work done on the shell due to axial forced is described as: (12) where is the axial load on edge of shell in x direction. The effect of and are null for both simply supported and clamped boundary conditions [32].…”

Section: Geometrical Configurationmentioning

confidence: 94%

Dynamic Analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method

Daneshjou

Talebitooti

et al. 2013

Lat. Am. j. solids struct.

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This paper presents effects of boundary conditions and axial loading on frequency characteristics of rotating laminated conical shells with meridional and circumferential stiffeners, i.e., stringers and rings, using Generalized Differential Quadrature Method (GDQM). Hamilton's principle is applied when the stiffeners are treated as discrete elements. The conical shells are stiffened at uniform intervals and it is assumed that the stiffeners have similar material and geometric properties. Equations of motion as well as equations of the boundary condition are transformed into a set of algebraic equations by applying the GDQM. Obtained results discuss the effects of parameters such as rotating velocities, depth to width ratios of the stiffeners, number of stiffeners, cone angles, and boundary conditions on natural frequency of the shell. The results will then be compared with those of other published works particularly with a non-stiffened conical shell and a special case where angle of the stiffened conical shell approaches zero, i.e. a stiffened cylindrical shell. In addition, another comparison is made with present FE method for a non-rotating stiffened conical shell. These comparisons confirm reliability of the present work as a measure to approximate solutions to the problem of rotating stiffened conical shells.

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Section: Geometrical Configurationmentioning

confidence: 94%

Dynamic Analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method

Daneshjou

Talebitooti

et al. 2013

Lat. Am. j. solids struct.

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“…At first it was thought that GBT can only be applied for members with constant cross section along the longitudinal axis. Recent studies showed that GBT can be extended to structural members with variable cross section [3], [4]. This paper presents a GBT-based finite element formulation for elastic buckling analysis of conical shells.…”

Section: Discussionmentioning

confidence: 99%

“…FEM). In the case of the conical shell, initially a Runge-Kutta numerical method was used by the first author [3], namely the collocation method Lobatto IIIA of forth order [5] [3]. Due to various limitations, in this study, a FEM-based formulation was adapted for the special case of variable cross-section along the member's axis.…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…The following paper focuses on the application of GBT for conical shells. A GBT formulation was developed by Nedelcu [3] to analyse the buckling behaviour of isotropic conical shells under simple loading and boundary conditions applied at the bar's ends. As in the case of GBT formulation for thin walled bars with variable cross section [4], the mechanical and geometrical properties are not constant along the element's length.…”

Section: Introductionmentioning

confidence: 99%

“…Naturally, the proposed GBT formulation for conical shells accepts members with constant cross sections such as cylinders and tubes. The GBT member analysis (the eigenvalue problem in the case of the bifurcation buckling) of the conical shells was previously solved in [3] by applying a Runge-Kutta numerical method, namely the collocation method Lobatto IIIA of forth order [5]. The method proved to have limitations regarding the application of arbitrary loading and boundary conditions and it proved to be unstable for a large number of coupled deformation modes in the case of the interactive buckling.…”

Section: Introductionmentioning

confidence: 99%

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05.39: GBT‐based Finite Element formulation for elastic buckling analysis of conical shells

Nedelcu

Mureşan

2017

ce papers

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The paper presents a finite element formulation based on the Generalised Beam Theory (GBT), for the analysis of elastic buckling behaviour of conical shells under various loading and boundary conditions. The GBT approach provides a general solution for 1 st and 2 nd order analysis using bar elements capable of describing the global and local deformations. Because of the cross-section variation specific to conical shells, the mechanical and geometric properties are no longer constant along the bar axis as it is the case of cylinders and prismatic thin-walled structures. This formulation is validated by comparison between GBT results and values obtained by means of shell finite element analyses. The study covers simply supported and end fixed members, under axial compression.

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Combining Shell and GBT‐based Finite Elements – the Best of Both Worlds?

Manta¹,

Gonçalves²,

Camotim³

2022

ce papers

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A general and efficient approach to model thin‐walled members and frames with complex geometries (including tapered and perforated members) is proposed, combining standard shell and GBT‐based (beam) finite elements. Each element type is employed where it is most effective: (i) shell elements in plastic and geometrically complex zones, and (ii) GBT elements in prismatic and elastic zones. After providing a brief overview of the finite elements employed, several illustrative numerical examples are presented and discussed, in order to show the capabilities and potential of the proposed approach – they concern linear static, bifurcation (linear stability – calculation of buckling loadings and mode shapes), vibration (calculation of natural frequencies and vibration mode shapes), dynamic and first‐order plastic zone analyses. These numerical examples involve members with tapered segments and/or perforations and frames with complex joint geometries. For validation and comparison purposes, full shell finite element results are provided – in all cases, an excellent match is obtained.

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GBT formulation to analyse the buckling behaviour of isotropic conical shells

Cited by 31 publications

References 21 publications

Dynamic Analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method

Dynamic Analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method

05.39: GBT‐based Finite Element formulation for elastic buckling analysis of conical shells

Combining Shell and GBT‐based Finite Elements – the Best of Both Worlds?

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