On the role of geometrically exact and second-order theories in buckling and post-buckling analysis of three-dimensional beam structures

Ibrahimbegović, Adnan; Shakourzadeh, H.; Batoz, Jean‐Louis; Mikdad, M. Ai; Guo, Ying

doi:10.1016/0045-7949(96)00181-2

Cited by 31 publications

(14 citation statements)

References 26 publications

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“…The present combination of update scheme with IGA-C has the additional advantages over the total Lagrangian Galerkinbased schemes of: (i) reflecting the theoretical kinematic model in a very simple and natural way, where only the familiar concept of linearization is required and no other geometric operators are involved; (ii) leading to simple linearized equations; (iii) requiring a minimal computational effort since in IGA-C only one point evaluation per element is required; (iv) avoiding the variational formulation. Moreover, it is expected in future studies that higher order approximation in the context of geometrically nonlinear problem will lead to improved results in the study of geometric instability and buckling phenomena [54][55][56].…”

Section: Introductionmentioning

confidence: 99%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

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Highlights• Isogeometric collocation is extended to geometrically exact beams.• Consistent linearization of the strong form of the governing equations is derived.• Incremental rotations are parametrized through Eulerian rotation vectors.• Numerical tests show efficiency and high accuracy. AbstractWe extend the isogeometric collocation method to the geometrically nonlinear beams. An exact kinematic formulation, able to represent three-dimensional displacements and rotations without any restriction in magnitude, is presented without the introduction of the moving frame concept. A displacement-based formulation is adopted. Full linearization of the strong form of the governing equations is derived consistently with the underlying geometric structure of the configuration manifold. Incremental rotations are parametrized through Eulerian rotation vectors and configuration updates are performed by means of the exponential map. Numerical tests demonstrate that the proposed combination of isogeometric collocation method with the chosen rotations parametrization results in an efficient computational scheme able to model complex problems with high accuracy.

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Section: Introductionmentioning

confidence: 99%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

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“…The complete post-buckling diagram of the present problem is known to be symmetric with respect to the moment axis, see e.g. Simo and Vu-Quoc [76] and Ibrahimbegovic et al [77]. This complete diagram is obtained when the analysis proceeds past the second critical point and another revolution is performed.…”

Section: Right-angle Simply-supported Frame Under End Momentsmentioning

confidence: 97%

“…13, which is fully clamped at end A and simply-supported (i.e., with translation along X and rotation about X allowed) at end B. This problem was first analyzed by Ziegler [79] and has since then been analyzed by many authors, including Argyris et al [74] and Ibrahimbegovic et al [77].…”

Section: Cable Hocklingmentioning

confidence: 97%

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A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

2011

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This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with

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“…An optimum nonlinear solution technique within the Newton-Raphson scheme was obtained by minimizing the residual displacements. The evaluation of geometrically exact beam theories and models based on a second order approximation of finite rotations for the buckling and postbuckling analysis of beam structures was carried out by Ibrahimbegovic et al [12]. Yu et al [13] developed a generalised Vlasov theory for composite beams by means of the variational-asymptotic method.…”

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

Hui

Pietro

Giunta

et al. 2018

Mathematical Problems in Engineering

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The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.

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On the role of geometrically exact and second-order theories in buckling and post-buckling analysis of three-dimensional beam structures

Cited by 31 publications

References 26 publications

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

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