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

Santos, H.A.F.A.; Pimenta, Paulo de Mattos; Almeida, J. P. Moitinho de

doi:10.1007/s00466-011-0608-3

Cited by 40 publications

(24 citation statements)

References 74 publications

(143 reference statements)

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“…Within the FE method framework, comparisons of different geometrically nonlinear beam formulations in terms of locking are discussed in [64] and a locking-free hybrid formulation is presented in [65]. Both papers confirm that the standard geometrically exact two-node displacement-based finite element formulation leads to severe locking, unless a one-point Gaussian integration rule is used.…”

Section: Locking Studymentioning

confidence: 87%

“…[66], represents the most common shear locking countermeasure used in geometrically exact beam formulations. We repeat the same test proposed in [65] that consists of a cantilever beam of length L = 1 subjected to a lateral concentrated tip load f = 10 −5 . The beam cross section width is 0.01 and the slenderness L/ h, where h denotes the beam thickness, varies from 1.25 up to 1000.…”

Section: Locking Studymentioning

confidence: 99%

“…10 we report also the tip deflections digitized from Fig. 4 of [65] (see black solid line marked with triangles) obtained using a standard two-node displacement-based total Lagrangian finite element formulation with five-point Gaussian integration scheme. The deflections tend to zero when the slenderness increases, indicating severe shear locking.…”

Section: Locking Studymentioning

confidence: 99%

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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: Locking Studymentioning

confidence: 87%

Section: Locking Studymentioning

confidence: 99%

Section: Locking Studymentioning

confidence: 99%

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

Marino

2016

Computer Methods in Applied Mechanics and Engineering

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“…Unfortunately, these signs are generally unknown a priori. Two-field complementary energy principles expressed in terms of stress-resultants and displacement fields have also been proposed in the literature for geometrically exact Reissner-Simo beams [120,121,123,124].…”

Section: Complementary-energy Based Principles For Non-linear Elasticmentioning

confidence: 99%

Complementary-Energy Methods for Geometrically Non-linear Structural Models: An Overview and Recent Developments in the Analysis of Frames

Santos

2011

Arch Computat Methods Eng

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Boundary-value problems in solid mechanics are often addressed, from both theoretical and numerical points of view, by resorting to displacement/rotation-based variational formulations. For conservative problems, such formulations may be constructed on the basis of the Principle of Stationary Total Potential Energy. Small deformation problems have a unique solution and, as a consequence, their corresponding total potential energies are globally convex. In this case, under the so-called Legendre transform, the total potential energy can be transformed into a globally concave total complementary energy only expressed in terms of stress variables. However, large deformation problems have, in general, for the same boundary conditions, multiple solutions. As a result, their associated total potential energies are globally non-convex. Notwithstanding, the Principle of Stationary Total Potential Energy can still be regarded as a minimum principle, only involving displacement/rotation fields. The existence of a maximum complementary energy principle defined in a truly dual form has been subject of discussion since the first contribution made by Hellinger in 1914. This paper provides a survey of the complementary energy principles and also accounts for the evolution of the complementary-energy based finite element models for geometrically non-linear solid/structural models proposed in the literature over the last 60 years, giving special emphasis to the complementary-energy based methods developed within the framework of the geometrically exact ReissnerSimo beam theory for the analysis of structural frames.

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“…In contrast, for equilibrium formulations, the stresses are computed as fundamental unknowns. Examples of equilibrium-based finite element formulations for geometrically non-linear beam problems were presented in [33,35,32]. An equilibrium-based formulation for non-linear elastic cables can be found in [34].…”

Section: Introductionmentioning

confidence: 99%

Hybrid equilibrium finite element formulation for composite beams with partial interaction

Santos

Silberschmidt

2014

Composite Structures

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Thanks to their various benefits, composite beams have been increasingly used in various applications. This study will focus on two-layer composite beams with a flexible shear interface between layers. The finite element method, in particular its displacement-based formulation, has been recognized as the most popular method for numerical analysis of composite beams. However, when applied to Timoshenko beams with partial interaction, the displacement-based formulation may suffer from the so-called shear-locking and slip-locking phenomena, leading to erroneous solutions. Hybrid and mixed finite element formulations have been viewed as competitive alternatives, since they naturally avoid locking effects. Special types of these formulations are the so-called equilibrium-based formulations, producing statically admissible solutions. This work introduces for the first time an equilibrium-based finite element formulation for the analysis of Timoshenko composite beams with partial interaction. The formulation relies on a variational principle of complementary energy involving only force/moment-like variables as fundamental unknown fields. The approximate field variables are selected such that all equilibrium equations hold in strong form. The inter-element equilibrium is enforced by resorting to the Lagrangian multiplier method. Unlike traditional displacement-based finite element formulations, the proposed scheme is naturally free from both shearand slip-locking phenomena. The accuracy and effectiveness of the new formulation is numerically assessed through the analysis of several numerical examples. In particular, the ability of the formulation to model accurately both very flexible and very stiff shear connections is numerically shown.

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

Cited by 40 publications

References 74 publications

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

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

Complementary-Energy Methods for Geometrically Non-linear Structural Models: An Overview and Recent Developments in the Analysis of Frames

Hybrid equilibrium finite element formulation for composite beams with partial interaction

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