A kinematically exact space finite strain beam model — finite element formulation by generalized virtual work principle

Jelenić, Gordan; Saje, Miran

doi:10.1016/0045-7825(94)00056-s

Cited by 96 publications

(56 citation statements)

References 22 publications

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“…We note that instead of the series (B.4), an exact formula for updating the curvature tensor can alternatively be used [40,68]. Following the same procedure (omitted here), and making use of (B.2), Eq.…”

Section: Derivative Of the Exponential Mapmentioning

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: Derivative Of the Exponential Mapmentioning

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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“…Notice how the kinematics of the beam introduces, in contrast to the continuum formulation, additional non-linearities into the problem through the nonvanishing second directional derivative of F (recall that this term vanishes in the more general continuum description). The first and second directional derivatives of the cofactor H are computed as 5 These directional derivatives need to comply with the orthogonality…”

Section: Linearisation Of the Beam Kinematicsmentioning

confidence: 99%

“…The present manuscript aims to extend the variational and computational framework recently introduced in Bonet et al [12] in the context of three dimensional elasticity to the geometrically exact Simo [13] beam model, the starting point of so many other finite element beam type formulations [1][2][3][4][5][6][7]. The variational approach proposed herein can therefore be viewed as a continuum degenerate formulation emerging from that presented in [12].…”

Section: Introductionmentioning

confidence: 99%

“…Work conjugates to those variables (typically denoted as resultant contact forces and resultant contact couples [9]) can be derived from a hyperelastic energy functional which is defined in terms of the beam strain measures [1][2][3][4][5][6][7][8]. Other authors prefer an alternative continuum degenerate approach [10,11] where, typically, the Lagrangian strain tensor is retained as the main strain measure and particularised for the kinematic description of the beam.…”

Section: Introductionmentioning

confidence: 99%

“…Most classical beam theories [1][2][3][4][5][6][7][8] are based on the definition of so called beam strain measures, namely the axial-shear and torsional-bending strain vectors. Work conjugates to those variables (typically denoted as resultant contact forces and resultant contact couples [9]) can be derived from a hyperelastic energy functional which is defined in terms of the beam strain measures [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A computational framework for polyconvex large strain elasticity for geometrically exact beam theory

et al. 2015

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In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094 in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55-70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the reexpression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney-Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.

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Shape optimal design of elastic space frames with non-linear response

Kegl

Antes

1998

Int. J. Numer. Meth. Engng.

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This paper describes an approach to shape optimal design of elastic space frames with kinematically non-linear response. A space frame structure is treated as to be assembled from several frame design elements each of them being defined as a skeleton lying on a rational Be´zier patch. The design variables may influence the control points of each patch and the cross-sectional quantities of beam elements. Highly accurate beam finite elements are employed based on a modified formulation of the beam element proposed by Jelenic´and Saje. The modified element is able to account for arbitrary initial curvature and it fits nicely into the context of both the proposed design element technique and the optimization process. The formulation of the shape optimal design problem in form of non-linear mathematical programming problem and its solution by employing gradient-based methods of mathematical programming are discussed briefly. The theory is illustrated in detail with three numerical examples.1998 John Wiley & Sons, Ltd.

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A kinematically exact space finite strain beam model — finite element formulation by generalized virtual work principle

Cited by 96 publications

References 22 publications

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

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

A computational framework for polyconvex large strain elasticity for geometrically exact beam theory

Shape optimal design of elastic space frames with non-linear response

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