3D beam element based on Saint Venànt’s rod theory

Petrolo, Antonio Salvatore; Casciaro, Raffaele

doi:10.1016/j.compstruc.2004.07.004

Cited by 41 publications

(17 citation statements)

References 11 publications

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“…When considering the results of the shear test, some differences can be seen in Figures 12 and 13, between the results from the ICM plate and beam models, even if the elastic compliance matrix of the beam section is evaluated by the procedure described in [Petrolo and Casciaro 2004] and so the beam modeling correctly accounts for all Saint-Venant couplings between shear and torsion. Moreover, in the case of plate analysis, the results are very sensitive to the boundary constraint details.…”

Section: Numerical Validationmentioning

confidence: 99%

“…In all cases the evaluation of the compliance operator H e has been obtained through the solution of the Saint-Venant equations using the FEM approach described in [Petrolo and Casciaro 2004] to which the reader is referred for further details (see also [Lacarbonara and Paolone 2007]). The proposed Kirchhoff plate element has been implemented in the KASP code [Garcea 2001].…”

Section: Numerical Validationmentioning

confidence: 99%

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Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method

Garcea

Madeo

Casciaro

2012

J. Mech. Mater. Struct.

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In our previous paper the implicit corotational method (ICM) was presented as a general procedure for recovering objective nonlinear models fully reusing the information obtained by the corresponding linear theories.The present work deals with the implementation of the ICM as a numerical tool for the finite element analysis of nonlinear structures using either a path-following or an asymptotic approach. Different aspects of the FEM modeling are discussed in detail, including the numerical handling of finite rotations, interpolation strategies, and equation formats.Two mixed finite elements are presented, suitable for nonlinear analysis: a three-dimensional beam element, based on interpolation of both the kinematic and static fields, and a rotation-free thin-plate element, based on a biquadratic spline interpolation of the displacement and piece-wise constant interpolation of stress. Both are frame invariant and free from nonlinear locking.A numerical investigation has been performed, comparing beam and plate solutions in the case of thinwalled beams. The good agreement between the recovered results and the available theoretical solutions and/or numerical benchmarks clearly shows the correctness and robustness of the proposed approach as a general strategy for numerical implementations.

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Section: Numerical Validationmentioning

confidence: 99%

Section: Numerical Validationmentioning

confidence: 99%

Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method

Garcea

Madeo

Casciaro

2012

J. Mech. Mater. Struct.

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“…For full details of the SV problem we refer readers to classic works such as [Timoshenko 1955;Fichera 1977] while a numerical solution of the problem can be found in [Petrolo and Casciaro 2004]. Interesting, also for comparison with the model presented here, is [Petrov and Géradin 1998a;1998b].…”

Section: Nonlinear Beam Model Based On Saint-venant General Rod Theorymentioning

confidence: 99%

“…Matrix H τ gives the contribution of tangential stresses and generally results in a full symmetric matrix which can however be obtained as a by-product of the FEM solution process which provides the stress functions d 2 [y, z] and d 3 [y, z] (see [Petrolo and Casciaro 2004] for details). It is convenient to introduce the vector quantities…”

Section: Nonlinear Beam Model Based On Saint-venant General Rod Theorymentioning

confidence: 99%

“…and vectorial stress functions d 2 [y, z] and d 3 [y, z] are defined by a Laplace/Neumann differential problem whose numerical solution can be easily obtained through a finite element discretization of the section as, for instance, performed in [Petrolo and Casciaro 2004]. Also as in that reference, the interpolation (31c) allows us to obtain the expression of the complementary energy ψ[s] associated with the current section [s] in terms of the strength vectors t σ and t τ :…”

Section: Nonlinear Beam Model Based On Saint-venant General Rod Theorymentioning

confidence: 99%

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The implicit corotational method and its use in the derivation of nonlinear structural models for beams and plates

Garcea

Madeo

Casciaro

2012

J. Mech. Mater. Struct.

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What we call the implicit corotational method is proposed as a tool to obtain geometrically exact nonlinear models for structural elements, such as beams or shells, undergoing finite rotations and small strains, starting from the basic solutions for the three-dimensional Cauchy continuum used in the corresponding linear modelings.The idea is to use a local corotational description to decompose the deformation gradient in a stretch part followed by a finite rigid rotation. Referring to this corotational frame we can derive, from the linear stress tensor and the deformation gradient provided by linear elasticity, an accurate approximation for the nonlinear stress and strain tensors which implicitly assure frame invariance. The stress and strain fields recovered in this way as functions of generalized stress and strain resultants are then used within a mixed variational formulation allowing us to recover an objective nonlinear modeling directly suitable for FEM implementations through a black-box process which maintains the full details of the linear solutions, such as shear warping and other subtle effects.The method is applied to the construction of three-dimensional beam and plate nonlinear models starting from the Saint-Venant rod and Kirchhoff and Mindlin-Reissner plate linear theories, respectively.

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Minkowski plasticity in 3D frames: Decoupled construction of the cross‐section yield surface and efficient stress update strategy

Magisano

Liguori

Leonetti

et al. 2018

Numerical Meth Engineering

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Summary This work makes the Minkowski sum of ellipsoids into a consolidated tool for the representation of the yield surface of arbitrarily shaped composite cross sections under axial force and biaxial bending and shows how best to use it within the incremental nonlinear analysis of three‐dimensional frames. A geometric interpretation of each term of the sum allows us to construct complex convex surfaces using a low number of ellipsoids, each of them evaluated in a robust and efficient decoupled manner. Specialized algorithms, which exploit the parameterization of the yield surface in terms of a cross‐section collapse mechanism, are proposed for an efficient stress update based on the elastic predictor–return mapping scheme on a three‐dimensional beam finite element. The derivation of the algorithmic tangent moduli for the Minkowski sum completes the elements required for an efficient path‐following nonlinear analysis. The proposed methodology is general and can be applied for the representation of any zonoid yield surface and the corresponding implicit stress integration to a variety of structural and plasticity models.

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3D beam element based on Saint Venànt’s rod theory

Cited by 41 publications

References 11 publications

Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method

Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method

The implicit corotational method and its use in the derivation of nonlinear structural models for beams and plates

Minkowski plasticity in 3D frames: Decoupled construction of the cross‐section yield surface and efficient stress update strategy

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