On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments

Dvorkin, Eduardo N.; Onte, Eugenio; Oliver, J.

doi:10.1002/nme.1620260710

Cited by 102 publications

(56 citation statements)

References 19 publications

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“…(5). The coil is discretized by a set of degenerated beam elements (e.g., Bathe, 1996;Dvorkin et al, 1988) based on Timoshenko beam theory, in which the deformation in the cross-section of the beam is assumed to be negligible. Schematic description of the beam element is shown in Fig.…”

Section: Description Of the Coil Configurationmentioning

confidence: 99%

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Computational model of coil placement in cerebral aneurysm with using realistic coil properties

Otani

Satoshi

Shigematsu

et al. 2015

JBSE

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This study presents a computational mechanical model of coil placement in cerebral aneurysms with using realistic coil properties. The mechanical behavior of the coil is expressed by solving a variational problem including the kinetic and elastic energies of the coil and geometric constraints due to the multiple contacts. The coil is discretized as a set of beam elements obeying Timoshenko beam theory, in which these elastic properties are determined based on the actual shape and material property of the coil. Numerical examples of the coil placement are presented for four cases with different coil properties in terms of the elastic property (hard and soft) and reference configurations (helical loop and complex loop) within the realistic range. These results exhibit the effects of the coil properties on not only the transition of the coil configuration during the placement process but also the contact force of the coil against the aneurysm wall which has a fatal risk of bleeding in the operation. The proposed computational model will assist surgeons to select the appropriate coil and coil deployment protocol to achieve the sufficient treatment effectiveness with minimizing the risk of bleeding in the view of the mechanical sense.

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Section: Description Of the Coil Configurationmentioning

confidence: 99%

“…For detailed explanation about this beam element, one can find in (Bathe, 1996;Dvorkin et al, 1988;Hisada and Noguchi, 1995). …”

Section: V(v1 V2 V3mentioning

confidence: 99%

Computational model of coil placement in cerebral aneurysm with using realistic coil properties

Otani

Satoshi

Shigematsu

et al. 2015

JBSE

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“…Moreover, to account for the spread of yielding, numerical integration over the cross-section is also required. In this case, one of the advantages of Reissner-Simo beam theory over the so-called continuum based (or degenerate continuum) approach [33][34][35] is lost. Nevertheless, plastic behaviour in beams is often restricted to localized areas (e.g.…”

Section: The Constitutive Law and The Reference Conÿgurationmentioning

confidence: 99%

On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory

Ritto‐Corrêa

Camotim

2002

Numerical Meth Engineering

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SUMMARYIn this paper we present a systematic way of di erentiating, up to the second directional derivative, (i) the Rodrigues formula and (ii) the spin-rotation vector variation relationship. To achieve this goal, several trigonometric functions are grouped into a family of scalar quantities, which can be expressed in terms of a single power series. These results are then applied to the vector-like parameterization of Reissner-Simo beam theory, enabling a straightforward derivation and leading to a clearer formulation. In particular, and in contrast with previous formulations, a relatively compact and obviously symmetric form of the tangent operator is obtained. The paper also discusses several relevant issues concerning a beam ÿnite element implementation and concludes with the presentation of a few selected illustrative examples.

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“…where U 1 , U 3 and Z 1 are strain and change of curvature vectors, the variations of which are deÿned in the preceding section by equation (20).…”

Section: Virtual Work Of Stressesmentioning

confidence: 99%

Finite rotation quadrilateral element for multi-layer beams

Wisniewski

1999

Int. J. Numer. Meth. Engng.

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SUMMARYThe paper presents the ÿnite rotations beam equations derived on use of the generalized Reissner hypothesis with a scalar parameter for the transverse extension. The beam strain and change of curvature measures are obtained from the right stretch strain, and the virtual work is given for Biot-type stress and couple resultants. The strain energy for the ÿrst-order isotropic elastic material is assumed in terms of the right stretch strain, and constitutive equations for the beam stress and couple resultants are derived.Two ÿnite rotation elements are developed from the derived beam equations: a beam element with the transverse stretch and a quadrilateral element. First, the beam element with the uniformly under-integrated tangent operator is developed. Next, the formula linking the middle-line variables and the interface variables of the beam is introduced consistently with the generalized Reissner kinematics. Linearization of this formula is performed, and the derived tangent operator is used to convert the two-node beam element to a four-node quadrilateral.Both the ÿnite elements have been tested on several numerical examples, some of highly non-linear characteristics, and their accuracy is very good. It has been established that the quadrilateral element, which is intended for applications to multi-layer beams, performs very well for high elemental aspect ratios, and can therefore be applied to modelling of very thin layers.

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On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments

Cited by 102 publications

References 19 publications

Computational model of coil placement in cerebral aneurysm with using realistic coil properties

Computational model of coil placement in cerebral aneurysm with using realistic coil properties

On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory

Finite rotation quadrilateral element for multi-layer beams

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