A large displacement analysis of a beam using a CAD geometric definition

Gontier, Camille; Vollmer, C.

doi:10.1016/0045-7949(95)00100-u

Cited by 20 publications

(10 citation statements)

References 5 publications

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“…Kegl et al [18], on the basis of Saje's exact kinematics element [30], propose a modified formulation of this element for shape optimal design, employing the Bezier curves. The Bezier curves concept is also used in a recent paper by Gontier and Vollmer [12], where Simo's [36] geometrically exact formulation is adapted. Three-dimensional arbitrary curved beam elements employing Reissner's beam theory are derived by Ibrahimbegović [15].…”

Section: Pak and Stauffermentioning

confidence: 99%

A kinematically exact finite element formulation of elastic–plastic curved beams

Saje

Turk

Kalagasidu

et al. 1998

Computers & Structures

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Section: Pak and Stauffermentioning

confidence: 99%

A kinematically exact finite element formulation of elastic–plastic curved beams

Saje

Turk

Kalagasidu

et al. 1998

Computers & Structures

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“…Even if the use of polynomial functions belonging to the spline family for the approximate solution of boundary value problems dates back almost four decades (see e.g. (Prenter 1975;de Boor 1978;Benedetti and Tralli 1989;Gontier and Vollmer 1995)) this new method, which is known as Iso-Geometric Analysis (IGA), was precisely developed to cover the wide existing gap between the worlds of FEM and CAD (see e.g. (Hughes et al 2005;Bazilevs et al 2006;Cottrell et al 2009;Benson et al 2010;Auricchio et al 2012) ).…”

Section: Introductionmentioning

confidence: 99%

ArchNURBS: NURBS-Based Tool for the Structural Safety Assessment of Masonry Arches in MATLAB

Chiozzi

Malagù

Tralli

et al. 2016

J. Comput. Civ. Eng.

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A new approach toward a fully computer-aided design (CAD) integrated structural analysis of arched masonry structures is proposed and a new MATLAB-based computational tool, named ArchNURBS, is developed. It is addressed to professionals dealing with the restoration or structural rehabilitation of historical constructions, who need to assess the safety of masonry arches under assigned load distributions. By using it, they can easily produce estimates of the carrying capacity of curved masonry members, and specifically arches of arbitrary shape. A CAD environment, which is very popular among professionals, can be employed to provide a nonuniform rational B-splines (NURBS) representation of arch geometry. On the basis of this representation, it is possible to perform both an elastic isogeometric analysis and a limit analysis of the structure up to the collapse load. Moreover, the developed tool is devised for handling the presence of fiber-reinforced polymers reinforcement strips at the extrados and/or intrados. This allows for the design of properly dimensioned reinforcement and its verification according to current building codes. The entire procedure relies upon a sound theoretical background. ArchNURBS is going to be freely distributed as an open-source project (http://sourceforge.net/projects/archnurbs/)

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“…[12][13][14][15][16][17].Since high continuity is required for the interpolation of the displacements in a Kirchhoff-Love rod model, the B-spline interpolation used in isogeometric analysis appears to be a natural choice for the development of numerical approximations of thin structural models. A first example of isogeometric interpolation for non polar rods can be found in [18] in which the authors have considered the polar formulation of rods developed in [19]. Many others numerical isogeometric formulations for rods have been proposed since (see, e.g., [20][21][22][23][24][25]).…”

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confidence: 99%

An isogeometric implicit G1 mixed finite element for Kirchhoff space rods

Greco

Cuomo

2016

Computer Methods in Applied Mechanics and Engineering

117

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configuration space is necessary for modelling the Kirchhoff rod (the centroid curve position vector and the torsional angle) [1,2]. In the literature this kind of manifold is also known as ribbon, see [3].Kirchhoff rod models have the advantage, with respect to shear deformable models, that shear locking is automatically avoided. Furthermore, it is used for modelling particular spatial structures, like cables with bending and torsional stiffness; for instance, in [4] the authors present a bending-stabilized cable model, while in [5,6] the authors consider the effect of torsional stiffness in aeroelastic analysis.In [1] a geometrically exact formulation of space rods based on a Lagrangian description was presented, that does not depend on the particular geometry of the centroid curve (differently from what has been done for instance in [7][8][9][10]). An orthogonal frame was introduced on the rod axis, that can be different from the natural frame (Bishop frame) used by Langer and Singer [11]. A pull-back of the strain along the directors was used to define the deformation of the cross section, analogously to what is done in non local and second gradient theory, i.e. [12][13][14][15][16][17].Since high continuity is required for the interpolation of the displacements in a Kirchhoff-Love rod model, the B-spline interpolation used in isogeometric analysis appears to be a natural choice for the development of numerical approximations of thin structural models. A first example of isogeometric interpolation for non polar rods can be found in [18] in which the authors have considered the polar formulation of rods developed in [19]. Many others numerical isogeometric formulations for rods have been proposed since (see, e.g., [20][21][22][23][24][25]).When multiple elements are used for discretizing the model, C 0 continuity for the end rotations of the element is needed, that for the Kirchhoff rod model means a G 1 continuity constraint on the deformation of the centroid curve, i.e., the unit tangent vectors have to coincide at the ends of adjacent elements; from an incremental point of view this means that the velocity of rotation at the ends of adjacent elements must be equal.In [26,27] G 1 continuity for space rods was obtained by means of a change of basis, generalizing Hermite's interpolation. The required geometric continuity was thus achieved without introducing Lagrangian or penalty terms in the formulation, as done for instance by the bending strip method [28]. An alternative strategy of a multi-patch approach for non polar shells can be found in [29].Although it has been claimed that sufficiently high degrees of interpolation avoid locking phenomena, isogeometric models, like all displacement based formulations, suffer from this pathology, that arises from the coupling terms appearing in the strain energy. Membrane and shear locking were observed in plane beam models [30][31][32][33] and membrane and flexural locking in space rod models [10,[34][35][36]. In [1,36] severe locking due to these interactions was fo...

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A large displacement analysis of a beam using a CAD geometric definition

Cited by 20 publications

References 5 publications

A kinematically exact finite element formulation of elastic–plastic curved beams

A kinematically exact finite element formulation of elastic–plastic curved beams

ArchNURBS: NURBS-Based Tool for the Structural Safety Assessment of Masonry Arches in MATLAB

An isogeometric implicit G1 mixed finite element for Kirchhoff space rods

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