A Geometrically-exact rod model incorporating shear and torsion-warping deformation

Simo, J. C.; Vu‐Quoc, L.

doi:10.1016/0020-7683(91)90089-x

Cited by 316 publications

(207 citation statements)

References 40 publications

Supporting

Mentioning

200

Contrasting

Unclassified

Order By: Relevance

“…the works presented by (Cardona and Geradin, 1988), (Simo and Vu-Quoc, 1991), (Pimenta and Yojo, 1993), (Simo et al, 1995), Ibrahimbegovic and Mikdad, 2000;Ibrahimbegovic and Knopf-Lenoir, 2003), (Saje et al, 1998), Jelenic and Crisfield, 1999), (Planinc and Saje, 1999), Atluri, 1988, 1989;Atluri, 1996, 1998;Atluri et al, 2001), (Betsch and Steinmann, 2002), (Zupan and Saje, 2003b), (Kapania and Li, 2003b,a), (Romero, 2004), (Mata et al, 2007), (Makinen, 2007), (Lens and Cardona, 2008), (Ghosh and Roy, 2008) and (Pimenta et al, 2008).…”

Section: The Geometrically Exact Three-dimensional Beam Theorymentioning

confidence: 96%

See 1 more Smart Citation

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

Santos¹,

Pimenta²,

Almeida³

2010

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints.

show abstract

Section: The Geometrically Exact Three-dimensional Beam Theorymentioning

confidence: 96%

“…The theory was later extended by (Simo and Vu-Quoc, 1991) to account for the cross-sectional warping phenomena. In fact, it was in this work that the denomination geometrically exact beam was firstly proposed.…”

Section: The Geometrically Exact Three-dimensional Beam Theorymentioning

confidence: 99%

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

Santos¹,

Pimenta²,

Almeida³

2010

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

show abstract

“…We consider the geometrically exact finite strain beam theory introduced by Reissner (1973Reissner ( , 1981 [34,35] and Antman (1974) [1] and further extended by Simo and co-workers (1985,1986,1991,1995) [43,45,46,44]. Since these pioneering works, considerable progress has been made on the geometrically exact analysis of three-dimensional framed structures, from both theoretical and numerical points of view, see e.g.…”

Section: The Geometrically Exact Finite Strain Beam Theory: Boundary-mentioning

confidence: 99%

Dual extremum principles for geometrically exact finite strain beams

Santos¹,

Almeida²

2011

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

Both necessary and sufficient conditions for the existence of two complementary-dual extremum principles for geometrically exact finite strain (one-dimensional) beam models are investigated by means of two different approaches. One is based on the results published by Gao and Strang, and the other relies on the approach proposed by Noble and Sewell. While the former is limited to beam models restricted to moderate large deformations, the latter is valid for arbitrarily large deformations (and strains). The numerical implementation of the complementary-dual extremum principles can lead to simple true global upper bounds of the error of the approximate solutions.

show abstract

“…This theory mainly targets the set of structures that are subjected to small strains (elastic response) but arbitrarily large deformations, such a scenario occurs in such essentially one-dimensional structures, implying that the cross-sectional dimension is much smaller than its length [2]. The work on the theory of geometrically exact beams was mainly contributed by Timoshenko, Iura and Atluri [3], Simo and Vu-Quoc [4], and Reissner [5][6][7], which are all based on the work of Euler beam theory, with more modern work by Kirchhoff, Love [8], and most importantly by Cosserat and Cosserat [9]. There is substantial literature on Cosserat theories including that by Rubin [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A Generalized Approach for Reconstructing the Three-Dimensional Shape of Slender Structures Including the Effects of Curvature, Shear, Torsion, and Elongation

Chadha

Todd

2017

Journal of Applied Mechanics

View full text Add to dashboard Cite

This paper extends the approach for determining the three-dimensional global displaced shape of slender structures from a limited set of scalar surface strain measurements. It is an exhaustive approach that captures the effect of curvature, shear, torsion, and elongation. The theory developed provides both a determination of the uniaxial strain (in a given direction) anywhere in the structure and the deformed shape, given a set of strain values. The approach utilizes Cosserat rod theory and exploits a localized linearization approach that helps to obtain a local basis function set for the displacement solution in the Cosserat frame. For the assumed deformed shape (both the midcurve and the crosssectional orientation), the uniaxial value of strain in any given direction is obtained analytically, and this strain model is the basis used to predict the shape via an approximate local linearized solution strategy. Error analysis due to noise in measured strain values and in uncertainty in the proximal boundary condition is performed showing uniform convergence with increased sensor count.

show abstract

A Geometrically-exact rod model incorporating shear and torsion-warping deformation

Cited by 316 publications

References 40 publications

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

Dual extremum principles for geometrically exact finite strain beams

A Generalized Approach for Reconstructing the Three-Dimensional Shape of Slender Structures Including the Effects of Curvature, Shear, Torsion, and Elongation

Contact Info

Product

Resources

About