Nonlinear Composite Beam Theory

Hodges, Dewey H.

doi:10.2514/4.866821

Cited by 366 publications

(307 citation statements)

References 91 publications

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“…So, for example, the inextensible Kirchhoff rod is simply a chain of rigid cylinders connected with bushings that are consistently derived from the continuum equations. But our discretisation approach stands in contrast to the usual way in computational continuum mechanics, where the finite element (FE) approach is favored [9,11,14,21,23,38,39]. The reason for that is, that the main focus in FE is accuracy, not computational efficiency.…”

Section: Discrete Geometrically Exact Rodsmentioning

confidence: 93%

“…Nevertheless, the dynamical analysis of fully nonlinear beams and rods in 3D is even today a challenging problem, both from the viewpoint of modeling and from the viewpoint of the efficient numerical solution of the resulting model equations [14,21,23,36,38,39]. In the present paper, we combine an objective/frame-indifferent geometrically exact space discretisation of Kirchhoff and Cosserat rods with standard methods for the time integration of the equations of motion for constrained mechanical systems [4,17,22].…”

Section: Introductionmentioning

confidence: 99%

“…We distinguish three basic types of classical rod models. In hierarchical descending order, these are the Cosserat, the extensible Kirchhoff and the inextensible Kirchhoff model [1,2,3,9,13,14,21,23,24,25,26,27,28,32,38,39]. Table 1 presents a short overview, including numerical problems in time integration to be discussed in this article.…”

Section: Introductionmentioning

confidence: 99%

“…We remark that these rod models serve as kinematic 'skeletons' for the full three dimensional elastic problem. The reconstruction of the three dimensional displacement, stress and strain distributions can be conveniently carried out in a postprocessing by the use of 'warping functions' [15,21,28]. In this section, we describe the basic equations in terms of energies for the smooth Cosserat and Kirchhoff rods, where we parametrise the rotatory degrees of freedom directly with quaternions.…”

Section: Introductionmentioning

confidence: 99%

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Numerical aspects in the dynamic simulation of geometrically exact rods

Lang

Arnold

2012

Applied Numerical Mathematics

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Classical geometrically exact Kirchhoff and Cosserat models are used to study the nonlinear deformation of rods. Extension, bending and torsion of the rod may be represented by the Kirchhoff model. The Cosserat model additionally takes into account shearing effects. Second order finite differences on a staggered grid define discrete viscoelastic versions of these classical models. Since the rotations are parametrisecl by unit quaternions, the space discretisation results in differential-algebraic equations that are solved numerically by standard techniques like index reduction and projection methods. Using absolute coordinates, the mass and constraint matrices are sparse and this sparsity may be exploited to speed-up time integration. Further improvements are possible in the Cosserat model, because the constraints are just the normalisation conditions for unit quaternions such that the null space of the constraint matrix can be given analytically. The results of the theoretical investigations are illustrated by numerical tests

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Section: Discrete Geometrically Exact Rodsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical aspects in the dynamic simulation of geometrically exact rods

Lang

Arnold

2012

Applied Numerical Mathematics

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“…20 The material constants in the equation are the cross-sectional mass, M , and flexibility (or compliance), C, matrices, which can be obtained from a structural homogenisation process. 21 They are full symmetric matrices that may vary with the arc length, s. Finally, the matrix E includes the effect of the initial strain γ 0 and curvature k 0 by…”

Section: Intrinsic Beam Formulationmentioning

confidence: 99%

Robust Aeroelastic Control of Very Flexible Wings using Intrinsic Models

Wang

Wynn

Palacios

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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This paper explores the robust control of large flexible wings when their dynamics are written in terms of intrinsic variables, that is, velocities and stress resultants. Assuming 2-D strip theory for the aerodynamics, the resulting nonlinear aeroelastic equations of motion are written in modal coordinates. It is seen that a system which experiences large displacements can nonetheless be accurately described by a system with only weak nonlinear couplings in this description of the wing dynamics. As result, a linear robust controller acting on a control surface is able to effectively provide gust load alleviation and flutter suppression even when the wing structure undergoes large deformations. This is numerically demonstrated on various representative test cases.

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Bibliography

2013

Mathematical Models of Beams and Cables

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Nonlinear Composite Beam Theory

Cited by 366 publications

References 91 publications

Numerical aspects in the dynamic simulation of geometrically exact rods

Numerical aspects in the dynamic simulation of geometrically exact rods

Robust Aeroelastic Control of Very Flexible Wings using Intrinsic Models

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