Convergence of consistently derived Timoshenko beam finite elements

Nickel, Robert E.; Secor, G.A.

doi:10.1002/nme.1620050210

Cited by 74 publications

(30 citation statements)

References 10 publications

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“…Different orders of interpolation for w and 0 were employed in the development of shear deformable elements [13,141. Both w and 0 and their respective spatial derivatives were considered as nodal degrees of freedom by Thomas and Abbas [IS] for their version of the Timoshenko element.…”

Section: First-order Theorymentioning

confidence: 99%

On the performance of higher order theories for transient dynamic analysis of sandwich and composite beams

Marur¹,

Kant

1997

Computers & Structures

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Abstract-Higher-order shear-deformable refined theories, based on isoparametric elements, are adopted for transient dynamic analysis of symmetric and unsymmetric sandwich and composite beam constructions. These shear-correction coefficient free theories model cross sectional warping using nonlinear variation of inplane displacements across the depth. They also incorporate transverse shear stress in the formulation. A special lumping scheme is employed for the evaluation of diagonal mass matrix, and a central difference scheme is used for carrying out the integration of the equation of motion, to obtain the response history. Through numerical experiments, the efficacy of higher-order models in predicting displacements and stress, resultants over from the first-order theory, with respect to time, is clearly brought out in this paper. 0 1997 Elsevier Science Ltd.

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Section: First-order Theorymentioning

confidence: 99%

On the performance of higher order theories for transient dynamic analysis of sandwich and composite beams

Marur¹,

Kant

1997

Computers & Structures

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“…In the finite element literature, much emphasis has been placed on the development of higher order Timoshenko beam elements. Higher order elements [6,7,8] were necessary in order to satisfy all geometric and natural boundary conditions of a Timoshenko beam. The simplest shear deformable beam possible was introduced by Hughes et.…”

Section: Thesis Overviewmentioning

confidence: 99%

“…The succeeding sections introduced two alternative modelling assumptions with regards to the flexible appendage mass distribution: lumped mass ( §2. 6) and lumped mass/inertia ( §2.7). In either case the stiffness matrix is …”

Section: Specification Of Equations Of Motionmentioning

confidence: 99%

Assessment of finite element approximations for nonlinear flexible multibody dynamics

Roberts

1991

32nd Structures, Structural Dynamics, and Materials Conference

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Systematic investigation is made of effects of kinematic assumptions and finite element approximations in the context of nonlinear flexible multibody dynamics. Two nonlinear beam finite elements are consistently derived from virtual work principle using Bernoulli-Euler and Timoshenko beam kinematics. Initial assessment is made by studying convergence properties of element formulations with eigenvalue problems: free vibration, static buckling, and dynamic buckling. Equations of motion are derived for rigid central body with flexible appendage using virtual work principle. Virtual work principle allows natural and consistent discretization of flexible appendage using finite element method. Nonlinearities in flexibility are explored through dynamics examples using beam finite elements. Application of dynamics formulation is made to a realistic scenario involving space shuttle remote manipulator arm with attached payload. Contribution of nonlinear theory, in both formulation and solution, is assessed.

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“…Let us mention here that Nickel and Secor [10] have already used Gurtin's principle in order to derive the equations of Timoshenko's beam theory.…”

Section: Definition Of One-dimensional Theoriesmentioning

confidence: 99%

One-dimensional theories of motion for beams

Gamby

1977

J Elasticity

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Using Gurtin's variational principle, a rational method for deducing the approximate one-dimensional theories of Medick from three-dimensional elasticity is presented.By using suitable unknowns, matrix equations are obtained; these exhibit a hyperbolic structure. RI~SUMI~Dans le cadre des schrmatisations de Medick, on prrsente une mrthode permettant de drduire de la throrie tridimensionelle des throries approchres h une dimension de plus en plus fines. Aprrs un choix convenable des inconnues, on obtient les 6quations matricieUes du problrme qui mettent en 6vidence une structure de syst~me hyperbolique.Three-dimensional continuum theories usually lead to rather involved problems. When "slender" bodies (like strings, rods, beams) are considered, the motion of the medium can usually be properly described by a "one-dimensional theory" or "rod theory". Such bodies will be termed "curvilinear media".To give such a one-dimensional theory is tantamount to:• selecting a definite number of functions of two variables, the arc-length on a certain curve and time, which are meant to describe the state of the system • giving the equations and the initial and boundary conditions these functions should meet.Among the methods that yield a hierarchy of approximations, let us mention director theories [1], [2] in which the curvilinear medium is defined axiomatically without direct reference to the theory of elasticity, and several methods [3][4][5][6] in which displacements within the cross-section are represented by polynomials in the transverse coordinates, using as a starting point the theory of three-dimensional elasticity.

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Convergence of consistently derived Timoshenko beam finite elements

Cited by 74 publications

References 10 publications

On the performance of higher order theories for transient dynamic analysis of sandwich and composite beams

On the performance of higher order theories for transient dynamic analysis of sandwich and composite beams

Assessment of finite element approximations for nonlinear flexible multibody dynamics

One-dimensional theories of motion for beams

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