A comparison of finite element formulations for dynamics of viscoelastic beams

Pálfalvi, Attila

doi:10.1016/j.finel.2008.06.009

Cited by 19 publications

(7 citation statements)

References 9 publications

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“…In their formulation, they employed the EBT for the outer faces and the TBT for the inner viscoelastic core. Pálfalvi [18] also employed the ADN formulation in the analysis of viscoelastic Euler-Bernoulli beams.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Payette

Reddy

2009

Numer Methods Biomed Eng

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SUMMARYWeak form finite element models for the nonlinear quasi-static bending and extension of initially straight viscoelastic Euler-Bernoulli and Timoshenko beams are developed using the principle of virtual work. The mechanical properties of the beams are considered to be linear viscoelastic. However, large transverse displacements, moderate rotations and small strains are allowed by retaining the von Kármán strain components of the Green-Lagrange strain tensor in the formulation. The fully discretized finite element equations are developed using the trapezoidal rule in conjunction with a two-point recurrence relation. The resulting finite element equations, therefore, necessitate data storage from the previous time step only, and not the entire deformation history. Membrane locking is eliminated from the Euler-Bernoulli formulation through the use of selective reduced Gauss-Legendre quadrature. Membrane and shear locking are both circumvented in the Timoshenko beam finite element by employing a family of high-order Lagrange polynomials. A Newton-Raphson iterative scheme is used to solve the nonlinear finite element equations.

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Section: Introductionmentioning

confidence: 99%

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Payette

Reddy

2009

Numer Methods Biomed Eng

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“…The history variables are expressed explicitly in Appendix B. It is now possible to express the fully discretized finite element equations at the current time step as [K e ] k+1 {∆ e } k+1 = {F e } k+1 − {Q e } k+1 (28) where each of the components in the above equation are given in Appendix B. In the proposed high-order finite element formulation, we employ an unequal spacing of the nodes within each element.…”

Section: Kinematics Of Deformationmentioning

confidence: 99%

“…Additional numerical formulations for viscoelastic beams are based on the Fourier transform method [7], the anelastic displacement (ADN) procedure [40,28] and the Golla-Hughes-McTavish (GHM) method [24,25,4,3]. It has been noted that when the relaxation moduli are given as Prony series, the convolution form of linear viscoelastic constitutive equations may be equivalently expressed as a set of ordinary differential equations in terms of a collection of internal strain variables.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory

Payette¹,

Reddy

2013

Journal of Engineering Materials and Technology

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A weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory. The formulation assumes linear viscoelastic material properties and is applicable to problems involving small strains and moderate rotations. The viscoelastic constitutive equations are efficiently discretized using the trapezoidal rule in conjunction with a two-point recurrence formula. Locking is avoided through the use of standard low-order reduced integration elements as well through the employment of a family of elements constructed using high-polynomial order Lagrange and Hermite interpolation functions.

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“…7–10 The time dependency of material properties usually lead to complexity of the solution procedure so that some researchers challenged the problem by presenting various solution approaches. 11–17 Reddy 11 applied variational principles for integro-differential equations which were arisen from the time-dependent viscoelastic constitutive equations. Kaminskii and Selivanov 12 used the branching operator continued fraction approximation for the deformation analysis of cracked composite plates.…”

Section: Introductionmentioning

confidence: 99%

“…Finite element, finite difference, and differential quadrature methods were other prominent numerical techniques used by various researchers for viscoelastic problems. 15–18…”

Section: Introductionmentioning

confidence: 99%

Accurate damping analysis of viscoelastic composite beams and plates on suppressive foundation

Zamani

Bodaghi

Aghdam

et al. 2014

Journal of Composite Materials

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An accurate study for dynamic behavior of viscoelastic thin laminated composite beams and plates resting on viscoelastic foundations is presented. Boltzmann superposition integral based on the dynamic mechanical analysis results is adapted to accurately predict viscoelastic behavior of polymeric fiber-reinforced composite structures. Also, foundation viscoelasticity is described based on the Kelvin–Voigt model. Integro-differential governing equations of motion are derived based on classical lamination theory via Hamilton principle. Galerkin weighted residual method, iterative QZ algorithm, and Fourier transform are applied to obtain natural frequency, loss factor, and transient response of structures resting on suppressive foundations. Influence of foundation and geometrical parameters and also boundary conditions on the dynamic behavior is put into evidence via a parametric study, and pertinent conclusions are outlined. Due to the absence of similar results in the literature, this paper is likely to fill a gap in the state of the art of this problem.

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A comparison of finite element formulations for dynamics of viscoelastic beams

Cited by 19 publications

References 9 publications

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

A Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory

Accurate damping analysis of viscoelastic composite beams and plates on suppressive foundation

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