Alternative Kelvin viscoelastic procedure for finite elements

Mesquita, A.D.; Coda, Humberto Breves

doi:10.1016/s0307-904x(01)00048-8

Cited by 35 publications

(31 citation statements)

References 12 publications

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“…This strategy is originally described here for nonlinear strain measure, but was inspired in Mesquita and Coda (2002), Mesquita and Coda (2003) and Mesquita and Coda (2007) where linear viscoelastic models are proposed. As far as the authors knowledge goes it is different from all nonlinear viscoelastic formulations present in literature, see for example, Lemaitre and Chaboche (1990), Lemaitre (2001), Lima et al (2015), Holzapfel (1996), Simo (1987), Huber and Tsakmakis (2000), Petiteau et al (2013), Marko et al (2006) and Clough and Penzien (1985).…”

Section: Latin American Journal Of Solids and Structures 13 (2016) 96mentioning

confidence: 99%

“…(ii) a technique based on Lagrange multipliers for the consideration of passive mass / spring / damper vibration control mechanisms and (iii) an innovative approach to the consideration of viscous damping in the form of the rheological model of Kelvin/Voigt adapted to the Green nonlinear strain derived from linear applications (Mesquita and Coda (2002), Mesquita and Coda (2003) and Mesquita and Coda (2007)). …”

Section: Introductionmentioning

confidence: 99%

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Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control

Madeira

Coda

2016

Lat. Am. j. solids struct.

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This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. The structure is modeled by the geometrically exact Finite Element Method based on positions. The introduction of the device's mass is made by means of Lagrange multipliers that imposes its movement along the straight line of a finite element. A pure numerical Kelvin/Voigt like rheological model capable of nonlinear large deformations is originally proposed here. It is numerically solved along time to accomplish the damping parameters of the device. Examples are solved to validate the formulation and to show the practical possibilities of the proposed technique

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Section: Latin American Journal Of Solids and Structures 13 (2016) 96mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control

Madeira

Coda

2016

Lat. Am. j. solids struct.

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“…Here the resulting matrix differential equation could be solved by a time marching scheme without the need to store system matrices at every time step. They also presented a new Finite Element formulation for viscoelasticity [39,40] and a coupling procedure for BEM-FEM [41].…”

Section: Introductionmentioning

confidence: 99%

Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings

Mesquita

Antes

Thomazo

et al. 2012

Lat. Am. j. solids struct.

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This article analyzes the transient wave propagation phenomena that take place at 2D viscoelastic half-spaces subjected to spatially distributed surface loadings and to distinct temporal excitations. It starts with a fairly detailed review of the existing strategies to describe transient analysis for elastic and viscoelastic continua by means of the Boundary Element Method (BEM). The review explores the possibilities and limitations of the existing transient BEM procedures to describe dynamic analysis of unbounded viscoelastic domains. It proceeds to explain the strategy used by the authors of this article to synthesize numerically fundamental solutions or auxiliary states that allow an accurate analysis of transient wave propagation phenomena at the surface of viscoelastic half-spaces. In particular, segments with spatially constant and linear stress distributions over a halfspace surface are considered. The solution for the superposition of constant and discontinuous adjacent elements as well as linear and continuous stress distributions is addressed. The influence of the temporal excitation type and duration on the transient response is investigated. The present study is based on the numerical solution of stress boundary value problems of (visco)elastodynamics. In a first stage, the solution is obtained in the frequency domain. A numerical integration strategy allows the stationary solutions to be determined for very high frequencies. The transient solutions are obtained, in a second stage, by applying the Fast Fourier Transform (FFT) algorithm to the previously synthesized frequency domain solutions. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. By analyzing the transient solution of the stress boundary value problems, it is possible to show that from every surface stress discontinuity three wave fronts are generated. (continued on next The displacement velocity of these wave fronts can be associated to compression, shear and Rayleigh waves. It is shown that the half-space transient displacement solutions present abrupt jumps or oscillations which can be correlated to the arrival of these wave fronts at the observation point. Such a detailed analysis connecting half-space transient responses to the wave propagation fronts in viscoelastic half-spaces have not been reported in the reviewed literature.

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“…Yan Wei et al [13] investigated the three dimensional solution of a laminated orthotropic rectangular plate with viscoelastic interfaces, described by the Kelvin-Voigt model. Mesquita and Coda [14] considered an alternative Kelvin Viscoelastic formulation for the finite element method. Lekszycki et al [15] characterized the constitutive parameters of the Voigt model and described viscoelastic materials applied in sandwich beams.…”

Section: Introductionmentioning

confidence: 99%

Transient response of a laminated sandwich plate with viscoelastic core subjected to air blast: theory and experiment

Balkan¹,

Acar²,

Türkmen³

et al. 2010

WIT Transactions on the Built Environment

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This paper is focused on the theoretical and experimental study of the dynamic behavior of sandwich composite plates with a viscoelastic core subjected to blast load. The sandwich plate has carbon/epoxy face sheets and an aramid honeycomb core. The clamped boundary conditions are considered for all edges of the plate. The sandwich plate is modeled using first order shear deformation theory considering the geometrical nonlinearities. The equations of motion are derived by the use of the virtual work principle for the sandwich plate. The viscoelastic behavior is modeled by using the Kelvin-Voigt theory. The equations of motion are reduced into the time domain using Galerkin's method. The nonlinear-coupled equation system is solved by Mathematica Software. In the experimental study, the pressurized air in a shock tube is impinged on the sandwich composite plate by rupturing a membrane in front of the shock tube. The strain-time histories obtained from the theoretical analysis are compared with the experimental ones and a good agreement is found.

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Alternative Kelvin viscoelastic procedure for finite elements

Cited by 35 publications

References 12 publications

Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control

Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control

Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings

Transient response of a laminated sandwich plate with viscoelastic core subjected to air blast: theory and experiment

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