An Application of the Rigid Finite Element Method to Modelling of Flexible Structures

Wittbrodt, Edmund; Wojciech, Stanisław

doi:10.1007/978-3-7091-2698-1_8

Cited by 2 publications

(2 citation statements)

References 5 publications

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“…Several beam modeling methods exist, such as, for a small displacement: the Euler-Bernoulli beam theory [60], the Timoshenko beam theory, and the Rayleigh-Ritz beam theory [61], and for a large displacement such as the Galerkin finite element method to solve second order nonlinear differential equations [62], as well as the RFEM [63]. RFEM allows us to take into account the nonlinear dynamic mechanical behavior of the actuator easily, and to account for inertia [39,64,65]. Effects of mass have been left out of previous models since CP actuators have historically been slow.…”

Section: Electro-mechanical Couplingmentioning

confidence: 99%

“…where i=1, K, n, and T, V, and D are the kinetic energy, potential energy, and dissipation energy, respectively, of the system of (n+1) elements. The terms in the equation are now described mathematically, following the treatment presented by Wittbrodt et al [65] and Moghadam et al [34,36]: Considering a differential element dm i on RFE i , the kinetic energy of this element is:…”

Section: Electro-mechanical Couplingmentioning

confidence: 99%

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Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

Nguyen

Dobashi

Soyer

et al. 2018

Smart Mater. Struct.

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Trilayer conducting polymer (CP) actuators are potential alternatives to piezoelectric and electrostatic actuators due to their large strain, and recently demonstrated operation at hundreds of Hertz. However, these actuators exhibit nonlinear electrical and mechanical properties as a function of their oxidation state, when operated over their full strain range, making it more challenging to accurately predict their mechanical behavior. In this paper, an analytical multiphysics model of the CP actuators is proposed to predict their nonlinear dynamic mechanical behavior. To demonstrate the accuracy of the model, a trilayer actuator composed of a solid polymer electrolyte sandwiched between two poly(3,4-ethylenedioxythiophene) (PEDOT) electrodes was fabricated and characterized. This system consists of an electrical subsystem represented by an RC equivalent circuit, an electro-mechanical coupling matrix, and a mechanical subsystem described by using a rigid finite element method. The electrical conductivity and the volumetric capacitance, an empirical strain-to-charge ratio, and Young's modulus of the actuator as a function of the PEDOT electrode charge state were also implemented into the model, using measured values. The proposed model was represented using a bond graph formalism. The concordance between the simulations and the measurements confirmed the accuracy of the model in predicting the nonlinear dynamic electrical and mechanical response of the actuators. In addition, the information extracted from the model also provided an insight into the critical parameters of the actuators and how they affect the actuator efficiency, as well as the energy distribution including dissipated, stored, and transferred energy. These are the key parameters for designing, optimizing, and controlling the actuation behavior of a trilayer actuator.

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Section: Electro-mechanical Couplingmentioning

confidence: 99%

Section: Electro-mechanical Couplingmentioning

confidence: 99%

Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

Nguyen

Dobashi

Soyer

et al. 2018

Smart Mater. Struct.

View full text Add to dashboard Cite

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A Novel Rigid Finite Element Formulation for Dynamic Analysis of Flexible Plates

Kermanian

Taghvaeipour

2022

Int. J. Str. Stab. Dyn.

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This paper introduces a new rigid finite element method (RFEM) formulation for dynamic analysis of plates. In RFEM, a flexible body is divided into several rigid elements which are interconnected by spring and damping elements. Mainly, RFEM has been used to model systems with beam-like slender components, such as ropes and cables, and few RFEM formulations were developed to model plates and shells. In this study however, by means of the Timoshenko beam theory and cuboid rigid elements, a novel RFEM formulation is developed to model flexible flat plates with generic geometries of the surface, considering large deformation. For this purpose, an RFEM formulation is presented for straight beams with rectangular cross-section by means of the Timoshenko beam theory. Next, this formulation is expanded to model flexible rectangular plates with uniform thickness and then, it is elaborated on how to model non-rectangular plates with uniform thickness using only cuboid elements and consequently, the development of the proposed RFEM formulation is completed. After investigating various case studies, the competence of the proposed formulation is evaluated thoroughly. The results of RFEM came on a proper agreement with the FEM results in a way that the maximum difference between these results in dynamic analysis was about 3%.

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An Application of the Rigid Finite Element Method to Modelling of Flexible Structures

Cited by 2 publications

References 5 publications

Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

A Novel Rigid Finite Element Formulation for Dynamic Analysis of Flexible Plates

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