Large deformation analysis of two-dimensional visco-hyperelastic beams and frames

Dadgar‐Rad, Farzam; Firouzi, Nasser

doi:10.1007/s00419-021-02008-x

Cited by 7 publications

(2 citation statements)

References 55 publications

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“…They carried out static and dynamic analyses of incompressible hyperelastic silicone plates. Dadgar-Rad and Firouzi [ 16 ] presented a nonlinear finite element formulation for the viscoelastic deformation of hyperelastic structures under several loadings and boundary conditions. Ansari et al [ 17 ] developed a numerical approach to survey the deformations of hyperelastic Mindlin rectangular plates in compressible and nearly incompressible regimes based on the Neo-Hookean model.…”

Section: Introductionmentioning

confidence: 99%

Viscoelasticity in Large Deformation Analysis of Hyperelastic Structures

2022

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In this paper, an annular/circular plate made of hyperelastic material and considering the viscoelastic property was investigated based on a novel nonlinear elasticity theory. A new approach for hyperelastic materials in conjunction with the Kelvin–Voigt scheme is employed to obtain the structure’s large deformation under uniform transverse loading. The constitutive equations were extracted using the energy method. The derived partial differential time-dependent equations have been solved via the semi-analytical polynomial method (SAPM). The obtained results have been validated by ABAQUS software and the available paper. In consequence, a good agreement between the results was observed. Finally, several affecting parameters on the analysis have been attended to and studied, such as the nonlinear elasticity analysis, the boundary conditions, loading, and the material’s viscosity. It can be possible to obtain the needed time for achieving the final deformation of the structure based on the applied analysis in this research.

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Section: Introductionmentioning

confidence: 99%

Viscoelasticity in Large Deformation Analysis of Hyperelastic Structures

2022

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“…Lanzoni and coworker [45] studied the nonuniform bending of a beam made of the hyperelastic beam, taking the Mooney-Rivlin into account. The large deformation response of hyperelastic beams was explored by Dadgar-Rad and Firouzi [46]. They incorporated Fung's quasilinear viscoelasticity theory and Mooney-Rivlin model.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

et al. 2021

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In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler–Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton’s principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton’s technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.

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Investigation on dynamic stability of Timoshenko beam using axial parametric excitation

Firouzi,

Kazemi

2023

Appl. Phys. A

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Large deformation analysis of two-dimensional visco-hyperelastic beams and frames

Cited by 7 publications

References 55 publications

Viscoelasticity in Large Deformation Analysis of Hyperelastic Structures

Viscoelasticity in Large Deformation Analysis of Hyperelastic Structures

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

Investigation on dynamic stability of Timoshenko beam using axial parametric excitation

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