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Layer-wise dynamic analysis of a beam with global and local viscoelastic contributions using an FE/Laplace transform approach

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Abstract

In this research, the mechanism of energy dissipation in viscoelastic materials is presented by extracting time-dependent displacement and stress–strain distribution analysis in a beam, which contains a viscoelastic part. The structure is discretized into finite beam elements, the kinematic theory of which is based on Carrera unified formulation using Lagrange expansion on the cross section. For the viscoelastic contribution, the integral form of viscoelastic constitutive law in which the stress is related to the integral form of the viscous module and the strain rate is executed. The governing equations of the finite element model of the structure are derived using Hamilton’s principle, and to avoid the computational cost of convolution integral, we have exploited the Laplace transform to the three-dimensional displacement, stress, and strain fields. Finally, the results are transformed to the time domain using numerical inversion methods. A numerical model that has been validated with the results in the literature is considered. To highlight the depreciating consequence of the viscoelastic material, simulation of the multi-layered beam that is isotropic and elastic in all parts except for a certain part that contains the viscoelastic contribution is undertaken, and the temporal response and the stress–strain fields are extracted and discussed. As a result, extreme variations in stress distribution in the location of viscoelastic contributions, hysteresis stress–strain, and changes in beam temporal history to viscoelastic contribution displacement have been observed.

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Authors and Affiliations

  1. Faculty of Aerospace Engineering, Amirkabir University of Technology, Tehran, 159163-4311, Iran

    Sh. Kiasat & A. S. Nobari

  2. Mul2 Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129, Torino, Italy

    Sh. Kiasat, M. Filippi & E. Carrera

  3. Aeronautics Engineering Department, Imperial College, New York, USA

    A. S. Nobari

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  1. Sh. Kiasat
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  2. M. Filippi
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  3. A. S. Nobari
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  4. E. Carrera
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Kiasat, S., Filippi, M., Nobari, A.S. et al. Layer-wise dynamic analysis of a beam with global and local viscoelastic contributions using an FE/Laplace transform approach. Acta Mech 233, 4747–4761 (2022). https://doi.org/10.1007/s00707-022-03349-6

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