Multi-Layered Non-Linear Viscoelastic Beams Subjected to Torsion at a Constant Speed: A Delamination Analysis
A non-linear mechanical model with a linear spring, a linear dashpot and a non-linear dashpot is used for studying the non-linear viscoelastic behaviour of a multi-layered inhomogeneous beam with a delamination crack. The beam with a circular cross-section is under a torsion moment that increases at a constant speed. The non-linear stress-strain-time constitutive law of the model is obtained by adding the non-linear shear strain to the strain in the linear spring and linear dashpot. Solutions of the time-dependent strain energy release rate are derived, which take into account the non-linear viscoelastic behaviour of the beam and the torsion moment rate.
Bohidar S.K., Sharma R., Mishra P.R., Functionally graded materials: A critical review, International Journal of Research, 1(7): 289–301, 2014.
Mahamood R.M., Akinlabi E.T., Functionally Graded Materials, Springer International Publishing, 2017, doi: 10.1007/978-3-319-53756-6.
Çallioğlu H., Sayer M., Demir E., Stress analysis of functionally graded discs under mechanical and thermal loads, Indian Journal of Engineering and Materials Sciences, 18(2): 111–118, 2011.
Çallioğlu H., Sayer M., Demir E., Elastic-plastic stress analysis of rotating functionally graded discs, Thin-Walled Structures, 94: 38–44, 2015, doi: 10.1016/j.tws.2015.03.016.
Demir E., Çallioǧlu H., Sayer M., Free vibration of symmetric FG sandwich Timoshenko beam with simply supported edges, Indian Journal of Engineering and Materials Sciences, 20(6): 515–521, 2013, http://nopr.niscair.res.in/handle/123456789/25586.
Akbulut M., Sonmez F.O., Optimum design of composite laminates for minimum thickness, Computers & Structures, 86(21–22): 1974–1982, 2008, doi: 10.1016/j.compstruc.2008.05.003.
Akbulut M., Sarac A., Ertas A.H., An investigation of non-linear optimization methods on composite structures under vibration and buckling loads, Advances in Computational Design, 5(3): 209–231, 2020, doi: 10.12989/acd.2020.5.3.209.
Nguyen S.-N., Lee J., Han J.-W., Cho M., A coupled hygrothermo-mechanical viscoelastic analysis of multilayered composite plates for long-term creep behaviors, Composite Structures, 242: 112030, 2020, doi: 10.1016/j.compstruct.2020.112030.
Nguyen S.-N., Lee J., Cho M., Application of the Laplace transformation for the analysis of viscoelastic composite laminates based on equivalent single-layer theories, International Journal of Aeronautical and Space Sciences, 13(4): 458–467, 2012, doi: 10.5139/ijass.2012.13.4.458.
Rizov V.I., Analysis of two lengthwise cracks in a viscoelastic inhomogeneous beam structure, Engineering Transactions, 68(4): 397–415, 2020, doi: 10.24423/EngTrans.1214.20201125.
Rizov V.I., Longitudinal vertical crack analysis in beam with relaxation stresses, World Journal of Engineering, 18(3): 452–457, 2020, doi: 10.1108/WJE-05-2020-0181.
Zubchaninov V.G., Fundamentals of Theory of Elasticity and Plasticity, Moscow: Vishaya Shkola Press, 1990.
Lukash P.A., Fundamentals of Non-linear Structural Mechanics [in Russian], Moscow: Stroiizdat, 1978.
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