Advances in Computational Design

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Viscoelastic inhomogeneous beam under time-dependent strains: A longitudinal crack analysis

  • Rizov, Victor I. (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • Received : 2020.08.04
  • Accepted : 2020.11.10
  • Published : 2021.04.25
⟨ Previous Next ⟩

Abstract

The present paper is concerned with analysis of two longitudinal cracks in a viscoelastic inhomogeneous cantilever beam. The loading of the beam is applied by two stages. At the first stage, the strains increase with time at a constant speed up to a given magnitude. At the second stage, the strains remain constant with time. The viscoelastic behavior of the beam is described by using a viscoelastic model with a linear spring in series with a linear dashpot and a second linear dashpot connected parallel to the spring and the first dashpot. Stress-strain-time relationships of the viscoelastic model are derived for both stages (at increasing strain and at constant strain with time). Time-dependent strain energy release rates are obtained for both longitudinal cracks by analyzing the balance of the energy. Solutions to the time-dependent strain energy release rate are derived also by considering the time-dependent strain energy stored in the beam structure. The solutions are used to analyze the change of the strain energy release rate with time at both stages of loading.

Keywords

References

  1. Akbulut, M. and Sonmez, F.O. (2008), "Optimum design of composite laminates for minimum thickness", Comput. Struct., 86(21-22), 1974-1982. https://doi.org/10.1016/j.compstruc.2008.05.003.
  2. Akbulut, M., Sarac, A. and Ertas, A.H. (2020), "An investigation of non-linear optimization methods on composite structures under vibration and buckling loads", Advan. Comput. Des., 5(3), 209-231 doi.org/10.12989/acd.2020.5.3.209 209
  3. Altunsaray, E. (2017), "Static deflections of symmetrically laminated quasi-isotropic super-elliptical thin plates", Ocean Eng., 141(1), 337-350. https://doi.org/10.1016/j.oceaneng.2017.06.032.
  4. Altunsaray, E. and Bayer, I. (2014), "Buckling of symmetrically laminated quasi-isotropic thin rectangular plates", Steel Compos. Struct., 17(3), 305-320. https://doi.org/10.12989/scs.2014.17.3.305.
  5. Altunsaray, E., Unsalan, D., Neser, G., Turgut, Gursel, K.T. and Taner, M. (2019), "Parametric study for static deflections of symmetrically laminated rectangular thin plates", Sci. Bull. Mircea cel Batran NavalAcademy, Constanta, 22(1), 1-12. 10.21279/1454-864X-19-I1-041.
  6. Butcher, R.J., Rousseau, C.E. and Tippur, H.V. (1999), "A functionally graded particulate composite: Measurements and failure analysis", Acta. Mater., 47(2), 259-268. https://doi.org/10.1016/S1359-6454(98)00305-X.
  7. Dolgov, N.A. (2002), "Effect of the elastic modulus of a coating on the serviceability of the substratecoating system", Strength Mater., 37(2), 422-431. https://doi.org/10.1007/s11223-005-0053-7.
  8. Dolgov, N.A. (2005), "Determination of stresses in a two-layer coating", Strength Mater., 37(2), 422-431. https://doi.org/10.1007/s11223-005-0053-7.
  9. Dolgov, N.A. (2016), "Analytical methods to determine the stress state in the substrate-coating system under mechanical loads", Strength Mater., 48(1), 658-667. https://doi.org/10.1007/s11223-016-9809-5.
  10. Gasik, M.M. (2010), "Functionally graded materials: bulk processing techniques", Int. J. Mater. Product Technol., 39(1-2), 20-29. https://doi.org/10.1504/IJMPT.2010.034257.
  11. Hedia, H.S., Aldousari, S.M., Abdellatif, A.K. and Fouda, N.A. (2014), "New design of cemented stem using functionally graded materials (FGM)", Biomed. Mater. Eng., 24(3), 1575-1588. 10.3233/BME-140962.
  12. Hirai, T. and Chen, L. (1999), "Recent and prospective development of functionally graded materials in Japan", Mater. Sci. Forum, 308-311(4), 509-514. https://doi.org/10.4028/www.scientific.net/MSF.308-311.509.
  13. Mahamood, R.M. and Akinlabi, E.T. (2017), Functionally Graded Materials, Springer.
  14. Markworth, A.J., Ramesh, K.S. and Parks, Jr. W.P. (1995), "Review: modeling studies applied to functionally graded materials", J. Mater. Sci., 30(3), 2183-2193. https://doi.org/10.1007/BF01184560.
  15. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (1999), Functionally Graded Materials: Design, Processing and Applications, Kluwer Academic Publishers, Dordrecht/London/Boston.
  16. Nemat-Allal, M.M., Ata, M.H., Bayoumi, M.R. and Khair-Eldeen, W. (2011), "Powder metallurgical fabrication and microstructural investigations of Aluminum/Steel functionally graded material", Mater. Sci. Appl., 2(5), 1708-1718. 10.4236/msa.2011.212228.
  17. Rezaiee-Pajand, M. and Hozhabrossadati, S.M. (2016), "Analytical and numerical method for free vibration of double-axially functionally graded beams", Compos. Struct., 152, 488-498. doi.org/10.1016/j.compstruct.2016.05.003.
  18. Rezaiee-Pajand, M., Masoodi, A.R. and Mokhtari, M. (2018), "Static analysis of functionally graded nonprismatic sandwich beams", Advan. Comput. Des., 3(2), 165-190. http://dx.doi.org/10.12989/acd.2018.3.2.165.
  19. Rezaiee-Pajand, M., Sani, A.A. and Hozhabrossadati, S.M. (2017), "Application of differential transform method to free vibration of gabled frames with rotational springs", Int. J. Struct. Stab. Dynam., 17(1), 1750012. doi.org/10.1142/S0219455417500122.
  20. Rizov, V.I. (2017), "Analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity", Frattura ed Integrita Strutturale, 41, 498-510. https://doi.org/10.3221/IGF-ESIS.41.61
  21. Rizov, V.I. (2018), "Non-linear fracture in bi-directional graded shafts in torsion", Multidiscipline Modeling Mater. Struct., 15(1), 156-169. https://doi.org/10.1108/MMMS-12-2017-0163.
  22. Rizov, V.I. (2020), "Longitudinal fracture analysis of inhomogeneous beams with continuously changing radius of cross-section along the beam length", Strength, Fracture Complexity: Int. J., 13, 31-43. 10.3233/SFC-200250.
  23. Tokovyy, Y. (2019), "Solutions of axisymmetric problems of elasticity and thermoelasticity for an inhomogeneous space and a half space", J. Mathenat. Sci., 240(1), 86-97. https://doi.org/10.1007/s10958-019-04337-3.
  24. Tokovyy, Y. and Ma, C.C. (2017), "Three-dimensional elastic analysis of transversely-isotropic composites", J. Mech., 33(6), 821-830. https://doi.org/10.1017/jmech.2017.91.
  25. Tokovyy, Y. and Ma, C.C. (2019), "Elastic analysis of inhomogeneous solids: History and development in brief", J. Mech., 18(1), 1-14. https://doi.org/10.1017/jmech.2018.57.
  26. Uslu Uysal, M. (2016), "Buckling behaviours of functionally graded polymeric thin-walled hemispherical shells", Steel Compos. Struct., 21(1), 849-862. https://doi.org/10.12989/scs.2016.21.4.849.
  27. Uslu Uysal, M. and Guven, U. (2015), "Buckling of functional graded polymeric sandwich panel under different load cases", Compos. Struct., 121, 182-196. https://doi.org/10.1016/j.compstruct.2014.11.012.
  28. Uslu Uysal, M. and Guven, U. (2016), "A bonded plate having orthotropic inclusion in adhesive layer under in-plane shear loading", J. Adhesion. 92, 214-235. https://doi.org/10.1080/00218464.2015.1019064.
  29. Uslu Uysal, M. and Kremzer, M. (2015), "Buckling behaviour of short cylindrical functionally gradient polymeric materials", Acta Physica Polonica, A127, 1355-1357. 10.12693/APhysPolA.127.1355.