Browse > Article
http://dx.doi.org/10.12989/csm.2020.9.5.397

Thermomechanical interactions in a non local thermoelastic model with two temperature and memory dependent derivatives  

Lata, Parveen (Department of Basic and applied Sciences, Punjabi University Patiala)
Singh, Sukhveer (Punjabi University APS Neighbourhood Campus)
Publication Information
Coupled systems mechanics / v.9, no.5, 2020 , pp. 397-410 More about this Journal
Abstract
The present investigation is concerned with two-dimensional deformation in a homogeneous isotropic non local thermoelastic solid with two temperatures due to thermomechanical sources. The theory of memory dependent derivatives has been used for the study. The bounding surface is subjected to concentrated and distributed sources (mechanical and thermal sources). The Laplace and Fourier transforms have been used for obtaining the solution to the problem in the transformed domain. The analytical expressions for displacement components, stress components and conductive temperature are obtained in the transformed domain. For obtaining the results in the physical domain, numerical inversion technique has been applied. Numerical simulated results have been depicted graphically for explaining the effects of nonlocal parameter on the components of displacements, stresses and conductive temperature. Some special cases have also been deduced from the present study. The results obtained in the investigation should be useful for new material designers, researchers and physicists working in the field of nonlocal material sciences.
Keywords
thermoelasticity; nonlocality; nonlocal theory of thermoelasticity; Eringen model of nonlocal theories; two temperature; memory dependent derivative; concentrated and distributed sources;
Citations & Related Records
Times Cited By KSCI : 45  (Citation Analysis)
연도 인용수 순위
1 Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.   DOI
2 Jahangir, A., Tanvir, F. and Zenkour, A. (2020), "Reflection of photothermoelastic waves in a semiconductor material with different relaxations", Ind. J. Phys., 1-9. https://doi.org/10.1007/s12648-020-01690-x.
3 Karami, B., Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.   DOI
4 Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysus of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391.   DOI
5 Kumar, R., Sharma, N. and Lata, P. (2016a), "Thermomechanical interactions in the transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Model., 40, 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061.   DOI
6 Kumar, R., Sharma, N. and Lata, P. (2016b), "Effects of Hall current in a transversely isotropic magnetothermoelastic two temperature medium with rotation and with and without energy dissipation due to normal force", Struct. Eng. Mech., 57(1), 91-103. https://doi.org/10.12989/sem.2016.57.1.091.   DOI
7 Lata, P. (2018a), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66 (1), 113-124. https://doi.org/10.12989/sem.2018.66.1.113.   DOI
8 Lata, P. (2018b), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(2), 439-451. https://doi.org/10.12989/scs.2018.27.4.439.
9 Lata, P. and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., 33 (1), 123-131. https://doi.org/10.12989/scs.2019.33.1.123.   DOI
10 Sarkar, N., Ghosh, D. and Lahiri, A. (2018), "A two-dimensional magnetothermoelastic problem based on a new two-temperature generalized thermoelasticity model with memory-dependent derivative", Mech. Adv. Mater. Struct., 1-10. https:/doi.org/10.1080/15376494.2018.1432784.
11 Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177/1099636217727577.   DOI
12 Youssef, H.M. (2005), "Theory of two-temperature-generalized thermoelasticity", IMA J. Appl. Math., 71, 383-390. https://doi.org/10.1093/imamat/hxh101.   DOI
13 Sharma, N., Kumar, R. and Lata, P. (2016), "Thermomechanical interactions in transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipiation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Model., 40, 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061.   DOI
14 Soleimani, A., Dastani, K., Hadi, A. and Naei, M.H. (2019), "Effect of out of plane defects on the postbuckling behaviour of graphene sheets based on nonlocal elasticity theory", Steel Compos. Struct., 30(6), 517-534. https://doi.org/10.12989/scs.2019.30.6.517.   DOI
15 Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.   DOI
16 Youssef, H.M. and Al-Lehaibi, E.A. (2007), "State space approach of two-temperature generalized thermoelasticity of one-dimensional problem", Int. J. Solid. Struct., 44, 1550-1562. https://doi.org/10.1016/j.ijsolstr.2006.06.035.   DOI
17 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.   DOI
18 Marin, M. (1994), "The Lagrange identity method in thermoelasticity of bodies with microstructure", Int. J. Eng. Sci., 32(8), 1229-1240.   DOI
19 Belkorissat, I., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new non-local refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063.   DOI
20 Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., Mahmoud, S.R., Adda Bedia, E.A. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.   DOI
21 Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircraft Spacecraft Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001.   DOI
22 Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.   DOI
23 Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.   DOI
24 Edelen, D.G.B, Green, A.E. and Laws, N. (1971), "Nonlocal continuum mechanics", Arch. Rat. Mech. Anal., 43, 36-44. https://doi.org/10.1007/BF00251543.   DOI
25 Yu, Y.J., Hu, W. and Tian, X.G. (2014), "A novel generalized thermoelasticity model based on memory-dependent derivative", Int. J. Eng. Sci., 811, 23-134. https://doi.org/10.1016/j.ijengsci.2014.04.014.
26 Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.   DOI
27 Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", J. Appl. Math. Phys. (ZAMP), 19, 614-627. https://doi.org/10.1007/BF01594969.   DOI
28 Dhaliwal, R.S. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publisher Corporation, New Delhi, India.
29 Ebrahimi, F. and Shafiei, N. (2016), "Application of eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837.   DOI
30 Edelen, D.G.B. and Laws, N. (1971), "On the thermodynamics of systems with nonlocality", Arch. Rat. Mech. Anal., 43, 24-35. https://doi.org/10.1007/BF00251543.   DOI
31 Eringen, A.C. (2002), Nonlocal Continum Field Theories, Springer, New York, USA.
32 Ezzat, M.A., El-Karamany, A.S. and El-Bary, A. (2014), "Generalized thermo-viscoelasticity with memory-dependent derivatives", Int. J. Mech. Sci., 89, 470-475. https:/doi.org/10.1016/j.ijmecsci.2014.10.006.   DOI
33 Abbas, I.A. (2014), "Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties", Meccanica, 49, 1697-1708. https://doi.org/10.1007/s11012-014-9948-3.   DOI
34 Abbas, I.A. and Youssef, H.M. (2012), "A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method", Int. J. Thermophys., 33, 1302-1313. https://doi.org/10.1007/s10765-012-1272-3.   DOI
35 Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Nonsimple material problems addressed by the Lagrange's identity", Bound. Value Prob., 2013, 1-14. https://doi.org/10.1186/1687-2770-2013-135.   DOI
36 Marin, M. (2014), "Lagrange identity method for microstretch thermoelastic materials", J. Math. Anal. Appl., 363(1), 275-286. https://doi.org/10.1016/j.jmaa.2009.08.045.   DOI
37 Marin, M. and Florea, O. (2014), "On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies", Analele Universitatii "Ovidius" Constanta-Seria Matematica, 22(1), 169-188. https://doi.org/10.2478/auom-2014-0014.   DOI
38 Marin, M. and Nicaise, S. (2016), "Existence and stability results for thermoelastic dipolar bodies with double porosity", Continuum. Mech. Thermodyn., 28(6), 1645-1657. https://doi.org/10.1007/s00161-016-0503-4.   DOI
39 Marin, M., Craciun, E.M. and Pop, N. (2016), "Considerations on mixed initial-boundary value problems for micropolar porous bodies", Dyn. Syst. Appl., 25 (1-2), 175-196.
40 Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of saint-venant's problem for elastic dipolar bodies with voids", Carpath. J. Math., 33(2), 219-232.   DOI
41 Marin, M., Vlase, S., Ellahi, R. and Bhatti, M.M. (2019), "On the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure", Symmetry, 11(7), 1-16. https://doi.org/10.3390/sym11070863.
42 Artan, R. (1996), "Nonlocal elastic half plane loaded by a concentrated force", Int. J. Eng. Sci., 34(8), 943-950. https://doi.org/10.1016/0020-7225(95)00132-8.   DOI
43 Abbas, I.A. and Zenkour, A.M. (2014), "Two temperature generalized thermoelastic interaction in an infinite fibre- reinforced anisotropic plate containing a circular cavity with two relaxation times", J. Comput. Theor. Nanosci., 11(1), 1-7. https://doi.org/10.1166/jctn.2014.3309.   DOI
44 Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.   DOI
45 Alzahrani, F.S. and Abbas, I. A. (2016), "The effect of magnetic field on a thermoelastic fiber-reinforced material under GN-III theory", Steel Compos. Struct., 22(2), 369-386. https://doi.org/10.12989/scs.2016.22.2.369.   DOI
46 Asghar, S., Naeem, M.N., Hussain, M., Taj, M. and Tounsi, A. (2020), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis", Comput. Concrete, 25(2), 133-144. https://doi.org/10.12989/cac.2020.25.2.133.   DOI
47 Abbas, I.A. (2014), "A GN model based upon two temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity", Appl. Math. Comput., 245, 108-115. https://doi.org/10.1016/j.amc.2014.07.059.   DOI
48 Abbas, I.A. (2014), "Eigenvalue approach for an unbounded medium with a spherical cavity based upon two-temperature generalized thermoelastic theory", J. Mech. Sci. Technol., 28, 4193-4198. https://doi.org/10.1007/s12206-014-0932-6.   DOI
49 Atwa, S.Y. and Jahangir, A. (2014), "Two temperature effects on plane waves in generalized thermo-microstretch elastic solid", Int. J. Thermophys., 35(1), 175-193. https://doi.org/10.1007/s10765-013-1541-9.   DOI
50 Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A, Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.   DOI
51 Said, S.M. and Othman, M.I.A. (2016), "Wave propagation in a two-temperature fibre-reinforced magneto-thermoelastic medium with three-phase-lag-model", Struct. Eng. Mech., 57(2), 201-220. https://doi.org/10.12989/sem.2016.57.2.201.   DOI
52 Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.   DOI
53 Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.   DOI
54 Othman, M.I.A. and Abbas, I.A. (2012), "Generalized thermoelasticity of thermal-shock problem in a non-homogeneous isotropic hollow cylinder with energy dissipation", Int. J. Thermophys., 33, 913-923. https://doi.org/10.1007/s10765-012-1202-4.   DOI
55 Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2015), "The effect of rotation on plane waves in generalized thermo-microstretch elastic solid for a mode-I crack under green naghdi theory", J. Comput. Theor. Nanosci., 12(11), 4987-4997. https://doi.org/10.1166/jctn.2015.4022.   DOI
56 Press, W.H., Teukolshy, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipes in Fortran, Cambridge University Press, Cambridge, UK.
57 Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlin. Anal.: Real World Appl., 10(3), 1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001.   DOI
58 Marin, M. (2010), "Some estimates on vibrations in thermoelasticity of dipolar bodies", J. Vib. Control, 16(1), 33-47. https://doi.org/10.1177%2F1077546309103419.   DOI
59 Ezzat, M.A., El-Karamany, A.S. and El-Bary, A. (2016), "Generalized thermoelasticity with memory-dependent derivatives involving two temperatures", Mech. Adv. Mater. Struct., 23, 545-553. https:/doi.org/10.1080/15376494.2015.1007189.   DOI
60 Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of laplace transform", J. Comput. Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X.   DOI