Deformation of modified couple stress thermoelastic diffusion in a thick circular plate due to heat sources

• Autorzy: Kumar R. , Devi S.

Identyfikatory

DOI

10.12921/cmst.2018.0000034

• Języki publikacji: EN

Abstrakty

EN

The aim of this study is to present a mathematical model for predicting the results for displacements, stress components, temperature change and chemical potential with considering independently a particular type of heat source. The general solution for the two-dimensional problem of a thick circular plate with heat sources in modified couple stress thermoelastic diffusion has been obtained in the context of one and two relaxation times. Laplace and Hankel transforms technique is applied to obtain the solutions of the governing equations. Resulting quantities are obtained in the transformed domain. The numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of time on the resulting quantities are shown graphically.

Słowa kluczowe

EN

thick circular plate; heat sources; modified couple stress theory; thermoelasticity; Laplace and Hankel transforms

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2019
• Tom: Vol. 25, No. 4
• Strony: 167--176
• Opis fizyczny: Bibliogr. 24 poz., rys.

Twórcy

autor

Kumar R.

• Department of Mathematics Kurukshetra University Kurukshetra, India

autor

Devi S.

• Department of Mathematics & Statistics Himachal Pradesh University Shimla, India

Bibliografia

• [1] R.S. Lakes, Dynamical study of couple stress effects in human compact bone, Journal of Biomechanical Engineering 104, 6–11 (1982).
• [2] D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, Journal of Mechanics and Physics of Solids 51, 1477–1508 (2003).
• [3] F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39, 2731–2743 (2002).
• [4] S.K. Park, X.L. Gao, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Micro engineering 16, 23–55 (2006).
• [5] M. Simsek, J.N. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, International Journal of Engineering Sciences 64, 37–53 (2013).
• [6] M. Shaat, F.F. Mahmoud, X.L. Gao, A.F. Faheem, Sizedependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects, International Journal of Mechanical Sciences 79, 31–37 (2014).
• [7] A. Arani Ghorbanpour, M. Abdollahian, H.M. Jalaei, Vibration of bioliquid-filled microtubules embedded in cytoplasm including surface effects using modified couple stress theory, Journal of Theoretical Biology 367, 29–38 (2015).
• [8] H. Darijani, A.H. Shahdadi, A new shear deformation model with modified couple stress theory for microplates, Acta Mechanica 226, 2773–2788 (2015).
• [9] W.Y. Gang, L.W. Hui, N. Liu, Nonlinear bending and postbuckling of extensible microscale beams based on modified couple stress theory, Applied Mathematical Modelling 39, 117–127 (2015).
• [10] I.S. Podstrigach, Differential equations of the problem of thermodiffusion in isotropic deformed solid bodies, Doklady. Akademii. Nauk Ukrainskoi. SSR 169–172 (1961).
• [11] W. Nowacki, Dynamical problems of thermo diffusion in solids I, Bulletin of Polish Academy of Science and Technology 22, 55–64 (1974).
• [12] W. Nowacki, Dynamical problems of thermo diffusion in solids II, Bulletin of Polish Academy of Science and Technology 22, 129–135 (1974).
• [13] W. Nowacki, Dynamical problems of thermo diffusion in solids III, Bulletin of Polish Academy of Science and Technology 22, 257–266 (1974).
• [14] W. Nowacki, Dynamical problems of thermo diffusion in solids, Engineering Fracture Mechanics 8, 261–266 (1976).
• [15] H.H. Sherief, H. Saleh, F. Hamza, The theory of generalized thermoelastic diffusion, International Journal of EngineeringSciences 42, 591–608 (2004).
• [16] H.H. Sherief, H. Saleh, A half-space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 42, 4484–4493 (2005).
• [17] R. Kumar, T. Kansal, Propagation of Lamb waves in transversely isotropic thermoelastic diffusion plate, International Journal of Solids and Structures 45, 5890–5913 (2008).
• [18] N.M. El-Maghraby, A.A. Abdel-Halim, A generalized thermoelasticity problem for a half space with heat sources under axisymmetric distributions, Australian journal of basic and applied sciences 4, 3803–3814 (2010).
• [19] H.W Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity, Journal of Mechanics and Physics of Solids 15, 299–309 (1967).
• [20] J.J. Tripathi, G.D. Kedar, K.C. Deshmukh, Dynamic problem of generalized thermoelasicity for a semi-infinite cylinder with heat sources, Journal of Thermoelasticity 2, 1–8 (2014).
• [21] J.J. Tripathi, G.D. Kedar, K.C. Deshmukh, Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply, Acta Mechanica 226, 2121–2134 (2015).
• [22] G. Honig, U. Hirdes, A method for the numerical inversion of the Laplace transforms, Journal of Computational and Applied Mathematics 10, 113–132 (1984).
• [23] W.H. Press, S.A. Teukolsky, W.T. Vellerling, B.P. Flannery, Numerical recipes, Cambridge University Press, 1986.
• [24] R.S. Daliwal, A. Singh, Dynamical coupled thermoelasticity, Hindustan Publishers, Delhi, 1980.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).