Numerical analysis of a thermal problem arising in microstretch elastic plates

References

• A. C. Eringen, “Micropolar elastic solids with stretch,” in Prof. Dr. Mustafa Inan Anici. Istanbul: Ari Kitabevi Matbaasi, 1971, pp. 1–18.
   Google Scholar
• A. C. Eringen, “Theory of thermo-microstretch elastic solids,” Znt. J. Eng. Sci., vol. 28, no. 12, pp. 1291–1301, 1990. DOI: 10.1016/0020-7225(90)90076-U.
   Google Scholar
• A. C. Eringen, “Microcontinuum field theories I,” in Foundations and Solids, New York: Springer-Verlag, 1999.
   Google Scholar
• M. Ciarletta, “On the bending on microstretch elastic plates,” Int. J. Eng. Sci., vol. 37, no. 10, pp. 1309–1318, 1999. DOI: 10.1016/S0020-7225(98)00123-2.
   Web of Science ®Google Scholar
• M. Bîrsan, “A bending theory of porous thermoelastic plates,” J. Therm. Stress., vol. 26, no. 1, pp. 67–90, 2003. DOI: 10.1080/713855760.
   Web of Science ®Google Scholar
• A. C. Eringen, “Electromagnetic theory of microstretch elasticity and bone modeling,” Int. J. Eng. Sci., vol. 42, no. 3–4, pp. 231–242, 2004. DOI: 10.1016/S0020-7225(03)00288-X.
   Web of Science ®Google Scholar
• M. Ciarletta and A. Scalia, “Some results in linear theory of thermomicrostretch elastic solids,” Meccanica, vol. 39, no. 3, pp. 191–206, 2004. DOI: 10.1023/B:MECC.0000022843.48821.af.
   Web of Science ®Google Scholar
• M. Svanadze and S. Cicco, “Fundamental solution in the theory of thermomicrostretch elastic solids,” Int. J. Eng. Sci., vol. 43, no. 5–6, pp. 417–431, 2005. DOI: 10.1016/j.ijengsci.2004.09.011.
   Web of Science ®Google Scholar
• P. Neff, J. Jeong, I. Münch, and H. Ramezani, “Mean field modeling of isotropic random Cauchy elasticity versus microstretch elasticity,” Z. Angew. Math. Phys., vol. 60, no. 3, pp. 479–497, 2009. DOI: 10.1007/s00033-008-8090-2.
   Web of Science ®Google Scholar
• M. Marin, “A partition of energy in thermoelasticity of microstretch bodies,” Nonlinear Anal. Real World Appl., vol. 11, no. 4, pp. 2436–2447, 2010. DOI: 10.1016/j.nonrwa.2009.07.014.
   Web of Science ®Google Scholar
• F. Passarella, V. Tibullo, and V. Zampoli, “On microstretch thermoviscoelastic composite materials,” Eur. J. Mech. A Solids, vol. 37, pp. 294–303, 2013. DOI: 10.1016/j.euromechsol.2012.07.002.
   Web of Science ®Google Scholar
• M. Marin, R. P. Agarwal, and S. R. Mahmoud, “Modeling a microstretch thermoelastic body with two temperatures,” Abstr. Appl. Anal., vol. 2013, pp. 1–7, 2013. Art. ID 583464, DOI: 10.1155/2013/583464.
   Google Scholar
• C. Galeş and N. Baroiu, “On the bending of plates in the electromagnetic theory of microstretch elasticity,” Z. Angew. Math. Mech., vol. 94, no. 1–2, pp. 55–71, 2014. DOI: 10.1002/zamm.201200219.
   Web of Science ®Google Scholar
• M. Serpilli, “Asymptotic piezoelectric plate models in microstretch elasticity,” Z. Angew. Math. Mech., vol. 98, no. 3, pp. 454–473, 2018. DOI: 10.1002/zamm.201700073.
   Web of Science ®Google Scholar
• D. Ieşan, “Deformation of microstretch elastic beams loaded on the lateral surface,” Math. Mech. Solids, vol. 24, no. 7, pp. 2274–2294, 2019. DOI: 10.1177/1081286518824141.
   Web of Science ®Google Scholar
• D. Ieşan and R. Quintanilla, “Themal stresses in microstretch elastic plates,” Int. J. Eng. Sci., vol. 43, no. 11–12, pp. 885–907, 2005. DOI: 10.1016/j.ijengsci.2005.03.005.
   Web of Science ®Google Scholar
• P. G. Ciarlet, “The finite element method for elliptic problems,” in Handbook of Numerical Analysis, vol. II, P. G. Ciarlet, Ed. Amsterdam: North Holland, 1991, pp. 17–352.
   Google Scholar
• M. Campo, J. R. Fernández, K. L. Kuttler, M. Shillor, and J. M. Viaño, “Numerical analysis and simulations of a dynamic frictionless contact problem with damage,” Comput. Methods Appl. Mech. Eng., vol. 196, no. 1–3, pp. 476–488, 2006. DOI: 10.1016/j.cma.2006.05.006.
   Web of Science ®Google Scholar
• M. Barboteu, J. R. Fernández, and T.-V. Hoarau-Mantel, “A class of evolutionary variational inequalities with applications in viscoelasticity,” Math. Models Methods Appl. Sci., vol. 15, no. 10, pp. 1595–1617, 2005. DOI: 10.1142/S0218202505000820.
   Web of Science ®Google Scholar