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Articles

Thermostatics of micropolar elastic thin beams with a circular axis with independent fields of displacements and rotations and the finite element method

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Pages 993-1008 | Received 18 Mar 2022, Accepted 16 Sep 2022, Published online: 17 Oct 2022

References

  • W. Nowacki and W. Olszak, Micropolar Thermoelasticity. Vienna: Springer-Verlag, CISM Courses and Lectures, 151, 1974.
  • W. Nowacki, Theory of Asymmetric Elasticity. Oxford, New York, Toronto, Sydney, Paris, Frankfurt: Pergamon Press, 1986, p. 383.
  • E. Bosch and D. Iesan, “A generalized theory of linear micropolar thermoelasticity,” Meccanica, vol. 7, pp. 154–157, 1973.
  • R. B. Hetnarski and I. Ignaczak, “Generalized thermoelasticity,” J. Thermal Stresses, vol. 22, pp. 451–476, 1999.
  • D. Iesan, “Some theorems in the theory of elastic materials with voids,” J. Elasticity: The Physical and Mathematical Science of Solids, vol. 15, no. 2, pp. 215–224, 1985.
  • M. Marin, I. A. Mohamed Othman and A. I. Abbas, “An extension of the domain of influence theorem for generalized thermoelasticity of anisotropic material with voids,” J. Comput. Theor. Nanosci., vol. 12, no. 8, pp. 1594–1598, 2015. DOI: 10.1166/jctn.2015.3934.
  • S. H. Sargsyan, “Mathematical model of micropolar thermo-elasticity of thin shells,” J. Thermal Stresses, vol. 36, no. 11, pp. 1200–1216, 2013. DOI: 10.1080/01495739.2013.819265.
  • S. H. Sargsyan, “Thermoelastisity of thin shells on the basis of asymmetrical theory of elasticity,” J. Thermal Stresses, vol. 32, no. 8, pp. 791–818, 2009. DOI: 10.1080/01495730903018515.
  • N. S. Aslanyan and S. H. Sargsyan, “Thermoelasticity of micropolar thin beams,” J. Thermal Stresses, vol. 41, no. 6, pp. 687–705, 2018. DOI: 10.1080/01495739.2018.1426066.
  • S. H. Sargsyan and M. V. Khachatryan, “Construction of the bending model of micropolar elastic thin beams with a circular axis and its implementation using finite element method,” Comp. Contin. Mech, vol. 13, no. 3, pp. 256–268, 2020. (in Russian). DOI: 10.7242/1999-6691/2020.13.3.20.
  • S. P. Timoshenko, Strength of Materials, 3rd ed Part I: Elementary Theory and Problems, vol. I, Toronto, New York, London: D. Van Nostrand Company, Inc., Paperback – December 1, 2004.
  • S. P. Timoshenko and J. Gere, Mechanics of Materials. St. Petersburg-Moscow: Publishing House “Lan”, 2002, (in Russian).
  • R. S. Lakes and W. J. Drugan, “Bending of a Cosserat elastic bar of square cross section - theory and experiment,” J. Appl. Mech., vol. 82, no. 9, pp. 091002, 2015. DOI: 10.1115/1.4030626.
  • S. Nakamura, R. L. Benedict and R. S. Lakes, “Finite element method for orthotropic micropolar elasticity,” Intern. J. Eng. Sci., vol. 22, no. 3, pp. 319–330, 1984. DOI: 10.1016/0020-7225(84)90013-2.
  • V. V. Korepanov, M. A. Kulesh, V. P. Matveenko and IN. Shardakov, “Analytical and numerical solutions in the context of Cosserat continuum as the basis for experiments on detection of couple-stress effects in materials,” Comp. Contin. Mech., vol. 2, no. 4, pp. 76–91, 2009. (in Russian). DOI: 10.7242/1999-6691/2009.2.4.33.
  • S. H. Sargsyan and K. A. Zhamakochyan, “Finite Element Method for Solving Boundary Value Problems of Bending of Micropolar Elastic Thin Bars,” Proceedings of the XLII Summer School-Conference. Advanced Problems in Mechanics. APM 2014. St. Petersburg, June 30-July 5, pp. 427–434, 2014.

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