Thermal stresses in an elastic parallelepiped

References

• G. Lamé, Leçons Sur la Théorie Mathématique de L’élasticité Des Corps Solids. Paris: Bachelier, 1852, p. 335.
   Google Scholar
• V. V. Meleshko, “Selected topics in the history of the two-dimensional biharmonic problem,” Appl. Mech. Rev., vol. 56, no. 1, pp. 33–85, 2003. DOI: 10.1115/1.1521166.
   Google Scholar
• S. O. Papkov, “Three-dimensional dynamic problem of the theory of elasticity for a parallelepiped,” J. Math. Sci., vol. 215, no. 2, pp. 121–142, 2016. DOI: 10.1007/s10958-016-2827-9.
   Google Scholar
• S. A. Lurie and V. V. Vasiliev, The Biharmonic Problem in the Theory of Elasticity. Luxembourg: Gordon and Breach, 1995,
   Google Scholar
• A. M. Al-Mukhtar, “Case studies of aircraft fuselage cracking,” AEF, vol. 33, pp. 11–18, 2019. DOI: 10.4028/www.scientific.net/AEF.33.11.
   Google Scholar
• P. A. Withey, “Fatigue failure of the De Havilland Comet 1,” Eng. Failure Anal., vol. 4, no. 2, pp. 147–154, 1997. DOI: 10.1016/S1350-6307(97)00005-8.
   Web of Science ®Google Scholar
• T. Goto, I. Ohno, and Y. Sumino, “The determination of the elastic constants of natural almandine-pyrope garnet by rectangular parallelepiped resonance method,” J. Phys. Earth, vol. 24, no. 2, pp. 149–156, 1976. DOI: 10.4294/jpe1952.24.149.
   Google Scholar
• J. I. Etcheverry and G. A. Sánchez, “Resonance frequencies of parallelepipeds for determination of elastic moduli: An accurate numerical treatment,” J. Sound Vibration, vol. 321, no. 3–5, pp. 631–646, 2009. DOI: 10.1016/j.jsv.2008.10.026.
   Web of Science ®Google Scholar
• J. Aboudi, “Effective thermoelastic constants of short-fiber composites,” Fibre Sci. Technol., vol. 20, no. 3, pp. 211–225, 1984. DOI: 10.1016/0015-0568(84)90042-3.
   Google Scholar
• A. Vattré and E. Pan, “Thermoelasticity of multilayered plates with imperfect interfaces,” Int. J. Eng. Sci., vol. 158, pp. 103409, 2021. DOI: 10.1016/j.ijengsci.2020.103409.
   Web of Science ®Google Scholar
• A. V. Nasedkin, A. A. Nasedkina, and A. Rajagopal, “Finite element simulation of thermoelastic effective properties of periodic masonry with porous bricks,” in Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials, Advanced Structured Materials, vol. 59, M. Sumbatyan, Eds. Singapore: Springer, 2017.
   Google Scholar
• N. Y. Taits, A. G. Sabel’nikov, A. N. Minaev, and V. V. Moshura, “Maximum temperature drops and thermoelastic stresses in the symmetric heating of prisms and parallelepipeds,” Strength Mater., vol. 3, no. 12, pp. 1405–1406, 1971. DOI: 10.1007/BF01527701.
   Google Scholar
• M. N. Magomedov, “On dependences of the thermoelastic properties on size and shape of an iron nanocrystal,” Nanotechnol. Russia, vol. 10, no. 1–2, pp. 89–99, 2015. DOI: 10.1134/S1995078015010127.
   Google Scholar
• X. Sha and R. E. Cohen, “First-principles thermoelasticity of bcc iron under pressure,” Phys. Rev. B., vol. 74, no. 21, pp. 214111, 2006. DOI: 10.1103/PhysRevB.74.214111.
   Web of Science ®Google Scholar
• V. A. Şeremet, “Method to derive thermoelastic Green’s functions for bounded domains (on examples of two-dimensional problems for parallelepipeds),” Acta Mech., vol. 227, no. 12, pp. 3603–3620, 2016. DOI: 10.1007/s00707-016-1680-8.
   Web of Science ®Google Scholar
• V. Şeremet and D. Şeremet, “Solution in integrals of a 3D BVP of thermoelasticity: Green’s functions and integration formula for thermal stresses within a semi-bounded parallelepiped,” Acta Mech., vol. 228, no. 12, pp. 4471–4490, 2017. DOI: 10.1007/s00707-017-1923-3.
   Web of Science ®Google Scholar
• N. Khomasuridze, “Thermoelastic equilibrium of a parallelepiped with nongomogeneous symmetrt and antisymmetry conditions onits faces,” Georgian Math. J., vol. 7, no. 4, pp. 701–722, 2000. DOI: 10.1515/GMJ.2000.701.
   Google Scholar
• N. Khomasuridze, N. Zirakashvili, R. Janjgava, and M. Narmania, “Analytical solution of classical and non-classical boundary value contact problems of thermoelasticity for a rectangular parallelepiped consisting of compressible and incompressible elastic layers and numerical example of the solution of such problems,” Arch. Appl. Mech., vol. 84, no. 12, pp. 1701–1713, 2014. DOI: 10.1007/s00419-014-0867-5.
   Web of Science ®Google Scholar
• N. Khomasuridze and R. Janjgava, “Solution of some boundary value thermoelasticity problems for a rectangular parallelepiped taking into account microthermal effects,” Meccanica, vol. 51, no. 1, pp. 211–221, 2016. DOI: 10.1007/s11012-015-0207-z.
   Web of Science ®Google Scholar
• N. Khomasuridze and R. Janjgava, “Some non-classical boundary value problems of thermoelasticity and a three-dimensional analogue of Muskhelishvili’s thermal effect,” J. Thermal Stress., vol. 36, no. 7, pp. 699–713, 2013. DOI: 10.1080/01495739.2013.787850.
   Web of Science ®Google Scholar
• A. V. Berdakchiev, “Problems of coupled thermoelasticity for a parallelepiped,” J. Eng. Phys., vol. 41, no. 1, pp. 794–800, 1981. DOI: 10.1007/BF00824831.
   Google Scholar
• G. F. Dargush and P. K. Banerjee, “Boundary element methods in three-dimensional thermoelasticity,” Int. J. Solids Struct., vol. 26, no. 2, pp. 199–216, 1990. DOI: 10.1016/0020-7683(90)90052-W.
   Web of Science ®Google Scholar
• S. A. Lychev, A. V. Manzhirov, and S. V. Joubert, “Closed solutions of boundary-value problems of coupled thermoelasticity,” Mech. Solids, vol. 45, no. 4, pp. 610–623, 2010. DOI: 10.3103/S0025654410040102.
   Web of Science ®Google Scholar
• A. L. Levitin, S. A. Lychev, and I. N. Saifutdinov, “Transient dynamical problem for a accreted thermoelastic parallelepiped,” in Proc. World Congr. Eng., London, UK, July 2–4, 2014, vol. II, WCE 2014.
   Google Scholar
• A. L. Levitin and S. A. Lychev, “Transient problem for a accreted thermoelastic block,” in Transactions on Engineering Technologies, G. C. Yang, S. I. Ao, L. Gelman, Eds. Dordrecht: Springer, 2015.
   Google Scholar
• M. R. Eslami, R. B. Hetnarski, J. Ignaczak, N. Noda, N. Sumi, and Y. Tanigawa, Theory of Thermal Stresses. Explanations, Problems and Solutions, New York: Springer, 2013.
   Google Scholar
• V. Grinchenko, “The biharmonic problem and progress in the development of analytical methods for the solution of boundary-value problems,” J. Eng. Math., vol. 46, no. 3/4, pp. 281–297, 2003. DOI: 10.1023/A:1025049526317.
   Web of Science ®Google Scholar
• R. Kushnir, A. Yasinskyy, Y. Tokovyy, and E. Hart, “Inverse thermoelastic analysis of a cylindrical tribo-couple,” Materials, vol. 14, no. 10, pp. 2657, 2021. DOI: 10.3390/ma14102657.
   PubMed Web of Science ®Google Scholar
• R. M. Kushnir, A. V. Yasinskyy, and Y. V. Tokovyy, “Effect of material properties in the direct and inverse thermomechanical analyses of multilayer functionally graded solids,” Adv. Eng. Mater., vol. 24, no. 5, pp. 2100875, 2022. DOI: 10.1002/adem.202100875.
   Web of Science ®Google Scholar
• A. V. Yasinskyy and Y. V. Tokovyy, “Control of two-dimensional stationary thermal stresses in a half space with the help of external thermal loading,” J. Math. Sci., vol. 261, no. 1, pp. 115–126, 2022. DOI: 10.1007/s10958-022-05744-9.
   Google Scholar
• V. M. Vigak, “Control of thermal stresses and displacements in thermoelastic bodies,” J. Math. Sci., vol. 62, no. 1, pp. 2506–2511, 1992. DOI: 10.1007/BF01099140.
   Google Scholar
• Y. Tokovyy and C.-C. Ma, The Direct Integration Method for Elastic Analysis of Nonhomogeneous Solids. Newcastle: Cambridge Scholars Publishing, 2021.
   Google Scholar
• V. M. Vigak, “A direct method of integrating the equations of two-dimensional problems of elasticity and thermoelasticity for orthotropic materials,” J. Math. Sci., vol. 88, no. 3, pp. 342–346, 1998. DOI: 10.1007/BF02365249.
   Google Scholar
• B. M. Kalynyak, Y. V. Tokovyy, and A. V. Yasinskyy, “Direct and inverse problems of thermomechanics concerning the optimization and identification of the thermal stressed state of deformed solids,” J. Math. Sci., vol. 236, no. 1, pp. 21–34, 2019. DOI: 10.1007/s10958-018-4095-3.
   Google Scholar
• V. M. Vihak, M. Y. Yuzvyak, and A. V. Yasinskij, “The solution of the plane thermoelasticity problem for a rectangular domain,” J. Thermal Stress., vol. 21, no. 5, pp. 545–561, 1998. DOI: 10.1080/01495739808956162.
   Web of Science ®Google Scholar
• V. M. Vihak and Y. V. Tokovyi, “Investigation of the plane stressed state in a rectangular domain,” Mater. Sci. , vol. 38, no. 2, pp. 230–237, 2002. DOI: 10.1023/A:1020994204806.
   Web of Science ®Google Scholar
• M. Yuzvyak, Y. Tokovyy, and A. Yasinskyy, “Axisymmetric thermal stresses in an elastic hollow cylinder of finite length,” J. Thermal Stress., vol. 44, no. 3, pp. 1–18, 2020. DOI: 10.1080/01495739.2020.1826376.
   Web of Science ®Google Scholar
• Y. V. Tokovyy, M. Y. Yuzvyak, and A. V. Yasinskyy, “Representation of solutions to the plane elasticity problems for a rectangular domain via Vihak’s functions,” BKNUPhM, vol. 3, no. 3, pp. 123–126, 2021. DOI: 10.17721/1812-5409.2021/3.24.
   Google Scholar
• V. M. Vihak, “Continuity equations for a deformable solid,” J. Math. Sci., vol. 99, no. 5, pp. 1655–1661, 2000. DOI: 10.1007/BF02674189.
   Google Scholar
• V. M. Vigak and Y. V. Tokovyi, “Construction of elementary solutions to a plane elastic problem for a rectangular domain,” Int. Appl. Mech., vol. 38, no. 7, pp. 829–836, 2002. DOI: 10.1023/A:1020837409659.
   Web of Science ®Google Scholar
• S. P. Timoshenko and J. N. Goodier, Theory of Elasticity. New York: McGraw-Hill Book Company, Inc., 1951.
   Google Scholar