Research Article
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Year 2023, Volume: 26 Issue: 2, 46 - 55, 01.06.2023

G. Dhameja L. Khalsa Vinod Varghese

https://doi.org/10.5541/ijot.1170364
Cited By: 1

Abstract

References

  • K. B. Oldham and J. Spanier, The fractional calculus: Theory and applications of differentiation and integration to arbitrary order, Academic Press, New York, 1974.
  • K. S. Miller and B. Ross, An Introduction to the fractional integrals and derivatives: Theory and applications, Wiley, New York, 1993.
  • S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional integrals and derivatives: Theory and applications, Gordon and Breach, New York, 1993.
  • I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
  • R. Hilfer, Applications of fractional calculus in physics, World Scientific Publishing, Singapore, 2000.
  • R. Herrmann, Fractional calculus: An introduction for physicists, World Scientific Publishing, Singapore, 2011.
  • Y. Povstenko, "Fractional heat conduction equation and associated thermal stress," J. Therm. Stresses, 28(1), 83-102, 2004. DOI: 10.1080/014957390523741.
  • Y. Povstenko, "Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation," Int. J. Solids Struct., 44 (7–8), 2324-2348, 2007. DOI: 10.1016/j.ijsolstr.2006.07.008.
  • Y. Povstenko, "Fractional heat conduction equation and associated thermal stresses in an infinite solid with spherical cavity," Q. J. Mech. Appl. Math., 61(4), 523-547, 2008. DOI: 10.1093/qjmam/hbn016.
  • Y. Povstenko, "Time-fractional radial heat conduction in a cylinder and associated thermal stresses," Arch. Appl. Mech., 82, 345–362, 2012. DOI: 10.1007/s00419-011-0560-x.
  • Y. Povstenko, D. Avci, E. İskender and Ö. Necati, "Control of thermal stresses in axissymmetric problems of fractional thermoelasticity for an infinite cylindrical domain," Therm. Sci, 21 (1A), 19-28, 2017. DOI: 10.2298/TSCI160421236P.
  • H.M. Youssef and E. A. Al-Lehaibi, "Variational principle of fractional order generalized thermoelasticity," Appl. Math. Lett., 23(10), 1183-1187, 2010. DOI: 10.1016/j.aml.2010.05.008.
  • H.M. Youssef and E.A. Al-Lehaibi, "Fractional order generalized thermoelastic half-space subjected to ramp-type heating," Mech. Res. Commun., 37(5), 448-452, 2010. DOI: 10.1016/j.mechrescom.2010.06.003.
  • H.M. Youssef and E.A. Al-Lehaibi, "Fractional order generalized thermoelastic infinite medium with cylindrical cavity subjected to harmonically varying heat," Sci. Res. J., 3(1), 32-37, 2011. DOI: 10.4236/eng.2011.31004.
  • H.M. Youssef, "Two-dimensional thermal shock problem of fractional order generalized thermoelasticity," Acta Mech., 223, 1219–1231, 2012. DOI: 10.1007/s00707-012-0627-y.
  • H. M. Youssef, "State-space approach to fractional order two-temperature generalized thermoelastic medium subjected to moving heat source," Mech. Adv. Mater. Struct., 20, 47–60, 2013. DOI: 10.1080/15376494.2011.581414.
  • H. M. Youssef, K. A. Elsibai and A. A. El-Bary, Fractional order thermoelastic waves of cylindrical gold nano-beam, Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition IMECE2013, November 15-21, San Diego, California, USA, 1-5, 2013. DOI: 10.1115/IMECE2013-62876.
  • H. M. Youssef, "Theory of generalized thermoelasticity with fractional order strain," J. Vib. Control, 22(18), 3840–3857, 2015. DOI: 10.1177/1077546314566837.
  • A. S. El-Karamany and M.A. Ezzat, "On fractional thermoelasticity," Math. Mech. Solids, 16 (3), 334-346, 2011. DOI: 10.1177/1081286510397228.
  • M. A. Ezzat and A. S. El-Karamany, "Two-temperature theory in generalized magneto-thermoelasticity with two relaxation times," Meccanica, 46, 785–794, 2011. DOI: 10.1007/s11012-010-9337-5.
  • M. A. Ezzat, A. S. El-Karamany, A.A. El-Bary and M.A. Fayik, "Fractional calculus in one-dimensional isotropic thermo-viscoelasticity," Comptes Rendus Mécanique, 341 (7), 553-566, 2013. DOI: 10.1016/j.crme.2013.04.001.
  • M. A. Ezzat, A. S. El-Karamany and A. A. El-Bary, "Application of fractional order theory of thermoelasticity to 3D time-dependent thermal shock problem for a half-space," Mech. Adv. Mater. Struct., 24(1), 27-35, 2017. DOI: 10.1080/15376494.2015.1091532.
  • H. H. Sherief, A.M.A. El-Sayed and A.M. Abd El-Latief, "Fractional order theory of thermoelasticity," Int. J. Solids Struct., 47(2), 269-275, 2010. DOI: 10.1007/978-94-007-2739-7_366.
  • H. H. Sherief and A. M. Abd El-Latief, "Application of fractional order theory of thermoelasticity to a 1D problem for a half-space," J. Appl. Math. Mech., 94(6), 509-515, 2014. DOI: 10.1002/zamm.201200173.
  • H. H. Sherief and A. M. Abd El-Latief, "A one-dimensional fractional order thermoelastic problem for a spherical cavity," Math Mech Solids, 20(5), 512-521, 2015. DOI: 10.1177/1081286513505585.
  • A. Sur and M. Kanoria, "Fractional order two-temperature thermoelasticity with finite wave speed," Acta Mech., 223(12), 2685-2701, 2012. DOI: 10.1007/s00707-012-0736-7.
  • D. Bhattacharya and M. Kanoria, "The influence of two-temperature fractional order generalized thermoelastic diffusion inside a spherical shell," Int. j. appl. innov., 3(8), 96-108, 2014. A. M. Zenkour and A. E. Abouelregal, "State-space approach for an infinite medium with a spherical cavity based upon two-temperature generalized thermoelasticity theory and fractional heat conduction," Z. Angew. Math. Phys., 65, 149–164, 2014. DOI: 10.1007/s00033-013-0313-5.
  • M. Bachher, "Deformations due to periodically varying heat sources in a reference temperature dependent thermoelastic porous material with a time-fractional heat conduction law," Int Res J Eng Techn., 2(4), 145-152, 2015.
  • S. Santra, N. C. Das, R. Kumar and A. Lahiri, "Three-dimensional fractional order generalized thermoelastic problem under the effect of rotation in a half space," J. Therm. Stresses, 38(3), 309-324, 2015. DOI: 10.1080/01495739.2014.985551.
  • N. D. Gupta and N. C. Das, "Eigenvalue approach to fractional order generalized thermoelasticity with line heat source in an infinite medium," J. Therm. Stresses, 39(8), 977-990, 2016. DOI: 10.1080/01495739.2016.1187987.
  • M. Bachher and N. Sarkar, Fractional order magneto-thermoelasticity in a rotating media with one relaxation time," Mathematical Models in Engineering, 2(1), 56-68, 2016.
  • I. A. Abbas, "Fractional order generalized thermoelasticity in an unbounded medium with cylindrical cavity," J. Eng. Mech., 142(6), 04016033-1-5, 2016. DOI: 10.1061/(ASCE)EM.1943-7889.0001071.
  • I. A. Abbas, "A Study on fractional order theory in thermoelastic half-space under thermal loading," Phys Mesomech, 21, 150–156, 2018. DOI: 10.1134/S102995991802008X.
  • P. Lata, "Fractional order thermoelastic thick circular plate with two temperatures in frequency domain," Appl. Appl. Math., 13(2), 1216 – 1229, 2018.
  • G. Mittal and V. S. Kulkarni, "Two temperature fractional order thermoelasticity theory in a spherical domain," J. Therm. Stresses, 42(9), 1136-1152, 2019. DOI: 10.1080/01495739.2019.1615854.
  • S. Bhoyar, V. Varghese and L. Khalsa, "An exact analytical solution for fractional-order thermoelasticity in a multi-stacked elliptic plate," J. Therm. Stresses, 43(6), 762-783, 2020. DOI: 10.1080/01495739.2020.1748553.
  • M. Haskul, "Elastic state of functionally graded curved beam on the plane stress state subject to thermal load," Mech. Based Des. Struct. Mach., 48(6), 739-754. 2020. DOI: 10.1080/15397734.2019.1660890.
  • E. Arslan, M. Haskul, "Generalized plane strain solution of a thick-walled cylindrical panel subjected to radial heating," Acta Mech, 226, 1213–1225, 2015. https://doi.org/10.1007/s00707-014-1248-4.
  • M. Haskul, E. Arslan and W. Mack, "Radial heating of a thick-walled cylindrically curved FGM-panel," Z. Angew. Math. Mech., 97, 309-321, 2017. https://doi.org/10.1002/zamm.201500310.
  • M. Haskul, "Yielding of functionally graded curved beam subjected to temperature," Pamukkale University Journal of Engineering Sciences, 26(4), 587-593, 2020. DOI: 10.5505/pajes.2019.92331.
  • M. E. Gurtin and A. C. Pipkin, "A general theory of heat conduction with finite wave speed," Arch. Rat. Mech. Anal., 31, 113–126, 1968.
  • P.J. Chen and M.E. Gurtin, "A second sound in materials with memory," Z. Angew. Math. Phys., 21, 232–241, 1970.
  • C. Cattaneo, "On the conduction of heat," Atti. Semin. Fis. Univ. Modena, 3, 3–21, 1948.
  • C. Cattaneo, "Sur une forme de l’´equation de la chaleur ´eliminant le paradoxe d’une propagation instantan´ee," C. R. Acad. Sci., 247, 431–433, 1958.
  • P. Vernotte, "Les paradoxes de la th´eorie continue de l’´equation de la chaleur," ibid., 246, 3154–3155, 1958.
  • S. Kaliski, "Wave equation of thermoelasticity," Bull. Acad. Polon. Sci. S'er. Sci. Techn., 13, 253–260, 1965.
  • H. W. Lord and Y. Shulman, "A generalized dynamical theory of thermoelasticity," J. Mech. Phys. Solids, 15, 299–309, 1967.
  • A. E. Green and P. M. Naghdi, "Thermoelasticity without energy dissipation," J. Elast., 31, 189–208, 1993.
  • R. Gorenflo and F. Mainardi, Fractional calculus: integral and differential equations of fractional order, In: A. Carpinteri, F. Mainardi (eds.), Fractals and fractional calculus in continuum mechanics, 223-276, Springer, New York, 1997.
  • A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equation, Elsevier, Amsterdam, 2006.
  • N. Noda, R. B. Hetnarski, Y. Tanigawa, Thermal Stresses (2nd ed.), Taylor and Francis, New York, 2003.
  • M. R. Eslami, R. B. Hetnarski, J. Ignaczak, N. Noda, N. Sumi, and Y. Tanigawa, Theory of elasticity and thermal stresses, Springer New York, 2013. DOI: 10.1007/978-94-007-6356-2.
  • E. Ventsel, T. Krauthammer, Thin plates and shells-Theory, Analysis, and Applications, Marcel Dekker, New York, 2001.
  • D. P. Gaver, "Observing stochastic processes and approximate transform inversion," Oper. Res., 14(3), 444–459, 1966. DOI: 10.1287/opre.14.3.444.
  • H. Stehfest, Algorithm 368, Numerical inversion of Laplace transforms," Comm. Assn. Comp. Mach., 13(1), 47–49, 1970. DOI: 10.1145/361953.361969.
  • H. Stehfest, "Remark on algorithm 368: Numerical inversion of Laplace transforms," Commun. Assn. Comput. Mach., 13(10), 624, 1970. DOI: 10.1145/355598.362787.
  • A. Kuznetsov, "On the convergence of the Gaver–Stehfest algorithm," SIAM J. Num. Anal., 51(6), 2984–2998, 2013. DOI: 10.1137/13091974X.

Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework

Year 2023, Volume: 26 Issue: 2, 46 - 55, 01.06.2023

G. Dhameja L. Khalsa Vinod Varghese

https://doi.org/10.5541/ijot.1170364
Cited By: 1

Abstract

This paper considers a transient thermoelastic problem in an isotropic homogeneous elastic thin circular plate with clamped edges subjected to thermal load within the fractional-order theory framework. The prescribed ramp-type surface temperature is on the plate's top face, while the bottom face is kept at zero. The three-dimensional heat conduction equation is solved using a Laplace transformation and the classical solution method. The Gaver–Stehfest approach was used to invert Laplace domain outcomes. The thermal moment is derived based on temperature change, and its bending stresses are obtained using the resultant moment and resultant forces per unit length. The results are illustrated by numerical calculations considering the material to be an Aluminum-like medium, and corresponding graphs are plotted.

Keywords

Heat conduction thin circular plate thermal deflection thermal stresses integral transform fractional-order derivatives

References

  • K. B. Oldham and J. Spanier, The fractional calculus: Theory and applications of differentiation and integration to arbitrary order, Academic Press, New York, 1974.
  • K. S. Miller and B. Ross, An Introduction to the fractional integrals and derivatives: Theory and applications, Wiley, New York, 1993.
  • S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional integrals and derivatives: Theory and applications, Gordon and Breach, New York, 1993.
  • I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
  • R. Hilfer, Applications of fractional calculus in physics, World Scientific Publishing, Singapore, 2000.
  • R. Herrmann, Fractional calculus: An introduction for physicists, World Scientific Publishing, Singapore, 2011.
  • Y. Povstenko, "Fractional heat conduction equation and associated thermal stress," J. Therm. Stresses, 28(1), 83-102, 2004. DOI: 10.1080/014957390523741.
  • Y. Povstenko, "Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation," Int. J. Solids Struct., 44 (7–8), 2324-2348, 2007. DOI: 10.1016/j.ijsolstr.2006.07.008.
  • Y. Povstenko, "Fractional heat conduction equation and associated thermal stresses in an infinite solid with spherical cavity," Q. J. Mech. Appl. Math., 61(4), 523-547, 2008. DOI: 10.1093/qjmam/hbn016.
  • Y. Povstenko, "Time-fractional radial heat conduction in a cylinder and associated thermal stresses," Arch. Appl. Mech., 82, 345–362, 2012. DOI: 10.1007/s00419-011-0560-x.
  • Y. Povstenko, D. Avci, E. İskender and Ö. Necati, "Control of thermal stresses in axissymmetric problems of fractional thermoelasticity for an infinite cylindrical domain," Therm. Sci, 21 (1A), 19-28, 2017. DOI: 10.2298/TSCI160421236P.
  • H.M. Youssef and E. A. Al-Lehaibi, "Variational principle of fractional order generalized thermoelasticity," Appl. Math. Lett., 23(10), 1183-1187, 2010. DOI: 10.1016/j.aml.2010.05.008.
  • H.M. Youssef and E.A. Al-Lehaibi, "Fractional order generalized thermoelastic half-space subjected to ramp-type heating," Mech. Res. Commun., 37(5), 448-452, 2010. DOI: 10.1016/j.mechrescom.2010.06.003.
  • H.M. Youssef and E.A. Al-Lehaibi, "Fractional order generalized thermoelastic infinite medium with cylindrical cavity subjected to harmonically varying heat," Sci. Res. J., 3(1), 32-37, 2011. DOI: 10.4236/eng.2011.31004.
  • H.M. Youssef, "Two-dimensional thermal shock problem of fractional order generalized thermoelasticity," Acta Mech., 223, 1219–1231, 2012. DOI: 10.1007/s00707-012-0627-y.
  • H. M. Youssef, "State-space approach to fractional order two-temperature generalized thermoelastic medium subjected to moving heat source," Mech. Adv. Mater. Struct., 20, 47–60, 2013. DOI: 10.1080/15376494.2011.581414.
  • H. M. Youssef, K. A. Elsibai and A. A. El-Bary, Fractional order thermoelastic waves of cylindrical gold nano-beam, Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition IMECE2013, November 15-21, San Diego, California, USA, 1-5, 2013. DOI: 10.1115/IMECE2013-62876.
  • H. M. Youssef, "Theory of generalized thermoelasticity with fractional order strain," J. Vib. Control, 22(18), 3840–3857, 2015. DOI: 10.1177/1077546314566837.
  • A. S. El-Karamany and M.A. Ezzat, "On fractional thermoelasticity," Math. Mech. Solids, 16 (3), 334-346, 2011. DOI: 10.1177/1081286510397228.
  • M. A. Ezzat and A. S. El-Karamany, "Two-temperature theory in generalized magneto-thermoelasticity with two relaxation times," Meccanica, 46, 785–794, 2011. DOI: 10.1007/s11012-010-9337-5.
  • M. A. Ezzat, A. S. El-Karamany, A.A. El-Bary and M.A. Fayik, "Fractional calculus in one-dimensional isotropic thermo-viscoelasticity," Comptes Rendus Mécanique, 341 (7), 553-566, 2013. DOI: 10.1016/j.crme.2013.04.001.
  • M. A. Ezzat, A. S. El-Karamany and A. A. El-Bary, "Application of fractional order theory of thermoelasticity to 3D time-dependent thermal shock problem for a half-space," Mech. Adv. Mater. Struct., 24(1), 27-35, 2017. DOI: 10.1080/15376494.2015.1091532.
  • H. H. Sherief, A.M.A. El-Sayed and A.M. Abd El-Latief, "Fractional order theory of thermoelasticity," Int. J. Solids Struct., 47(2), 269-275, 2010. DOI: 10.1007/978-94-007-2739-7_366.
  • H. H. Sherief and A. M. Abd El-Latief, "Application of fractional order theory of thermoelasticity to a 1D problem for a half-space," J. Appl. Math. Mech., 94(6), 509-515, 2014. DOI: 10.1002/zamm.201200173.
  • H. H. Sherief and A. M. Abd El-Latief, "A one-dimensional fractional order thermoelastic problem for a spherical cavity," Math Mech Solids, 20(5), 512-521, 2015. DOI: 10.1177/1081286513505585.
  • A. Sur and M. Kanoria, "Fractional order two-temperature thermoelasticity with finite wave speed," Acta Mech., 223(12), 2685-2701, 2012. DOI: 10.1007/s00707-012-0736-7.
  • D. Bhattacharya and M. Kanoria, "The influence of two-temperature fractional order generalized thermoelastic diffusion inside a spherical shell," Int. j. appl. innov., 3(8), 96-108, 2014. A. M. Zenkour and A. E. Abouelregal, "State-space approach for an infinite medium with a spherical cavity based upon two-temperature generalized thermoelasticity theory and fractional heat conduction," Z. Angew. Math. Phys., 65, 149–164, 2014. DOI: 10.1007/s00033-013-0313-5.
  • M. Bachher, "Deformations due to periodically varying heat sources in a reference temperature dependent thermoelastic porous material with a time-fractional heat conduction law," Int Res J Eng Techn., 2(4), 145-152, 2015.
  • S. Santra, N. C. Das, R. Kumar and A. Lahiri, "Three-dimensional fractional order generalized thermoelastic problem under the effect of rotation in a half space," J. Therm. Stresses, 38(3), 309-324, 2015. DOI: 10.1080/01495739.2014.985551.
  • N. D. Gupta and N. C. Das, "Eigenvalue approach to fractional order generalized thermoelasticity with line heat source in an infinite medium," J. Therm. Stresses, 39(8), 977-990, 2016. DOI: 10.1080/01495739.2016.1187987.
  • M. Bachher and N. Sarkar, Fractional order magneto-thermoelasticity in a rotating media with one relaxation time," Mathematical Models in Engineering, 2(1), 56-68, 2016.
  • I. A. Abbas, "Fractional order generalized thermoelasticity in an unbounded medium with cylindrical cavity," J. Eng. Mech., 142(6), 04016033-1-5, 2016. DOI: 10.1061/(ASCE)EM.1943-7889.0001071.
  • I. A. Abbas, "A Study on fractional order theory in thermoelastic half-space under thermal loading," Phys Mesomech, 21, 150–156, 2018. DOI: 10.1134/S102995991802008X.
  • P. Lata, "Fractional order thermoelastic thick circular plate with two temperatures in frequency domain," Appl. Appl. Math., 13(2), 1216 – 1229, 2018.
  • G. Mittal and V. S. Kulkarni, "Two temperature fractional order thermoelasticity theory in a spherical domain," J. Therm. Stresses, 42(9), 1136-1152, 2019. DOI: 10.1080/01495739.2019.1615854.
  • S. Bhoyar, V. Varghese and L. Khalsa, "An exact analytical solution for fractional-order thermoelasticity in a multi-stacked elliptic plate," J. Therm. Stresses, 43(6), 762-783, 2020. DOI: 10.1080/01495739.2020.1748553.
  • M. Haskul, "Elastic state of functionally graded curved beam on the plane stress state subject to thermal load," Mech. Based Des. Struct. Mach., 48(6), 739-754. 2020. DOI: 10.1080/15397734.2019.1660890.
  • E. Arslan, M. Haskul, "Generalized plane strain solution of a thick-walled cylindrical panel subjected to radial heating," Acta Mech, 226, 1213–1225, 2015. https://doi.org/10.1007/s00707-014-1248-4.
  • M. Haskul, E. Arslan and W. Mack, "Radial heating of a thick-walled cylindrically curved FGM-panel," Z. Angew. Math. Mech., 97, 309-321, 2017. https://doi.org/10.1002/zamm.201500310.
  • M. Haskul, "Yielding of functionally graded curved beam subjected to temperature," Pamukkale University Journal of Engineering Sciences, 26(4), 587-593, 2020. DOI: 10.5505/pajes.2019.92331.
  • M. E. Gurtin and A. C. Pipkin, "A general theory of heat conduction with finite wave speed," Arch. Rat. Mech. Anal., 31, 113–126, 1968.
  • P.J. Chen and M.E. Gurtin, "A second sound in materials with memory," Z. Angew. Math. Phys., 21, 232–241, 1970.
  • C. Cattaneo, "On the conduction of heat," Atti. Semin. Fis. Univ. Modena, 3, 3–21, 1948.
  • C. Cattaneo, "Sur une forme de l’´equation de la chaleur ´eliminant le paradoxe d’une propagation instantan´ee," C. R. Acad. Sci., 247, 431–433, 1958.
  • P. Vernotte, "Les paradoxes de la th´eorie continue de l’´equation de la chaleur," ibid., 246, 3154–3155, 1958.
  • S. Kaliski, "Wave equation of thermoelasticity," Bull. Acad. Polon. Sci. S'er. Sci. Techn., 13, 253–260, 1965.
  • H. W. Lord and Y. Shulman, "A generalized dynamical theory of thermoelasticity," J. Mech. Phys. Solids, 15, 299–309, 1967.
  • A. E. Green and P. M. Naghdi, "Thermoelasticity without energy dissipation," J. Elast., 31, 189–208, 1993.
  • R. Gorenflo and F. Mainardi, Fractional calculus: integral and differential equations of fractional order, In: A. Carpinteri, F. Mainardi (eds.), Fractals and fractional calculus in continuum mechanics, 223-276, Springer, New York, 1997.
  • A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equation, Elsevier, Amsterdam, 2006.
  • N. Noda, R. B. Hetnarski, Y. Tanigawa, Thermal Stresses (2nd ed.), Taylor and Francis, New York, 2003.
  • M. R. Eslami, R. B. Hetnarski, J. Ignaczak, N. Noda, N. Sumi, and Y. Tanigawa, Theory of elasticity and thermal stresses, Springer New York, 2013. DOI: 10.1007/978-94-007-6356-2.
  • E. Ventsel, T. Krauthammer, Thin plates and shells-Theory, Analysis, and Applications, Marcel Dekker, New York, 2001.
  • D. P. Gaver, "Observing stochastic processes and approximate transform inversion," Oper. Res., 14(3), 444–459, 1966. DOI: 10.1287/opre.14.3.444.
  • H. Stehfest, Algorithm 368, Numerical inversion of Laplace transforms," Comm. Assn. Comp. Mach., 13(1), 47–49, 1970. DOI: 10.1145/361953.361969.
  • H. Stehfest, "Remark on algorithm 368: Numerical inversion of Laplace transforms," Commun. Assn. Comput. Mach., 13(10), 624, 1970. DOI: 10.1145/355598.362787.
  • A. Kuznetsov, "On the convergence of the Gaver–Stehfest algorithm," SIAM J. Num. Anal., 51(6), 2984–2998, 2013. DOI: 10.1137/13091974X.
There are 57 citations in total.

Details

Primary Language English
Subjects Thermodynamics and Statistical Physics
Journal Section Research Articles
Authors

G. Dhameja This is me

L. Khalsa This is me

Vinod Varghese 0000-0002-9660-7610

Early Pub Date April 27, 2023
Publication Date June 1, 2023
Published in Issue Year 2023 Volume: 26 Issue: 2

Cite

APA Dhameja, G., Khalsa, L., & Varghese, V. (2023). Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework. International Journal of Thermodynamics, 26(2), 46-55. https://doi.org/10.5541/ijot.1170364
AMA Dhameja G, Khalsa L, Varghese V. Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework. International Journal of Thermodynamics. June 2023;26(2):46-55. doi:10.5541/ijot.1170364
Chicago Dhameja, G., L. Khalsa, and Vinod Varghese. “Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate Within the Fractional-Order Framework”. International Journal of Thermodynamics 26, no. 2 (June 2023): 46-55. https://doi.org/10.5541/ijot.1170364.
EndNote Dhameja G, Khalsa L, Varghese V (June 1, 2023) Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework. International Journal of Thermodynamics 26 2 46–55.
IEEE G. Dhameja, L. Khalsa, and V. Varghese, “Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework”, International Journal of Thermodynamics, vol. 26, no. 2, pp. 46–55, 2023, doi: 10.5541/ijot.1170364.
ISNAD Dhameja, G. et al. “Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate Within the Fractional-Order Framework”. International Journal of Thermodynamics 26/2 (June 2023), 46-55. https://doi.org/10.5541/ijot.1170364.
JAMA Dhameja G, Khalsa L, Varghese V. Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework. International Journal of Thermodynamics. 2023;26:46–55.
MLA Dhameja, G. et al. “Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate Within the Fractional-Order Framework”. International Journal of Thermodynamics, vol. 26, no. 2, 2023, pp. 46-55, doi:10.5541/ijot.1170364.
Vancouver Dhameja G, Khalsa L, Varghese V. Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework. International Journal of Thermodynamics. 2023;26(2):46-55.

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Thermomechanical interaction in a living tissue due to variable thermal loading with memory
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
https://doi.org/10.1002/zamm.202400398
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