Skip to main content
SpringerLink
Log in

Spatial Thermoviscoplastic Problems

  • Published:
International Applied Mechanics Aims and scope

Abstract

Methods and results of studies of the three-dimensional viscoplastic stress–strain state of engineering structures under thermomechanical loading are presented. The following classes of thermoviscoplastic problems are considered: axisymmetric problems, nonaxisymmetric problems for bodies of revolution, three-dimensional problems for bodies of arbitrary shapes, and three-dimensional problems for anisotropic bodies of revolution

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. A. V. Amel'yanchik, V. T. Lapteva, Z. P. Mel'nikova, and E. P. Strunina, “Calculation of stress and displacement fields in welded joints of pipelines subject to elastoplastic strains and creep on an Ural-2 computer,” in: Thermal Stresses in Structural Elements [in Russian], Issue 8 (1969), pp. 171–176.

    Google Scholar 

  2. A. V. Amel'yanchik, V. T. Lapteva, and E. P. Strunina, “Strength analysis of solid-forged multidisk rotors of thermal turbines on an Ural-2 computer,” in: The Dynamics and Strength of Machines [in Russian], Issue 5 (1967), pp. 80–85.

    Google Scholar 

  3. A. V. Amel'yanchik, V. T. Lapteva, and E. P. Strunina, “Solution of two-dimensional axisymmetric problems of the theory of elasticity, elastoplastic strains, and creep on an Ural-2 computer,” in: Thermal Stresses in Structural Elements [in Russian], Issue 7 (1967), pp. 18–23.

    Google Scholar 

  4. M. E. Babeshko, “The stress state of a short solid cylinder under nonisothermal loading,” in: Thermal Stresses in Structural Elements [in Russian], Issue 11 (1971), pp. 121–127.

    Google Scholar 

  5. M. E. Babeshko, The Thermoplastic Stress State of Short Cylinders with Allowance for the Loading History [in Russian], Author's Abstract of Ph. D. Thesis, Kiev (1975).

  6. M. E. Babeshko, V. V. Piskun, V. G. Savchenko, and Yu. N. Shevchenko, “Study of the elastoplastic state of elements of engineering structures under complex nonisothermal loading,” in: General Problems and Methods for Studying the Plasticity and Viscoelasticity of Materials and Structures [in Russian], Sverdlovsk (1986), pp. 3–9.

  7. M. E. Babeshko and V. K. Stryuk, “Elastoplastic stress analysis of nonuniformly heated short solid cylinders,” in: Thermal Stresses in Structural Elements [in Russian], Issue 13 (1973), pp. 28–32.

    Google Scholar 

  8. M. E. Babeshko and V. K. Stryuk, “Stress analysis of a solid cylinder based on the isotropic-hardening flow theory,” Prikl. Mekh., 10, No. 6, 27–33 (1974).

    Google Scholar 

  9. M. E. Babeshko and V. K. Stryuk, “Elastoplastic stress analysis of a nonuniformly heated short solid cylinder,” in: Thermal Stresses in Structural Elements [in Russian], Issue 14 (1974), pp. 28–33.

    Google Scholar 

  10. M. E. Babeshko and V. K. Stryuk, “The thermoplastic stress state of a cylinder asymmetrically loaded along the length,” in: Thermal Stresses in Structural Elements [in Russian], Issue 15 (1975), pp. 49–53.

    Google Scholar 

  11. M. E. Babeshko and V. K. Stryuk, “The thermoplasticity of cylinders of finite length,” Vych. Prikl. Mat., Issue 48, 119–127 (1982).

    Google Scholar 

  12. M. E. Babeshko and V. K. Stryuk, “The thermoelastoplastic stress state of compound cylinders,” in: Thermal Stresses in Structural Elements [in Russian], Issue 18 (1978), pp. 40–43.

    Google Scholar 

  13. V. I. Bobyr', “The stress state of a nonaxisymmetrically heated engine valve,” in: Proc. 11th Sci. Conf. of Young Scientists of the Inst. Mech. Acad. Sci. Ukr. SSR [in Russian], Part. 3, Submitted to VINITI 07.28.86, No. 5507-V86, Kiev (1986), pp. 439–443.

  14. V. I. Bobyr', “Solution of the thermoplastic problem for solids of revolution under nonaxisymmetric loading along strain paths of small curvature,” Prikl. Mekh., 22, No. 7, 44–49 (1986).

    Google Scholar 

  15. V. I. Bobyr', The Thermoelastoplastic State of Solids of Revolution under Nonaxisymmetric Loading along Paths of Small Curvature [in Russian], Author's Abstract of Ph. D. Thesis, Kiev (1988).

  16. V. I. Bobyr' and D. A. Ishchenko, “The nonaxisymmetric deformation of solids of revolution under simple loading,” in: Proc. Semin. Young Scientists Inst. Mech. Acad. Sci. Ukr. SSR on Nonclassical and Mixed Problems of the Mechanics of a Deformable Body [in Russian], Submitted to VINITI 07.29.85, No. 5531-85Dep., Kiev (1985), pp. 6–8.

  17. V. I. Bobyr', D. A. Ishchenko, V. G. Savchenko, and I. K. Sakhatskaya, A Program for Studying the Axisymmetric Elastoplastic Stress–Strain State of Structural Elements under Variable Mechanical Loading and Heating with Allowance for Secondary Plastic Strains [in Russian], Registered in FAP AN Ukrainy 02.26.86, No. AP0092, Included in Gosfond No. 50860000641, Kiev (1986).

  18. A. A. Il'yushin, Plasticity. Fundamentals of General Mathematical Theory [in Russian], Izd. Akad. Nauk SSSR, Moscow (1963).

    Google Scholar 

  19. V. N. Ionov, “Stress analysis of cylindrical bodies with an arbitrary cross section,” Izv. Vuzov, Mashinostr., No. 11, 55–63 (1959).

    Google Scholar 

  20. V. N. Ionov, “One method for solution of spatial problems,” Izv. Vuzov, Mashinostr., No. 1, 3–9 (1960).

    Google Scholar 

  21. V. N. Ionov and P. M. Ogibalov, The Strength of Spatial Structural Elements [in Russian], Vyssh. Shk., Moscow (1972).

    Google Scholar 

  22. D. A. Ishchenko, “Solution of an axisymmetric thermoplastic problem for cyclic loading,” Prikl. Mekh., 20, No. 7, 108–111 (1984).

    Google Scholar 

  23. D. A. Ishchenko, The Elastoplastic State of Solids of Revolution under Cyclic Axisymmetric Thermal and Mechanical Loading [in Russian], Author's Abstract of Ph. D. Thesis, Kiev (1984).

  24. D. A. Ishchenko and V. G. Savchenko, “Study of the effect of allowing for secondary plastic strains on the solution of a thermoplastic problem,” Prikl. Mekh., 24, No. 3, 28–33 (1988).

    Google Scholar 

  25. D. A. Ishchenko and V. G. Savchenko, “The kinetics of viscoplastic contact disk–shaft interaction in a turbine rotor,” Probl. Proch., No. 4, 21–24 (1988).

    Google Scholar 

  26. B. I. Koval'chuk, “The theory of plastic deformation of anisotropic materials,” Probl. Proch., No. 9, 8–12 (1975).

    Google Scholar 

  27. S. G. Lekhnitskii, The Theory of Elasticity of an Anisotropic Body [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  28. Yu. N. Shevchenko, V. G. Savchenko, and D. A. Ishchenko, A Method and Program for Numerical Analysis of the Nonstationary Thermal Conduction and Elastoplastic Stress–Strain State of Structural Elements such as Solids of Revolution under Axisymmetric Mechanical and Thermal Loads (Procedural Recommendations) [in Russian], Inst. Mekh. Akad. Nauk Ukr. SSR, Kiev (1988).

    Google Scholar 

  29. V. M. Pavlychko, “Numerical solution of three-dimensional thermoplastic problems for bodies of complex form,” Prikl. Mekh., 24, No. 8, 24–30 (1988).

    Google Scholar 

  30. V. M. Pavlychko, “Solution of three-dimensional thermoplastic problems for simple loading,” Probl. Proch., No. 1, 77–81 (1986).

    Google Scholar 

  31. V. M. Pavlychko, “Solution of three-dimensional thermoplastic problems for simple loading with allowance for the loading history,” in: Proc. 10th Sci. Conf. Young Scientists Inst. Mech. Acad. Sci. Ukr. SSR [in Russian], Submitted to VINITI 07.30.84, No. 5535-84Dep, Kiev (1984), pp. 113–117.

  32. V. M. Pavlychko, The Three-Dimensional Thermoelastoplastic Stress–Strain State of Complex Bodies under Simple Loading [in Russian], Author's Abstract of Ph. D. Thesis, Kiev (1988).

  33. V. V. Piskun and V. G. Savchenko, “Change in strains in a rotor of complex form subject to elastoplastic deformation,” in: Thermal Stresses in Structural Elements [in Russian], Issue 16 (1976), pp. 85–89.

    Google Scholar 

  34. V. V. Piskun and V. G. Savchenko, “Application of the finite-element method to the thermoplastic analysis of solids of revolution,” in: Thermal Stresses in Structural Elements [in Russian], Issue 13 (1973), pp. 23–28.

    Google Scholar 

  35. V. V. Piskun and V. G. Savchenko, “Relaxation of interference stresses in a compound rotor,” in: Thermal Stresses in Structural Elements [in Russian], Issue 18 (1978), pp. 34–36.

    Google Scholar 

  36. V. V. Piskun, V. G. Savchenko, and Yu. N. Shevchenko, “Solution of a spatial axisymmetric thermoplastic problem for thick turbine disks,” Probl. Proch., No. 5, 8–13 (1974).

    Google Scholar 

  37. V. V. Piskun, V. G. Savchenko, and Yu. N. Shevchenko, “The stress state of a compound rotor with interference stresses,” Probl. Proch., No. 6, 93–95 (1977).

    Google Scholar 

  38. V. V. Piskun, V. G. Savchenko, and Yu. N. Shevchenko, “Application of the finite-element method to the determination of thermostresses in disks,” in: Thermal Stresses in Structural Elements [in Russian], Issue 15 (1975), pp. 54–57.

    Google Scholar 

  39. A. N. Podgornyi, “Differential equilibrium equations allowing for the creep of a thick-walled finite-length cylinder,” Prikl. Mekh., 9, No. 1, 77–85 (1963).

    Google Scholar 

  40. A. N. Podgornyi, “The creep of a thick-walled finite-length cylinder,” in: Thermal Stresses in Structural Elements [in Russian], Issue 5 (1965), pp. 260–269.

    Google Scholar 

  41. A. N. Podgornyi, “The steady and unsteady creep of a finite-length cylinder,” in: Thermal Stresses in Structural Elements [in Russian], Issue 8 (1969), pp. 236–243.

    Google Scholar 

  42. A. N. Podgornyi, “The thermocreep of a finite-length cylinder,” Prikl. Mekh., 6, No. 12, 50–54 (1970).

    Google Scholar 

  43. V. K. Prokopov, “Homogeneous solutions in elastic theory and their application to the theory of thin plates,” in: Proc. 2nd All-Union Congr. on Theoretical and Applied Mechanics. Mechanics of a Solid [in Russian], Nauka, Moscow (1966), pp. 253–259.

    Google Scholar 

  44. Yu. N. Shevchenko, V. G. Savchenko, D. A. Ishchenko, and V. M. Pavlychko, A Method and Software Package for Numerical Analysis of the Nonstationary Thermal Conduction and Elastoplastic Stress–Strain State of Structural Elements such as Solids of Revolution under Axisymmetric Mechanical and Thermal Loads. Strength Analysis and Tests (Recommendations R 54-284-90) [in Russian], VNIINMASH, Moscow (1990).

    Google Scholar 

  45. V. G. Savchenko, “Study of the nonaxisymmetric thermal and stress state of solids of revolution with regard for the rectilinear orthotropy of layers,” Prikl. Mekh., 30, No. 9, 9–15 (1994).

    Google Scholar 

  46. V. G. Savchenko, “Study of the elastoplastic state of solids of revolution under variable nonisothermal loading with allowance for creep,” Prikl. Mekh., 18, No. 12, 12–17 (1982).

    Google Scholar 

  47. V. G. Savchenko, “Stress analysis of circumferentially compound solids of revolution,” Prikl. Mekh., 32, No. 7, 32–37 (1996).

    Google Scholar 

  48. V. G. Savchenko, “The nonaxisymmetric temperature fields and the thermostressed state of laminated solids of revolution made of isotropic and curvilinearly orthotropic materials,” Prikl. Mekh., 29, No. 8, 13–21 (1993).

    Google Scholar 

  49. V. G. Savchenko, “One method for solution of spatial nonaxisymmetric thermoplastic problem,” in: Thermal Stresses in Structural Elements [in Russian], Issue 18 (1978), pp. 24–29.

    Google Scholar 

  50. V. G. Savchenko, “Determination of the temperature fields and the elastoplastic stress state of a piston of an internal-combustion engine,” in: The Dynamics and Strength of Machines [in Russian], Issue 35 (1982), pp. 55–58.

    Google Scholar 

  51. V. G. Savchenko, “Analysis of the nonaxisymmetric thermostressed state of discretely homogeneous solids of revolution with orthotropic layers,” Prikl. Mekh., 32, No. 2, 53–58 (1996).

    Google Scholar 

  52. V. G. Savchenko, “The thermostressed state of laminated solids of revolution made of isotropic and rectilinearly orthotropic materials,” Prikl. Mekh., 31, No. 4, 3–9 (1995).

    Google Scholar 

  53. V. G. Savchenko, Elastoplastic Deformation of Solids of Revolution under Complex Nonaxisymmetric Loading [in Russian], Author's Abstract of Ph. D. Thesis, Kiev (1983).

  54. V. G. Savchenko, V. V. Piskun, M. E. Babeshko, and I. V. Prokhorenko, “A numerical method for solution of axisymmetric problems of thermal conduction and thermoplasticity of solids of revolution,” in: Thermal Stresses in Structural Elements [in Russian], Issue 19 (1979), pp. 38–43.

    Google Scholar 

  55. V. G. Savchenko and Yu. N. Shevchenko, “Methods for studying the thermoviscoplastic deformation of three-dimensional structural elements (review),” Prikl. Mekh., 29, No. 9, 3–19 (1993).

    Google Scholar 

  56. V. G. Savchenko and Yu. N. Shevchenko, “The elastoplastic state of thick round plates with stepwise varying geometry under nonisothermal loading,” in: Proc. 12th All-Union Conf. on the Theory of Plates and Shells [in Russian], Vol. 3, Izd. Yerevanskogo Univ. (1980), pp. 192–198.

    Google Scholar 

  57. I. K. Sakhatskaya, “Study of the thermoelastoplastic stress state of cylindrical sector,” in: Proc. 10th Sci. Conf. Young Scientists Inst. Mech. Acad. Sci. Ukr. SSR [in Russian], Part 1, Submitted to VINITI 07.30.84, No. 5535-84 Dep, Kiev (1984), pp. 141–145.

  58. I. K. Sakhatskaya, “Solution of the thermoplastic problem for solids of revolution open in the circumferential direction,” Prikl. Mekh., 19, No. 9, 113–117 (1983).

    Google Scholar 

  59. I. K. Sakhatskaya, “The thermoelastoplastic stress–strain state of cylindrical sector with a loading history,” in: Proc. 11th Sci. Conf. Young Scientists Inst. Mech. Acad. Sci. Ukr. SSR [in Russian], Submitted to VINITI 07.27.86, No. 5507-V86Dep (1986), pp. 582–587.

  60. I. K. Sakhatskaya, The Elastoplastic Stress State of Solids of Revolution under Nonaxisymmetric Nonisothermal Loading [in Russian], Author's Abstract of Ph. D. Thesis, Kiev (1984).

  61. V. K. Stryuk, “The thermoelastoplastic stress state of a thick-walled cylinder of finite length,” in: Thermal Stresses in Structural Elements [in Russian], Issue 10 (1970), pp. 57–67.

    Google Scholar 

  62. V. K. Stryuk, “The elastoplastic stress state of a short cylinder,” in: Thermal Stresses in Structural Elements [in Russian], Issue 9 (1970), pp. 183–191.

    Google Scholar 

  63. V. K. Stryuk, The Elastoplastic Stress State of Short Cylinders under Nonisothermal Loading [in Russian], Author's Abstract of Ph. D. Thesis, Kiev (1973).

  64. V. L. Fomin, “The elastoplastic equilibrium of a hollow cylinder under the action of an axisymmetric temperature field,” Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk, Mekh. Mashinostr., No. 5, 127–128 (1961).

    Google Scholar 

  65. R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford (1950).

    Google Scholar 

  66. Yu. N. Shevchenko, “Solution of boundary-value thermoviscoplastic problems for complex nonisothermal loading,” Prikl. Mekh., 21, No. 4, 119–127 (1985).

    Google Scholar 

  67. Yu. N. Shevchenko, The Thermoplasticity under Variable Loading [in Russian], Naukova Dumka, Kiev (1970).

    Google Scholar 

  68. Yu. N. Shevchenko, Numerical Methods of Solution of Applied Problems, Vol. 6 of the six-volume series Spatial Problems of the Theory of Elasticity and Plasticity [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  69. Yu. N. Shevchenko, M. E. Babeshko, V. V. Piskun, et al., Solution of an Axisymmetric Thermoplastic Problem for Thinand Thick-Walled Solids of Revolution on a Unified-System Computer [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  70. Yu. N. Shevchenko, M. E. Babeshko, V. V. Piskun et al., “Solution of axisymmetric thermoplastic problems on a computer,” in: Applied Problems of Strength and Plasticity [in Russian], Issue 1 (1975), pp. 67–76.

    Google Scholar 

  71. Yu. N. Shevchenko, M. E. Babeshko, V. V. Piskun, and V. G. Savchenko, Spatial Thermoplastic Problems [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  72. Yu. N. Shevchenko, M. E. Babeshko, and R. G. Terekhov, The Thermoviscoelastoplastic Deformation of Structural Elements [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  73. Yu. N. Shevchenko and M. I. Goikhman, “Study of the laws governing the elastoplastic deformation of transversally isotropic bodies,” Prikl. Mekh., 26, No. 9, 50–54 (1990).

    Google Scholar 

  74. Yu. N. Shevchenko, V. V. Piskun, and V. A. Kovalenko, A Program for Thermoelastic Axisymmetric Stress–Strain Analysis of Curvilinearly Orthotropic Multilayered Solids of Revolution [in Russian], Registered in GFAP No. 50850001048, Kiev (1985).

  75. Yu. N. Shevchenko, V. V. Piskun, and V. A. Kovalenko, “The thermostressed state of curvilinearly orthotropic inhomogeneous solids of revolution,” Prikl. Mekh., 19, No. 7, 3–11 (1983).

    Google Scholar 

  76. Yu. N. Shevchenko, V. V. Piskun, and V. A. Kovalenko, “The elastoplastic state of axisymmetrically loaded laminated solids of revolution made of isotropic and orthotropic materials,” Prikl. Mekh., 28, No. 1, 31–39 (1992).

    Google Scholar 

  77. Yu. N. Shevchenko, V. V. Piskun, and V. G. Savchenko, Solution of an Axisymmetric Spatial Thermoplasticity Problem on an M-220 computer [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  78. Yu. N. Shevchenko and V. V. Piskun, “The thermoelastoplastic state of discretely inhomogeneous solids of revolution with nonlinear shear characteristic,” Prikl. Mekh., 31, No. 6, 34–41 (1995).

    Google Scholar 

  79. Yu. N. Shevchenko and V. G. Savchenko, Thermoviscoplasticity, Vol. 2 of the five-volume series The Mechanics of Coupled Fields in Structural Elements [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  80. Yu. N. Shevchenko and I. K. Sakhatskaya, “A mixed thermoplastic problem for open solids of revolution,” Prikl. Mekh., 24, No. 6, 3–9 (1988).

    Google Scholar 

  81. Yu. N. Shevchenko and R. G. Terekhov, Physical Thermoviscoplastic Equations [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

  82. M. E. Babeshko and V. G. Savchenko, “Method of successive approximations in boundary-value problems of thermoplasticity,” Int. Appl. Mech., 34, No. 3, 232–238 (1998).

    Google Scholar 

  83. M. E. Babeshko and V. G. Savchenko, “Improving the convergence of the additional-strain method in thermoplastic boundary problems with deformation along small-curvature trajectories,” Int. Appl. Mech., 34, No. 8, 771–776 (1998).

    Google Scholar 

  84. V. G. Savchenko and M. E. Babeshko, “Solution of nonaxisymmetric three-dimensional thermoplasticity problem by the secondary-stress method,” Int. Appl. Mech., 35, No. 12, 1207–1213 (1999).

    Google Scholar 

  85. V. G. Savchenko and M. E. Babeshko, “The nonaxisymmetric elastoplastic state of isotropic and cylindrically orthotropic solids of revolution under nonisothermal loading,” Int. Appl. Mech., 36, No. 2, 216–224 (2000).

    Google Scholar 

  86. V. G. Savchenko and M. E. Babeshko, “The nonaxisymmetric thermostressed state of laminated isotropic and rectilinearly orthotropic solids of revolution,” Int. Appl. Mech., 36, No. 4, 501–508 (2000).

    Google Scholar 

  87. Yu. N. Shevchenko, “Study of thermoviscoelastoplastic processes in the deformation of structural elements,” Int. Appl. Mech., 35, No. 9, 861–870 (1999).

    Google Scholar 

  88. Yu. N. Shevchenko, “Transformation of thermoviscoelastoplastic stress-deformed state of some constructional elements depending on heating regime,” in: Proc. 3rd Int. Congr. on Thermal Stresses (THERMAL STRESSES'99, June 13–17, Cracow, Poland) (1999), pp. 223–226.

    Google Scholar 

  89. Yu. N. Shevchenko, “Determining equations of thermoviscoplasticity describing the strain processes experienced by an element of an orthotropic body along low-curvature trajectories,” Int. Appl, Mech., 34, No. 10, 1042–1048 (1998).

    Google Scholar 

  90. J. H. Weiner and J. V. Huddleston, “Transient and residual stresses in heat-treated cylinders,” Paper. Amer. Soc. Mech. Engrs., No. A-21 (1958).

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev

    V. G. Savchenko & Yu. N. Shevchenko

Authors
  1. V. G. Savchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. N. Shevchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Savchenko, V.G., Shevchenko, Y.N. Spatial Thermoviscoplastic Problems. International Applied Mechanics 36, 1399–1433 (2000). https://doi.org/10.1023/A:1011336030354

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011336030354

Keywords

Search

Navigation