Advertisement

Plane Stress and Plane Strain Problems

  • Konstantin NaumenkoEmail author
  • Holm Altenbach
Chapter
  • 355 Downloads
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 112)

Abstract

Many structural members can be analyzed applying simplifying assumptions of plane stress or plane strain state. Examples include plates under in-plane loading, thick pipes under internal pressure, rotating discs, etc. Although many problems of this type can be solved in a closed analytical form assuming linear-elastic material behavior (Altenbach et al, 2016; Lurie, 2005; Timoshenko and Goodier, 1951), only few solutions for elementary examples exist, where plasticity and/or creep are taken into account (Boyle and Spence, 1983; Malinin, 1975, 1981; Odqvist, 1974; Skrzypek, 1993). Chapter 4 presents examples of inelastic structural analysis for plane stress and plane stress problems. In Sect. 4.1 basic assumptions are discussed and governing equations are introduced. Elementary structures including a pressurised thick cylinder, Sect. 4.2, a rotating disc, Sect. 4.3 and a plate with a circular hole, Sect. 4.4, are introduced to illustrate basic features of inelastic behavior under plane multi-axial stress and strain states. Classical results assuming the power law type creep as well as solutions with stress regime dependent inelastic behavior are presented.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abaqus Benchmarks (2017) Benchmarks ManualGoogle Scholar
  2. Altenbach H, Gorash Y, Naumenko K (2008) Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges. Acta Mechanica 195:263 – 274CrossRefGoogle Scholar
  3. Altenbach H, Altenbach J, Naumenko K (2016) Ebene Flächentragwerke. Springer, BerlinCrossRefGoogle Scholar
  4. Benaarbia A, Rae Y, Sun W (2018) Unified viscoplasticity modelling and its application to fatigue-creep behaviour of gas turbine rotor. International Journal of Mechanical Sciences 136:36–49CrossRefGoogle Scholar
  5. Betten J (2008) Creep Mechanics, 3rd edn. Springer, BerlinGoogle Scholar
  6. Boyle JT (2012) The creep behavior of simple structures with a stress range-dependent constitutive model. Archive of Applied Mechanics 82(4):495 – 514CrossRefGoogle Scholar
  7. Boyle JT, Spence J (1983) Stress Analysis for Creep. Butterworth, LondonCrossRefGoogle Scholar
  8. Hahn HG (1985) Elastizitätstheorie. B.G. Teubner, StuttgartCrossRefGoogle Scholar
  9. Hult JA (1966) Creep in Engineering Structures. Blaisdell Publishing Company, WalthamGoogle Scholar
  10. Kostenko Y, Almstedt H, Naumenko K, Linn S, Scholz A (2013) Robust methods for creep fatigue analysis of power plant components under cyclic transient thermal loading. In: ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, American Society of Mechanical Engineers, pp V05BT25A040 – V05BT25A040Google Scholar
  11. Lurie A (2005) Theory of Elasticity. Foundations of Engineering Mechanics, SpringerGoogle Scholar
  12. Malinin NN (1975) Prikladnaya teoriya plastichnosti i polzuchesti (Applied Theory of Plasticity and Creep, in Russ.). Mashinostroenie, MoskvaGoogle Scholar
  13. Malinin NN (1981) Raschet na polzuchest’ konstrukcionnykh elementov (Creep Calculations of Structural Elements, in Russ.). Mashinostroenie, MoskvaGoogle Scholar
  14. Naumenko K, Altenbach H (2016) Modeling High Temperature Materials Behavior for Structural Analysis: Part I: Continuum Mechanics Foundations and Constitutive Models, Advanced Structured Materials, vol 28. SpringerGoogle Scholar
  15. Naumenko K, Kostenko Y (2009) Structural analysis of a power plant component using a stress-range-dependent creep-damage constitutive model. Materials Science and Engineering: A 510:169–174CrossRefGoogle Scholar
  16. Naumenko K, Altenbach H, Gorash Y (2009) Creep analysis with a stress range dependent constitutive model. Archive of Applied Mechanics 79:619 – 630CrossRefGoogle Scholar
  17. Naumenko K, Kutschke A, Kostenko Y, Rudolf T (2011) Multi-axial thermo-mechanical analysis of power plant components from 9-12%Cr steels at high temperature. Engineering Fracture Mechanics 78:1657 – 1668Google Scholar
  18. Odqvist FKG (1974) Mathematical Theory of Creep and Creep Rupture. Oxford University Press, OxfordGoogle Scholar
  19. Rabotnov YN (1969) Creep Problems in Structural Members. North-Holland, AmsterdamGoogle Scholar
  20. Skrzypek JJ (1993) Plasticity and Creep. CRC Press, Boca RatonGoogle Scholar
  21. Timoshenko SP, Goodier JN (1951) Theory of Elasticity. McGraw-Hill, New YorkGoogle Scholar
  22. Wang W, Buhl P, Klenk A, Liu Y (2016) The effect of in-service steam temperature transients on the damage behavior of a steam turbine rotor. International Journal of Fatigue 87:471–483CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für MechanikFakultät für Maschinenbau, Otto-von-Guericke-UniversitätMagdeburgGermany

Personalised recommendations