Plane Stress and Plane Strain Problems

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


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.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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