# Plates and Shells

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

## Abstract

Thin and moderately thick shell structures are designed as structural components in many engineering applications because of light weight and high load-carrying capacity. In many cases they are subjected to high temperature environment and mechanical loadings, such that inelastic material behavior must be taken into account. Examples of high-temperature shell components include pressure vessels, boiler tubes, steam transfer lines, thin coatings, etc. A steam transfer line under long-term operation considering creep-damage material behavior is discussed in Naumenko and Altenbach (2016, Chap. 1). Chapter 5 presents examples of inelastic structural analysis of plates and shells. Section 5.1 gives an overview of modeling approaches including various theories of plates and shells as well as various constitutive models of inelastic material behavior. Governing equations of the first order shear deformation theory of plates are presented in Sect. 5.2. An emphasis is placed on the direct formulation of inelastic constitutive laws. Section 5.3 illustrates examples of steady-state creep analysis of circular plates. Advanced constitutive models with internal state variables, such as the damage parameter require the use of advanced plate theories to consider edge effects. Section 5.4 illustrates an example of a rectangular plate with different types of boundary conditions. The results based on the plate theory are compared with the results according to the three-dimensional theory. Section 5.5 presents governing equations and the solution procedure for the creep behavior of a thin-walled pipe subjected to the internal pressure and the bending moment.

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