Shakedown analysis of shell structures of kinematic hardening materials

Abstract

It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.

In this paper, some further understanding of the shakedown theorem for kinematic hardening materials has been made, and it is applied to analyze the shakedown of shell structures. Though the residual stress of a real state is related to plastic strain, the time-independent residual stress field$\bar \sigma _{ij}^r$ as we will show in the theorem may be unrelated to the time-independent kinematically admissible plastic strain field$\overline \varepsilon _{i^j }^\rho$. For the engineering application, it will be much more convenient to point this out clearly and definitely, otherwise it will be very difficult. Also we have proposed a new method of proving this theorem.

The above theorem is applied to the shakedown analysis of a cylindrical shell with hemispherical ends. According to the elastic solution, various possible residual stress and plastic strain fields, the shakedown analysis of the structure can be reduced to a mathematical programming problem.

The results of calculation show that the shakedown load of strain hardening materials is about 30–40% higher than that of ideal plastic materials. So it is very important to consider the hardening of materials in the shakedown analysis, for it can greatly increase the structure design capacity, and meanwhile provide a scientific basis to improve the design of shell structures.