A comprehensive analysis for the shakedown of a Bree plate made of functionally graded materials

The shakedown of a functionally graded (FG) plate subjected to coupled constant mechanical load and cyclically varying temperature is analyzed comprehensively. The material of the plate is composed of an elastoplastic matrix and elastic particles, and the particle volume fraction varies through the thickness. The distributions of the effective mechanical and thermal properties of the composites through the thickness are evaluated with mean-field approaches and described with an exponential law. The temperature dependence of the material properties is taken into account. The distribution of temperature change and the shakedown of a typical FG Bree plate are analyzed. The comparison with the results of its homogeneous counterpart and that without considering the temperature dependence of the material properties exhibits marked qualitative and quantitative difference. The effect of the temperature dependence of the elastic properties of materials is also investigated. Since FG structures are usually subject to severe coupled thermal-mechanical loadings, the approach developed and the results obtained are significant for the analysis and design of such kind of structures.