Static and kinematic shakedown analysis of FG plate subjected to constant mechanical load and cyclically varying temperature change

The static and kinematic shakedown of a plate made of functionally graded materials (FGMs) is analyzed. It is subjected to coupled constant mechanical load and cyclically varying temperature. The material is composed of elastoplastic matrix reinforced with linearly-elastic particles. The relevant mechanical and thermal properties of the plate are determined with self-consistent scheme and mixture theories. It is shown that the distributions of the material properties through the thickness of the plate can be approximated with exponential rules, provided the volume fraction of particles varies linearly through the thickness. The shakedown of an Al/SiC FG Bree plate is analyzed. The boundaries between the shakedown area and the areas of elasticity, incremental collapse and reversed plasticity are determined. The shakedown of its homogeneous counterpart with averaging material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinctly qualitative and quantitative difference, indicating the importance of a proper shakedown analysis for the FG plate. Since FG structures are usually subjected to coupled severe thermal–mechanical loads, the approach developed and the results obtained are significant for the analysis and design of FG structures.