Analysis for Shakedown of Functionally Graded Plate Subjected to Thermal-Mechanical Loading with Piecewise-Exponential Distribution of Material Properties

The static and kinematic shakedown of a functionally graded plate (FGP) is analyzed. The FGP is subjected coupled constant mechanical load and cyclically varying temperature. The FGP is composed of elastoplastic matrix and elastic particles, with the particle volume fraction varying along its thickness. The thermal and mechanical properties and their distributions are evaluated with a mean filed approach, which is based on the Eshelby's inclusion theory and takes into account directly the interaction between particles. The FGP is assumed to be separated into a number of thin layers, the thermal and mechanical properties in the thickness direction of each layer are assumed to vary exponentially over the layer thickness and continuum between neighboring layers. The above piecewise exponential modeling can replicate the actual distribution of the material properties of the FGP with sufficient accuracy. 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. The approach developed in this article can be used not only for the analysis of the shakedown of FGPs with high accuracy, but also for the optimum design of the FGPs, e.g., the optimization of the distribution of the material properties.