Shakedown Analysis And Optimization Of Functionally Graded Plates Subjected To Coupled Thermal And Mechanical Loading

The shakedown of a FG Bree plate is analyzed with static and kinematicshakedown theorems. The main work in this dissertation is listed as follows:（1） The mathematical model of shakedown analysis of a functionally graded Breeplate is proposed. The distribution of the material properties in the thickness direction isdescribed with a single exponential function. The shakedown of the plate with thehomogenized material properties is also analyzed. The comparison the distributionadopted is not satisfied and the optimization should be performed foe better shakedowncapability.（2） A micromechanics method considering the interactions between particles isused to predict thermal and mechanical properties of functionally graded materials, andthe piecewise exponential distribution model is adopted to describe more exactly theactual distribution of material properties in a FG plate. It aims to achieve a morerealistic distribution of the material properties for a more realistic shakedown analysis,because the piecewise exponential distribution model is capable in describing thedistribution of the actual distribution of material properties with sufficient accuracy.（3） The distribution of the material properties in a FG structure is described withthe piecewise exponential function model. The plate is separated into a number of layers,and the thermal-mechanical properties at the lower and the upper surfaces of eachsegment are obtained with the micromechanics mean-field scheme taking into accountthe interaction between particles. The shakedown of an Al/SiC FG Bree plate isanalyzed. The piecewise concept of the distribution of the material properties is inaccord with the piecewice approach used in the shakedown analysis, therefore, theproposed method is of particularly advantageous for the analysis of the shakedown ofFG structures.（4） An optimizeztion model for the analysis of the shakedown of the FG Bree plateis proposed, where the Genetics Algorithm is adopted, with which the distribution of theparticles in a FG plate can be optimized for different objective functions. In order toverify this model, two examples are given, in one of which an Al/SiC FG Bree plate isused, and in the other of which a Ti/Si₃N₄FG Bree plate is used. In both examples, theaverage volume fraction of the particles in the plate is fixed as15%, and the distributionof these particles is opitimized for the purpose to enhance the capability of the plate to bear the largest variation of temperature. The results show that the load-bearingcapability od the FG plate is substantially enhanced, demonstrating the capability of theproposed model.