Diskovsky A. Deformations and optimizations process of functionally graded structures homogeneous mathematical model

The thesis is devoted to the topical theoretical and practical issue - to the development of homogeneous mathematical models of the deformation processes and optimization of functionally graded structures (FGS) – constructions from functional-gradient materials and functionally graded nonhomogeneous (heterogeneous) structures. Two main gradient mode mechanisms are properties. The first periodic heterogeneity variable, such gradient mode called amplitude. Another type of gradient mode called walking, it provides identical inhomogeneity, but with variable pitch. The problems of mathematical simulation of processes of deformation and optimization of parameters for FGS cases, amplitude and walking gradient mode are considered separately. Accuracy of the proposed mathematical models of homogeneous FGS on the degree of their heterogeneity and gradient mode are dependence. The analysis of sensitivity of stress-strain state of structures made of functionally graded materials on the characteristics of such materials. FGS homogeneous mathematical model, with low concentration of inclusions (inhomogeneity), when the size of inclusions much small’s than the distances between them, are developed. The proposed homogeneous mathematical model of the processes of deformation and parameter optimization FY corrugated plates and shells based on the equations of the projections of the components of the stress-strain state on the axis of the base surface. Feasibility of separation of homogeneous mathematical models of optimization of parameters of FGS on the model of local and global optimizations is shows. Local optimization includes optimization of the parameters of individual cell heterogeneity. Global optimization includes determining the optimum law of parameters of cell heterogeneity on one or more coordinate. It is split into amplitude and step optimization, which is considered separately. It is shown that the optimal FGS are composite structures consisting of functionally graded and regular parts.The obtained results can be used in engineering practice when designing an FGS with predetermined optimal properties.