Mathematical methods for optimal synthesis of physical and mechanical structure of composites with required set of properties at extreme conditions

Abstract

Variational statements of composite structure with the required set of properties synthesis problems are investigated. The study of the limiting capabilities of composites to achieve required set of properties is necessarily associated with development of effective methods for finding global extremum of corresponding functionals. The article deals with problems of numerical analysis and optimal design of composite structure with required set of properties. Mathematical models describing the propagation of wave processes of various physical nature in layered-inhomogeneous structure of composite are investigated. Problems of optimal design for composite structure with required set of properties are formulated in variational formulation. Based on the theory of multi-valued mappings and methods of continuation by parameter, method for studying limiting capabilities of composites to achieve required set of properties is developed. Developed technique allows effective construction of layered composites with complex characteristics. The application of developed method of optimal synthesis for the study of limiting possibilities in reflection of energy of wave action from layered-inhomogeneous coating in given range of spectrum is considered.