Hart E. Models and projection-iterative modifications of the variational-grid methods in problems of elastic-plastic deformation of structurally inhomogeneous solids

The object of the study is the process of elastoplastic deformation of inhomogeneous bodies of finite dimensions (thin plates, cylindrical shells with apertures, reinforcements and inclusions) and infinite inhomogeneous media with a system of structures (pores, inclusions) under an external load. The purpose of the study is to solve the topical scientific problem of deformable solid mechanics which consists in solving a class of complex physically nonlinear problems of determining the stress and strain field in structurally inhomogeneous bodies with local stress concentrators under elastoplastic deformation by developing efficient calculation models, modifications, computational schemes, and algorithms for the implementation of variational-grid methods and associated software. Research methods - variational principles and numerical methods of mechanics; the functional analysis apparatus. Theoretical and practical significance of the obtained results: the new efficient numerical methods developed in the dissertation serve as a scientific and methodological basis, which provides a new level of knowledge in the mechanics of a deformable solid. The obtained results of the solved problems for plate-shell structural elements can be used directly in the prediction of safe operation of the corresponding constructions in mechanical engineering, power engineering, building, aerospace engineering, etc. The results of calculation of media with pores and inclusions can be used in powder metallurgy, nuclear power engineering, chemical industry and mining to prevent unwanted destructive deformations. Novelty of the newly introduced, the degree of introduction. The results obtained by the author have been used at Yuzhnoye State Design Office and introduced in the educational process of Oles Нonchar Dnipro National University of the Ministry of Education and Science of Ukraine in the teaching of professional disciplines on the fundamental, professional and practical training of specialists and masters, the preparation of master's, graduation and coursework by students of the specialty "Applied Mathematics" ("Computer Mechanics "). Field of application. The proposed general methodology and efficient computational algorithms can be used at research and design institutions in designing structural elements of novel facilities, in particular rocket and space hardware, calculating their stress and strain fields and evaluating their strength.