МАТЕМАТИЧЕСКИЕ МОДЕЛИ И АЛГОРИТМЫ ДЕФОРМАЦИИ КОНСТРУКЦИЙ С УЧЕТОМ ФИЗИЧЕСКОЙ И ГЕОМЕТРИЧЕСКОЙ НЕЛИНЕЙНОСТЕЙ

Аннотация

Subjects of research: the formation of stress-strain state of thin-walled structures. Purpose of work: development of mathematical model and algorithms for the solution the static problem of plates bending with physical and geometrical nonlinearity, which would allow automating process of the problem solution, and giving a chance to spend multiple experimental researches. Methods of research: In this paper for solving the problem was used the following approximate methods: the variation Ritz’s method, the method of clastic solutions by A. Ilyushin, the method of consecutive approximations. The result obtained and their novelty: the mathematical model solutions for physically and geometrically nonlinear bending problem of plates based on which was made the algorithm of calculating the stress-strain state of plates using the Ritz’s method, the elastic solution by Ilyushin and the method of successive approximations were found. The novelty of the proposed work is as follows: was derived a mathematical model for solving the nonlinear problem on the basis of the Ritz’s method, an algorithm for solving the problem, and a set of software tools to automate the process of solving the problem have been created. Practical value: the developed mathematical model, algorithm and software can be recommended for research and design institutes. Degree of embed and economic affectivity: the results of research can be used in various industries that use different type of the metal plates for design. The significant economic can be achieved by reducing the time and complexity of design-development using the algorithm and software tools have been created. Field of applications: mechanical engineering, shipbuilding, aircraft, power engineering, construction.