The article is devoted to the construction of the equation of fractal complex structures based on the theories of Rvachev R-functions (RFM), the application of the recursion procedure. Using the equation of objects elementary geometries and constructive means of the method of R-functions R0: R-conjunctions, R-disjunctions and R-reflections, various fractal equations are constructed. Based on these equations, specifying the number of iteration and the angle of inclination various pre-fractals are generated

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Mathematical model and computational experiments to solve the problems of bending of three-layer plates of complex configuration are considered in the paper. Mathematical model and computational algorithm given in the paper are developed on the basis of the Hamilton-Ostrogradky’s variation principle, the Bubnov-Galerkin methods and the Rvachev R-functions. Numerical results of the problem are presented. Results are given in tabular and graphical form. Numerical studies of the results obtained are analyzed using the R-function method in combination with the Bubnov-Galerkin variational method to solve the problem of calculating the vibration of three-layer plates of complex configuration.

Mathematical simulation of stress-strain state of loaded rods with account of transverse bending is considered in the paper. The urgency, the correctness of mathematical statement of the problem, the mathematical model, the computational algorithm and the computational experiments of the problem set are given in the paper. Results are presented in a graphical form. The oscillations of spatially loaded rods are shown. The analysis is made in linear and non-linear statements.

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