Osetrov A. Method of bending and vibration problems of shallow shells solution based on R-functions theory and spline-approximation

The object of research is bending and natural vibrations of thin walled elastic elements of multilayered and FG constructions, that can be modeled by shallow shells and plates with arbitrary geometric plan-forms. The goal of this study is the R-functions method further development combined with spline-approximation to study bending and vibrations of plate-shell elements of thin walled constructions, that are modeled by multilayered composite or FG shells and plates and corresponding software creation. Methods of investigation: R-functions theory, variational methods, spline-approximation, methods of Gauss-Seidel and Lanczos to solve SLAE and eigenvalue extraction problems for sparse matrices. The offered methods are presented as algorithms and universal set of programs, usage of which allows to investigate static and dynamic behavior of multilayered and FG thin walled construction elements with arbitrary geometrical shape and boundary conditions. The scientific novelty is in the development of method based on spline-approximation, R-functions theory and variational methods to investigate bending and vibrations of multilayered plate-shell elements of thin walled constructions allowing to obtain more accurate results for shells with technological holes and cutouts. The offered methods are used in educational and research process of applied mathematics department of NTU "KhPI". Also the method is considered as testing one when developing multilayered thin walled elements of airplane constructions on KSAMC. Areas of application - engineering, aeronautics, shipbuilding and others.