Gristchak D. An Approximate analytical solutions of mechanical problems for structures with variable parameters using of computer algebra.

Object of research – buckling and dynamic processes in structures with variable parameters of rectangular plates type, cylindrical shells from composite material, elastic conical shell with concentrated mass, which are basic structural elements of new technique structures. Subject of research – approximate analytical solutions for static stability and dynamic deformation of rectangular plates and shells of revolution under external load and with parameters variable in coordinates and time. The aim of research – solution of actual problems of mechanics of deformable solids, in particularly, buckling and dynamics of plates and shells with parameters dependable on coordinates and time, that cause singular differential equations with variable coefficients and with parameter close to the highest derivative and their systems with the help of computer algebra. Methods of research – asymptotic approaches based on phase integral method and hybrid WKB-Galerkin method for obtaining new approximate analytical solutions for the problems of mechanical structure with variable parameters with the help of modern systems of computer algebra. Direct Runge-Kutt numerical method is applied for the solution of dynamic problem for multilayer plates. New scientifically grounded approximate analytical solutions using computer algebra systems, which are important for the development of research in mechanics of deformable solids, in particularly, buckling and dynamic behavior of the structures with external load and parameters variable in coordinates and time, are obtained. Implementation - State enterprise “Construction Bureau “South”. Branch of implementation - aerospace technique, chemical and building industry.