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Information × Registration Number 0200U001788, 0196U016050 , R & D reports Title Development of theoretical basis and analysis of static and dynamic response processes of nonlinear systems subjected to various deterministic and stochastic power fields. popup.stage_title Head Bazhenov V.A., Registration Date 29-03-2000 Organization Kiev National University of bildiny and tecture popup.description2 During scientific researches the mathematical model which adequately described deformation of homogeneous and inhomogeneous axisymmetric solids was developed. Static and dynamic loads were assumed to be applied simultaneously. On the ground of elasticity equation for large deflections and in the framework of the moment scheme of the Method of Finite Elements a geometric stiffness matrix and a general stiffness matrix of the inhomogeneous ringlike finite element were built. The obtained governing relations were presented in the natural form for use in algorithms of the determination of space constructions dynamic parameters. The methodology of a strongly nonlinear space constructions study was developed on.the ground of the modern universal approaches to the analysis of a static and dynamic behaviour of long-spatial deformable shell systems with ribs, holes, stabilizing elements etc. On the base of modified scheme of a statistical trials method the technique of the determination of dangerous s tress conditions appearance probability in plates and shells under random loading was developed. With the help of static hypothesis about stress conditions in multi layered shells, which were considered as thin three-dimensional solids, the technique of a thermal-structural analysis of flexible inhomogeneous shells nonlinear deformation was developed. For further modernizing of the technique two variants of static hypothesis about thermal-structural conditions in inhomogeneous shells were considered.Method for solving of 3D transient problems of heat transfer and thermo-elasticity for cyclo-symmetric solids is developed. Approximation of solid is performed by using bilinear functions within cross-section and by truncated Fourier series in orthogonal direction. Governing equations for closed non-circular cyclo-symmetric finite element are developed and permit to simulate temperature fields in spatial solids with variable in circumferential direction thermo-physical properties of materials, conditions of he at transfer and geometrical characteristics of the objects. Heterogeneous closed circular finite element is used as a basis. While composing governing equations variability of metric characteristics of finite element in circumferential direction is taking into account. All matrices coefficients (heat conductivity, heat transfer, geomeric, physical) are calculated in nodes of integration along circumferential direction. Developed method permits to increase efficiency of numerical investigation of complicated 3D structures in transient temperature fields. Product Description popup.authors popup.nrat_date 2020-04-03 Close