Nonlinear Dynamics : міжнародна конференція
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/24521
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Документ Applicatin of R-functions Theory to Nonlinear Vibration Problems of Laminated Shallow Shells with Cutouts(NTU "KhPI", 2016) Kurpa, Lidiya; Timchenko, Galina; Osetrov, AndreyIn present work an effective method to research geometrically nonlinear free vibrations of elements of thinwalled constructions that can be modeled as laminated shallow shells with complex planform is applied. The proposed method is based on joint use of R-functions theory, variational methods and Bubnov-Galerkin procedure. It allows reducing an initial nonlinear system of motion equations of a shallow shell to the Cauchy problem. The mathematical formulation of the problem is performed in a framework of the refined first-order theory. The appropriate software is created within POLE-RL program system for polynomial results and using C+ + programs for splines. New problems of linear and nonlinear vibrations of laminated shallow shells with cutouts are solved. To confirm reliability of the obtained results their comparison with the ones obtained using spline-approximation and known in literature is provided. Effect o f boundary condition on cutout is studied.Документ Application of the Variational-Structural Method to Investigate the Elasto-Plastic Bending of Thin Shells and Plates(NTU "KhPI", 2016) Morachkovska, Irina; Timchenko, Galina; Lyubitska, KaterynaThe effective method basing on theory of R-functions and variational structural method is developedfor solving non-linear boundary problems. Elastic-plastic bending of thin shallow shells is considered. The problems are reduced to finding stationary points of suggested mixed variational functionals according to the initial linearization due to usage of subsequent loading and Newton-Kantorovich jointly with method of varying elastic parameters. The method is used for automatic calculations in «POLE» programming system for investigations of shell structural elements. The numerical justification of the method is given. New laws of nonlinear deformation of shallow shells and plates with complex shapes in plane are established.