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Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/35393
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Документ Nonlinear vibrations of functionally graded shallow shells of a complex planform in thermal environments(CongressLine Ltd., Hungary, 2017) Awrejcewicz, Jan; Kurpa, Lidiya; Shmatko, TatianaGeometrically nonlinear vibrations of FGM shallow shells of an arbitrary planform subjected to thermal environment are investigated with the use of R-functions theory and variational methods. Nonlinear firstorder shear deformation shallow shells are employed. Material properties are assumed to be temperaturedependent and varying along the thickness direction accordingly to Voigt’s law. The developed method is based on the combined applications of R-functions theory, variational Ritz’s method, procedure by Bubnov-Galerkin, and Runge-Kutta’s approach. The effect of the temperature rise, geometry of the shell, and constituent volume fraction index is examined. A comparison of the obtained results with available ones is also carried out for rectangular plates and shallow shells.Документ Geometrical analysis of vibrations of functionally graded shell panels using the R-functions theory(London Calling, 2017) Shmatko, T.; Kurpa, Lidiya; Bhaskar, AtulAn approach for investigation of geometrically nonlinear vibrations of functionally graded shallow shells and plates with complex planform is proposed. It combines the application of the R-functions theory (RFM), variational Ritz’s method, the procedure by Bubnov-Galerkin and Runge-Kutta method. The presented method is developed in the framework of the first–order shear deformation shallow shell theory (FSDT). Shell panels under consideration are made from a mixture of ceramics and metal. Power law of volume fraction distribution of materials through thickness is chosen. Investigation of nonlinear vibrations of functionally graded shallow shells and plates with arbitrary planform and different types of boundary conditions is carried out. Test problems and numerical results have been presented for one-mode approximation in time. Effect of volume fraction exponent, geometry of a shape and boundary conditions on the natural frequencies is brought out.Документ Research of Nonlinear Vibrations of Laminated Shallow Shells with Cutouts by R-functions Method(NTU "KhPI", 2016) Kurpa, Lidiya; Timchenko, Galina; Osetrov, Andriy OlexandrovichIn present work an effective method to research geometrically nonlinear free vibrations of elements of thin-walled 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 of boundary condition on cutout is studied.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.