Кафедри
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/35393
Переглянути
2 результатів
Результати пошуку
Документ Investigation of Geometrically Nonlinear Vibrations of Laminated Shallow Shells with Layers of Variable Thickness by Meshless Approach(Точка, 2013) Kurpa, Lidiya; Shmatko, T.Geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness are studied. Nonlinear equations of motion for shells based on the first order shear deformation and classical shells theories are considered. In order to solve this problem we use the numerically-analytical method proposed in work [1]. Accordingly to this approach the initial problem is reduced to consequences of some linear problems including linear vibrations problem, special elasticity ones and nonlinear system of ordinary differential equations in time. The linear problems are solved by the variational Ritz’ method and Bubnov-Galerkin procedure combined with the R-functions theory [2]. To construct the basic functions that satisfy all boundary conditions in case of simply-supported shells we propose new solutions structures. The proposed method is used to solve both test problems and new ones.Документ Investigating geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory(Elsevier Inc., 2015) Awrejcewicz, Jan; Kurpa, Lidiya; Shmatko, T.A novel numerical/analytical approach to study geometrically nonlinear vibrations of shells with variable thickness of layers is proposed. It enables investigation of shallow shells with complex forms and different boundary conditions. The proposed method combines application of the R-functions theory, variational Ritz’s method, as well as hybrid Bubnov–Galerkin method and the fourth-order Runge–Kutta method. Mainly two approaches, classical and first-order shear deformation theories of shells are used. An original scheme of discretization regarding time reduces the initial problem to the solution of a sequence of linear problems including those related to linear vibrations with a special type of elasticity, as well as problems governed by non-linear system of ordinary differential equations. The proposed method is validated by the investigation of test problems for shallow shells with rectangular planform and applied to new vibration problems for shallow shells with complex planforms and variable thickness of layers.