Showing papers by "Ya. M. Grigorenko published in 2001"
TL;DR: In this paper, the exact solution to a nonlinear problem on subcritical and postcritical deformation of a flexible long cylindrical shell with a noncircular cross-section and fixed periphery under uniform loading is constructed.
Abstract: The exact solution is constructed to a nonlinear problem on subcritical and postcritical deformation of a flexible long cylindrical shell with a noncircular cross-section and fixed periphery under uniform loading. The solution is represented by two relations in terms of elementary functions. The graphs demonstrate how the deflection behaves depending on the laws of change in the curvature and load distribution
8 citations
TL;DR: In this paper, the nonlinear problem on deformation of a hinged flexible long noncircular cylindrical shell under non-uniform loading is solved exactly, and the solution consists of two relations in terms of elementary functions.
Abstract: The nonlinear problem on deformation of a hinged flexible long noncircular cylindrical shell under nonuniform loading is solved exactly. The solution consists of two relations in terms of elementary functions. Plots are presented
6 citations
TL;DR: In this article, the effect of inhomogeneity of elastic properties in the circumferential direction on the distribution of stress and displacement fields in orthotropic cylindrical panels is studied.
Abstract: The effect of inhomogeneity of elastic properties in the circumferential direction on the distribution of stress and displacement fields in orthotropic cylindrical panels is studied. The mechanical properties of the panels and the load acting on them are constant in the axial direction, which makes it possible to neglect the influence of the curvilinear ends. From the initial relations of a three-dimensional problem of the elasticity theory of inhomogeneous anisotropic bodies, a resolving system of partial differential equations is obtained, whose solution is presented in the form of truncated Fourier series, so that the conditions of free support of the rectilinear ends are satisfied. This allows us to separate the variables and to get a system of ordinary high-order differential equations, which is integrated by a stable numerical method. The problem on the stress-strain state of an orthotropic composite panel with a varying relative volume content of reinforcing elements in the circumferential direction is solved. The effect of the change in the reinforcement density on the stresses and displacements of the panel is studied.
3 citations
TL;DR: In this article, a refined theory of flexible layered shells with orthotropic layers of variable thickness is considered, and the basic equations and calculation results are presented for a three-layer orthotropic toroidal shell under axisymmetric loading.
Abstract: A refined theory of flexible layered shells with orthotropic layers of variable thickness is considered. The theory assumes that each layer has a local rotation angle due to lateral shear. This makes it possible to derive equations whose order does not depend on the number of layers. The basic equations and calculation results are presented for a three-layer orthotropic toroidal shell under axisymmetric loading
2 citations
TL;DR: In this paper, a stress analysis of the teeth periodontium is carried out by invoking the theory of elasticity, theoretical mechanics, and spline functions that describe the lateral surfaces of the Periodontium.
Abstract: A stress analysis of the teeth periodontium is carried out. The periodontium has the form of a thin-walled elastic shell whose thickness varies along the generatrix. The problem is solved by invoking the theory of elasticity, theoretical mechanics, and spline functions that describe the lateral surfaces of the periodontium. Plots show how the change in the periodontium thickness affects the stress distribution