Two-dimensional statics problems of noncircular cylindrical shells

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev, Translated from Prikladnaya Mekhanika, Vol. 27, No. 10, pp. 90–95, October, 1991.     

Solving axisymmetric dynamic problems for reinforced shells of revolution on an elastic foundation

The dynamic behavior of reinforced shells of revolution in an elastic medium is modeled. Pasternak’s model is used. A problem of vibration of discretely reinforced shells of revolution is formulated and a numerical algorithm is developed to solve it. Results from an analysis of the dynamic behavior of a reinforced spherical shell on an elastic foundation are presented as an example Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 99–106, February 2009.     

Solving problems on the stress state of thin shells of revolution under local loads

An approach to the solution of problems on the deformation of locally loaded orthotropic shells of revolution is proposed. Some analytical transformations are carried out to reduce the initial resolving system of partial differential equations to the form where the constant terms representing the surface loads are continuous functions of the circumferential coordinate. This allows us to accelerate the convergence of the trigonometric series that represent the desired solution. One-dimensional boundary-value problems are solved by a stable numerical method. Examples of solving problems on the stress state of a cylindrical shell are presented. The scientific results of the present work were obtained during implementation of Project No. 14 of the Ukrainian Scientific and Technological Center. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 106–113, April, 2000.     

Using mesh-based methods to solve nonlinear problems of statics for thin shells

The paper outlines a numerical procedure for solving physically and geometrically nonlinear problems of statics for thin shells based on three mesh-based methods: finite-difference, variational difference, and finite-element methods. The methodological, algorithmic, and analytical aspects of implementing the Kirchhoff–Love hypotheses are analyzed. The algorithmic approach employs Lagrangian multipliers. The advantages and disadvantages of these methods are evaluated Translated from Prikladnaya Mekhanika, Vol. 45, No. 1, pp. 41–70, January 2009.     

The axial symmetrical edge problems for thin-walled shells of revolution

In this paper, the uniformly valid asymptotic solutions for the axial symmetrical edge problems of thin-walled shells of revolution in bending are given.     

Spline-approximation solution of problems of the statics of orthotropic shallow shells with variable parameters

An approach to the solution of problems of the statics of shallow orthotropic shells is proposed. It is based on reducing a two-dimensional boundary value problem to a one-dimensional one using the spline-collocation method and solution of the problem by the stable numerical method of discrete orthogonalization. Solutions are presented for problems on the stress state of orthotropic shells of double curvature for several values of the elastic constants of the material. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 60–66, July, 2000.     

Solution of two-dimensional problems of the statics of flexible shallow shells by spline approximation

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 4, pp. 10–16, April, 1995.