Nonclassical approach to the nonsteady deformation of discretely reinforced plates and shells

Institute of Geophysics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 8, pp. 88–94, August, 1991.     

Analysis of the nonaxisymmetric vibrations of flexible ellipsoidal shells discretely reinforced with transverse ribs under nonstationary loads

The problem of forced nonaxisymmetric vibrations of reinforced ellipsoidal shells under nonstationary loads is formulated. A numerical algorithm of solving it is developed and the results obtained are analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 63–73, October 2008.     

Dynamic Design of Compound Shell Structures of Revolution Under Nonstationary Loads*

International Applied Mechanics - A technique for solving dynamic problems of the behavior of compound shell structures (solving the equations of motion subject to appropriate boundary and initial...     

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.     

Comparative Analysis of the Dynamic Responses of Transiently Loaded Sandwich Shells Predicted by Various Applied Theories

The stress–strain state of sandwich shells of revolution under nonstationary loads is analyzed numerically by the Timoshenko and Kirchhoff–Love theories that treat the stack of layers as a whole and by a theory that deals with each layer individually. In a particular case, the results are compared with known analytical solutions and experimental data     

Forced Vibration of Three-Layered Spherical and Ellipsoidal Shells under Axisymmetric Loads

A variant of vibration theory for three-layered shells of revolution under axisymmetric loads is elaborated by applying independent kinematic and static hypotheses to each layer, with account of transverse normal and shear strains in the core. Based on the Reissner variational principle for dynamic processes, equations of nonlinear vibrations and natural boundary conditions are obtained. The numerical method proposed for solving initial boundary-value problems is based on the use of integrodifferential approach for constructing finite-difference schemes with respect to spatial and time coordinates. Numerical solutions are obtained for dynamic deformations of open three-layered spherical and ellipsoidal shells, over a wide range of geometric and physical parameters of the core, for different types of boundary conditions. A comparative analysis is given for the results of investigating the dynamic behavior of three-layered shells of revolution by the equations proposed and the shell equations of Timoshenko and Kirhhoff-Love type, with the use of unified hypotheses across the heterogeneous structure of shells.