Thermoelastic-plastic stress state of shells of revolution reinforced by annular ribs

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 1, pp. 50–55, January, 1991.     

Linear groups

The paper is based on material reviewed in RefZhMat during 1971–1977 and continues a survey of the same name which appeared in this series in 1971. In light of the Tits alternative two old areas have now acquired special importance-free linear groups and solvable linear groups; they are given special attention. Other areas are discussed in somewhat more detail than previously.Translated from Itogi Nauki i Tekhniki, Algebra, Topologiya, Geometriya, Vol. 16, pp. 35–89, 1978.     

Calculation of the Thermoelastoplastic Nonaxisymmetric Stress-Strain State of Layered Orthotropic Shells of Revolution

The methods for determining the nonaxisymmetric thermoelastoplastic stress-strain state of layered orthotropic shells of revolution are developed. It is assumed that the layered package deforms without mutual slippage or separation of layers. The problem is solved using the geometrically nonlinear theory of shells based on the Kirchhoff-Love hypotheses. In the isotropic layers, plastic deformations may appear, whereas the orthotropic layers deform in the elastic region. It is assumed that the mechanical properties of the materials are temperature-dependent. The thermoplasticity equations are presented in a form corresponding to the method of additional deformations. The order of the system of partial differential equations obtained is reduced with the help of trigonometric series in the circumferential coordinate. The resulting systems of ordinary differential equations are solved by the Godunov technique of discrete orthogonalization. The nonaxisymmetric thermoelastoplastic stress-strain states of layered shells of revolution are considered as examples.     

Determination of the stress-strain state of shells of revolution under localized effects

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 3, pp. 50–55, March, 1995.