Mechanics

Oscillations of shallow shells at abrupt influence of thermal flow

Authors: Mylcina O. A., Savina E. N., Belostochnyj G. N.

On the basis of the closed integrals of the initial and boundary problems for incoherent thermoelastisity of shallow shells the quantitative analysis of influence of the geometrical parameters on the oscillations of constant rotation and cylindrical shells, which are conditioned by the thermal shock to outbound surface of shallow shell are carried out.

field, action, least action principle, field equations, transformation group, Lie group, infinitesimal generator, variation, varied domain, constraint.

Authors: Lychev S. A., Mark A. V.

The finite deformations of the growing cylinder fabricated of an incompressible elastic material of Mooney–Rivlin type are under consideration. We assume that the deformations are axisymmetric and constant along the cylinder axis. The discrete and continuous types of growing are studied. The analytical solutions of the corresponding boundary-value problems are derived.

On a form of the first variation of the action integral over a varied domain

Authors: Kovalev V. A., Radaev Y. N.

Field theories of the continuum mechanics and physics based on the least action principle are considered in a unified framework. Variation of the action integral in the least action principle corresponds variations of physical fields while space-time coordinates are not varied. However notion of the action invariance, theory of variational symmetries of action and conservation laws require a wider variation procedure including variations of the space-time coordinates.