Stability of thin rectangular plates under local heating

We study the temperature fields, the precritical thermally stressed state, and the loss of stability of thin rectangular plates under local heating. We study the influence of the thermophysical characteristics on the magnitude of the critical parameters. Four figures. Bibliography: 5 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 1–4.     

Effect of a supporting rod on the integrity of a circular plate subjected to local heating

The authors examine the thermal field, subcritical stress state, and loss of stability in a circular plate reinforced along its boundary. The plate is subjected to axially symmetric heating by sources distributed over a region of the plate. The determination of critical parameters leads to the discovery of eigenvalues for a type-II Fredholm integral equation. It is shown that in the system under consideration both global and local failures of stability may occur. The effect of mechanical and thermal characteristics of the system on its thermal stress state and on the magnitude of the critical parameters is investigated.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 1–4, 1989.     

The Results of Studying Nonstationary Processes on the Sun by Radioastronomical Methods

This paper presents the results of studies of solar phenomena performed at the Radiophysical Research Institute (NIRFI) in the last years and based on the data of measuring the solar microwave radiation. We obtained new results concerning fragmentation of the regions of initial energy release during solar flares, their spatial and temporal dynamics, the physical conditions in flaring loops, the dynamics of energetic particles accelerated during flares, and the characteristics of sporadic radio emission during the formation and propagation of coronal mass ejections in the lower layers of the solar atmosphere.     

Time differentiation of tensors defined on a surface moving through a three-dimensional euclidean space

The well-known formulas for the derivatives of Eulerian and Lagrangian basis vectors are used to derive expressions for the derivatives of the surface, volume and double tensors defined on a surface moving through an Euclidean space. In the case of a plane moving through space with constant velocity, the results obtained correspond to the two-dimensional analogs of the results obtained in /1/. A relation connecting the derivatives in question with the derivative ( ) is given, and the concept of the derivative ( ) is introduced for the three-dimensional case.