Modeling of the two-phase body with account of carrying abilities of the fuild

T. V. Mal'tseva ; E. R. Trefilina

Matematičeskoe modelirovanie, Tome 16 (2004) no. 11, pp. 47-60

Résumé

A generalization of the one-dimensional kinematic model (Maltsev L. E.) of the two-phase environment is considered. It is based on two new hypothesizes, according to which the tense and deformed condition of the two-phase body is described by the system of linear elliptical equations. These equations differ from the Lame equations of the elasticity theory by two terms in each equation. These terms describe the carrying ability of the liquid phase or reduction of the tense in the hard phase. For the research of new characteristics of the Lame generalized differential operator the Hilbert space is introduced which is based on an energy product. A relation between the energy product with specific potential energy of the two-phase body is established. The statement of the problem of minimum square-law functional in Hilbert space is suggested. It allows us to use the variation methods of mathematical physics for the two-phase body. The original method of solution of the task of operating a single force on a two-phase elastic half-space with the help of a kinematic model is presented. Applying the obtained fundamental solution to research of the tight and strained state of the two-phase basis loaded by uniformly distributed load on round and on rectangular platforms is shown.