ANALYSIS OF GENERALIZED LAME OPERATOR AND FINITE ELEMENT CORRESPONDING TO THE OPERATOR

Abstract

An equation system of elliptic type is considered. The basic properties of the generalized differential Lame operator, formulated as the analogues of Betty and Klapeyron formulae, are analyzed using a quasi-energy product. The third Betty formula describes non-symmetry of the generalized operator. The analogue of Klapeyron indicates a contribution of capillary water into the deformation energy of a two-phase body. A practical application of the quasi-energy product consists in constructing a new finite-element, which allows to use a program complex of FEM.