| Abstract: | For three-dimensional problems of the mechanics of a deformable solid in a Cartesian coordinate system, we show that there are only three continuity equations in terms of deformations and not six, as was considered earlier. We obtain continuity equations of the integro-differential type. They are reduced to the corresponding three of the six well-known Saint-Venant continuity differential equations only if the necessary conditions of consistency between displacements and deformations at the domain boundary are satisfied. As a results, the problem of closedness of the equations of elasticity and thermoelasticity in terms of stresses for three-dimensional problems as well as the equations of the mechanics of a deformable solid is finally solved as a whole. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv. Translated from Matermatychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 117–123, April–June, 1998. |
