Integral-differential continuity equations in terms of strains and derivation of a closed system of equations of elasticity and thermoelasticity in terms of stresses (Q2753396)
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scientific article; zbMATH DE number 1668317
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integral-differential continuity equations in terms of strains and derivation of a closed system of equations of elasticity and thermoelasticity in terms of stresses |
scientific article; zbMATH DE number 1668317 |
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4 November 2001
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elasticity
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thermoelasticity
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continuity equations
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Cauchy relations
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Integral-differential continuity equations in terms of strains and derivation of a closed system of equations of elasticity and thermoelasticity in terms of stresses (English)
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By integrating three of six Cauchy relations between strains and displacements it is shown that there are just three (not six) continuity equations in strains. The obtained continuity equations have an integral-differential form. Only under certain conditions of agreement between displacements and strains at the boundary the derived equations are reduced to three of six Saint-Venant differential compatibility equations. Thus, the question regarding closeness of differential equations of elasticity and thermoelasticity in terms of stresses for spatial problems and equations for problems of mechanics of deformable solids as a whole is finally resolved.
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