The Korn-type inequality in a Cosserat model for thin thermoelastic porous rods. (English) Zbl 1293.74260

From the introduction: Within the theory of directed curves, we establish an inequality which is the counterpart of Korn’s inequality in the three-dimensional linear elasticity. This new Korn-type inequality is employed to prove the existence and uniqueness of weak solutions to the dynamical equations for thermoelastic porous rods, using the method of semigroup of operators. To describe the porosity effects for thermoelastic rods, we use the theory of materials with voids.
The results obtained show that the model of directed rods is mathematically well-formulated, since the field equations have the desirable properties of existence and uniqueness of solution in the linear theory.


74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74F05 Thermal effects in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)


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