Correct Analytical Solutions to the Thermoelasticity Problems in a Semi-Plane

Rychahivskyy, Andriy V.; Tokovyy, Yu. V.

doi:10.1080/01495730802250854

Cited by 12 publications

(8 citation statements)

References 11 publications

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“…Assume boundary

of the half-plane to be acted upon by locally distributed normal and tangential force loadings imposed by the following boundary conditions:

where

and

are the given functions of some local distribution profiles, i.e.,

. Note that for the correct formulation of the boundary value problem, the force loadings (5) and temperature

are to meet the necessary conditions derived in [ 32 ].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Elastic and Thermoelastic Responses of Orthotropic Half-Planes

et al. 2021

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A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.

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“…Assume boundary

of the half-plane to be acted upon by locally distributed normal and tangential force loadings imposed by the following boundary conditions:

where

and

are the given functions of some local distribution profiles, i.e.,

. Note that for the correct formulation of the boundary value problem, the force loadings (5) and temperature

are to meet the necessary conditions derived in [ 32 ].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Elastic and Thermoelastic Responses of Orthotropic Half-Planes

et al. 2021

Self Cite

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show abstract

“…Thus, condition (6) for a semi-plane is a consequence of application of solid mechanics to the oversimplified geometrical model. By denoting (1), when () kk y  , and following the strategy presented in (Rychahivskyy & Tokovyy, 2008), it can be shown that condition (6) holds for the case of inhomogeneous material. In addition, the resultant of the temperature is necessarily equal to zero…”

Section: Solution Of the Stated Heat Conduction Problem By Reducing Tmentioning

confidence: 99%

“…In the case when const k  , it has been shown (Rychahivskyy & Tokovyy, 2008) that for construction of a correct solution to equation (2) with boundary condition (4), the following necessary condition…”

Section: Solution Of the Stated Heat Conduction Problem By Reducing Tmentioning

confidence: 99%

“…Finally, by making use of the explicit-form analytical solution to the corresponding problem with boundary tractions, the displacements on the boundary can be expressed through the tractions. The technique for establishment of the one-to-one relations between the tractions and displacements on the boundary, as well as for deriving the necessary equilibrium and compatibility conditions in the case of homogeneous semi-plane has been developed in (Rychahivskyy & Tokovyy, 2008).…”

Section: Analysis Of Thermal Stresses In An Inhomogeneous Semi-planementioning

confidence: 99%

“…Therefore, when the stress-tensor components are found, then the displacement-vector components are also found automatically. Such relations have been derived for the case of one-dimensional problem for a thermoelastic hollow cylinder (Vigak, 1999a) and plane problems for elastic and thermoelastic semi-plane Vigak, 2004;Rychahivskyy & Tokovyy, 2008). Since application of this method rests upon the direct integration of the equilibrium equations, the proposed solution scheme offers ample opportunities for efficient analysis of inhomogeneous solids.…”

Section: Introductionmentioning

confidence: 99%

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