Reduction of Plane Thermoelasticity Problem in Inhomogeneous Strip to Integral Volterra Type Equation

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

doi:10.3846/13926292.2005.9637274

Cited by 9 publications

(2 citation statements)

References 6 publications

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“…By following the solution scheme proposed by Tokovyy and Rychahivskyy (2005), we opt for r y and r as the governing functions. To determine these functions, we shall use Eq.…”

Section: Solution Methods In the Case Of Inhomogeneous And Orthotropicmentioning

confidence: 99%

“…For inhomogeneous solids, the mentioned governing equation appears as the Volterra integral equation of the second kind (Goldberg, 1979), which has been treated by means of the simple iterations technique. An analogous method has been developed for treatment of isotropic, inhomogeneous strips, half-planes, and planes (Tokovyy and Rychahivskyy, 2005;Tokovyy and Ma, 2009a). In Tokovyy and Ma (2008), the governing integral equation for the thermoelasticity problem in radially inhomogeneous and orthotropic cylinders and disks has been solved by means of the resolvent-kernel method (Pogorzelski, 1966, p. 13;Porter and Stirling, 1990, pp.…”

Section: Introductionmentioning

confidence: 99%

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An explicit-form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids

Tokovyy¹,

Ma²

2009

International Journal of Solids and Structures

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a b s t r a c tThis paper presents an analytical approach to solve the plane elasticity and thermoelasticity problems for inhomogeneous, orthotropic planes, half-planes, and strips. Solution of the problems is reduced to the governing Volterra integral equation formulated for the key function and accompanied by the corresponding integral conditions. By making use of the resolvent-kernel technique, the governing equation is solved and the solution to the original problem is presented in explicit form.

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“…By following the solution scheme proposed by Tokovyy and Rychahivskyy (2005), we opt for r y and r as the governing functions. To determine these functions, we shall use Eq.…”

Section: Solution Methods In the Case Of Inhomogeneous And Orthotropicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An explicit-form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids

Tokovyy¹,

Ma²

2009

International Journal of Solids and Structures

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Analytical solutions to the 2D elasticity and thermoelasticity problems for inhomogeneous planes and half-planes

Tokovyy

2008

Arch Appl Mech

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This paper presents a method for analytical solving the plane elasticity and thermoelasticity problems for planes and half-planes which exhibit inhomogeneous material properties in one of the planar directions (in the case of half-plane, the inhomogeneity direction is assumed to be perpendicular to the boundary.) With the aid of direct integration of equilibrium equations, the original problems are reduced to the set of governing, harmonic equations with corresponding conditions. In the transform domain of the integral Fourier-transform, the governing equations are reduced to an integral equation which is solved by simple iteration technique. The rapid convergence of the iterative procedure is established to perform the numerical calculation.Keywords 2D plane elasticity and thermoelasticity problems · Inhomogeneous material · Plane and half-plane

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Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders

Tokovyy

2007

J Eng Math

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An analytical approach to solve plane static non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders is presented. This approach is based upon the direct integration method proposed by Vihak (Vigak). The essence of the method mentioned is in the integration of the original differential equilibrium equations, which are independent of the stress-strain relations. This gives the opportunity to deduce the relations, which are invariant with respect to various properties of the material, for the stress-tensor components. From these relations each of the stress-tensor components have been expressed in terms of the governing one. A solution of the equation for the governing stress in the form of Fourier series is presented. To determine the Fourier coefficients, an integral Volterra-type equation is derived and solved by a simple iteration method with rapid convergence. Other stress-tensor components are expressed through the obtained governing stress in the form of an explicit functional dependence on force and thermal loadings.

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Reduction of Plane Thermoelasticity Problem in Inhomogeneous Strip to Integral Volterra Type Equation

Cited by 9 publications

References 6 publications

An explicit-form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids

An explicit-form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids

Analytical solutions to the 2D elasticity and thermoelasticity problems for inhomogeneous planes and half-planes

Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders

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