Analytic Solution of the Plane Problem of the Theory of Elasticity for a Nonuniform Strip

Tokovyi, Yu. V.; Rychahivs’kyi, A. V.

doi:10.1007/s11003-005-0143-5

Cited by 4 publications

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“…In [9], an analytical solution was constructed for the plane problem of the theory of elasticity in stresses for a nonuniform bandwidth. To derive resolving equations, direct integration of the original equations is performed.…”

Section: Recent Research and Publication Analysismentioning

confidence: 99%

The solution of the plane problem of the theory of elasticity by the boundary elements method

et al. 2020

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An approach to solving the biharmonic equation of the plane problem of the theory of elasticity by the numerical-analytical method of boundary elements is developed. The reduction of the two-dimensional problem to the one-dimensional one was carried out by the KantorovichVlasov method. Systems of fundamental orthonormal functions and the Green function are constructed without any restrictions on the nature of the boundary conditions. A numerical example of solving a plane problem by the boundary element method for a rectangular plate is considered. The results are compared with the data of finite element analysis in the ANSYS program and those obtained by A.V. Aleksandrov.

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Section: Recent Research and Publication Analysismentioning

confidence: 99%

The solution of the plane problem of the theory of elasticity by the boundary elements method

et al. 2020

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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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Analytical solutions to the planar non-axisymmetric elasticity and thermoelasticity problems for homogeneous and inhomogeneous annular domains

Tokovyy

2009

International Journal of Engineering Science

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Analytic Solution of the Plane Problem of the Theory of Elasticity for a Nonuniform Strip

Cited by 4 publications

References 0 publications

The solution of the plane problem of the theory of elasticity by the boundary elements method

The solution of the plane problem of the theory of elasticity by the boundary elements method

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

Analytical solutions to the planar non-axisymmetric elasticity and thermoelasticity problems for homogeneous and inhomogeneous annular domains

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