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The Solution of the First Main Problem of the Theory of Elasticity for a Transtropic Body of Revolution |
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| รหัสดีโอไอ | |
| Creator | D.A. Ivanychev, E.Yu. Levina, E.A. Novikov, M.V. Polikarpov |
| Title | The Solution of the First Main Problem of the Theory of Elasticity for a Transtropic Body of Revolution |
| Contributor | - |
| Publisher | TuEngr Group |
| Publication Year | 2564 |
| Journal Title | International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies |
| Journal Vol. | 12 |
| Journal No. | 3 |
| Page no. | 12A3L: 1-9 |
| Keyword | Boundary state method, Transverse isotropy, Spatial problems, Axisymmetric problems, Isomorphism of state spaces, Elasticity for anisotropic bodies. |
| URL Website | http://TuEngr.com/Vol12_3.html |
| Website title | ITJEMAST V12(3) 2021 @ TuEngr.com |
| ISSN | 2228-9860 |
| Abstract | Based on the method of boundary states, this work investigates the elastic equilibrium of transversely isotropic bodies of revolution under the action of forces applied to the surface of a body. A new method is proposed for the formation of bases of internal and boundary states based on a general solution of plane deformation and formulas for the transition to a spatial axisymmetric state. Isomorphism of state spaces is proved. Isomorphism of spaces allows the search for an internal state to be reduced to the study of boundary states. In the case of the first and second main problems of the theory of elasticity, the problem is reduced to expanding the sought state in a series in terms of the orthonormal elements and finding the Fourier coefficients of this linear combination. Fourier coefficients are quadratures. The first main problem of the theory of elasticity for a transversely isotropic hemisphere with boundary conditions imitating inhomogeneous tension is solved. Verification of the solution is presented and accuracy is assessed. The results are presented graphically. |
