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THE METHOD OF BOUNDARY STATES IN PROBLEMS OF TORSION OF ANISOTROPIC CYLINDERS OF FINITE LENGTH |
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| รหัสดีโอไอ | |
| Creator | Ivanychev D.A. |
| Title | THE METHOD OF BOUNDARY STATES IN PROBLEMS OF TORSION OF ANISOTROPIC CYLINDERS OF FINITE LENGTH |
| Contributor | Levina E.Yu., Abdullakh L.S., Glazkova Yu. A. |
| Publisher | TUENGR Group |
| Publication Year | 2562 |
| Journal Title | International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies |
| Journal Vol. | 10 |
| Journal No. | 2 |
| Page no. | 183-191 |
| Keyword | Boundary state method, Torsion analysis, Anisotropic bodies, Saint-Venant problem, State spaces. |
| URL Website | http://tuengr.com |
| Website title | International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies |
| ISSN | 2228-9860 |
| Abstract | The work is devoted to the development of the boundary state method for the class of problems of torsion of cylindrical bodies with a nontrivial cross-sectional shape made from anisotropic materials. At the ends of the final cylinder, the forces are specified, resulting in torsion moments. The concepts of the spaces of internal and boundary states for an anisotropic medium are formulated. The theory of constructing bases of these spaces was developed using the general solution of Lekhnitsky. The basis of internal states includes the components of the displacement vector, the strain tensor, and the stress tensor. The basis of the boundary states includes the forces at the boundary of the cylinder, and the displacement of the boundary points. Scalar products are introduced in each of the spaces. In the basis of internal states, the scalar product expresses the internal energy of elastic deformation. In the basis of boundary states, it expresses the work of external forces. An isomorphism of the state space is established, which establishes a one-to-one correspondence between their elements. Isomorphism allows the search for the internal state to be reduced to the study of the boundary state that is isomorphic to it. The state spaces are orthogonalized and the desired state is decomposed into a Fourier series in terms of the orthonormal basis elements, where the given surface forces act as coefficients. The problem is solved for a cylinder whose cross section is in the shape of an I-beam made of anisotropic material. Signs of convergence of the solution are given. The main features of the problem solution are formulated. The results are presented in graphical form. |
