Geodesic
Mechanical plane problems of the straight beams with deformable protect fixed section of a finite length
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 89-96

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On the example of a semi-infinite beam with fixed section of finite dimensions on one of the front faces, it is shown that in order to study static and dynamic deformation processes, it is necessary to take into account the transformation of the types of the stress-strain state and the mathematical models used to describe them. Transformation takes place when crossing the border from a non-fixed area to a fixed one. The Kirchhoff–Love model does not allow taking into account the deformability of the fixed section of the beam, and when using the simplest refined shear model of S.P. Tymoshenko, its transformation is possible by fixing the site only on one of the front faces. Under the terms of using the described models and their combinations, the kinematic and force conditions for the conjugation of the fixed and non-fixed sections are formulated. On the basis of the derived proposals, an exact analytical solution is found for the simplest linear problem of the bending of a beam with its cantilever fixation. It is shown that taking into account the deformability of the fixing section having a finite length is especially important for thin-walled structural elements made of composite materials.
Keywords: beam, plane problem, fixed section, Timoshenko model, static loading
Mots-clés : equations of motion. 
@article{IVM_2022_3_a9,
     author = {V. N. Paimushin},
     title = {Mechanical plane problems of the straight beams with deformable protect fixed section of a finite length},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {89--96},
     publisher = {mathdoc},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_3_a9/}
}
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V. N. Paimushin. Mechanical plane problems of the straight beams with deformable protect fixed section of a finite length. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 89-96. http://geodesic.mathdoc.fr/item/IVM_2022_3_a9/