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Modeling a Synthesized Element of Complex Geometry Based upon Three-Dimensional and Two-Dimensional Finite Elements

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Abstract

This paper offers a description of an approach to modeling a synthesized element featuring a complex geometry. Owing to the region under examination being pre-parametrized with parameters of a parallelepiped and a synthesis of three-dimensional elements with a cubic approximation of unknown variables in all three directions of the region under examination and two-dimensional elements with cubic approximation of unknown variables in a thin layer on its edges, one is enabled to obtain high-precision curved aligned finite elements. The synthesized element obtained substantially expands the range of tasks which now may be solved. Specifically, it enables one to calculate the stress—strain state of coated structures, including those with local fibration while also allowing for specific surface properties which differ from the properties of the primary array to be taken into consideration, including the presence of distributed surface features resultant, for instance, from ion implantation, surface treatment and defects. Different cases have been studied to provide illustration for the method, in particular, a calculation of the stress-strain state of a three-layer plate.

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Authors and Affiliations

  1. Institute of Mechanics and Engineering, Kazan Scientific Center, Russian Academy of Sciences, 420111, Kazan, Russia

    S. N. Yakupov, H. G. Kiyamov & N. M. Yakupov

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  1. S. N. Yakupov
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  2. H. G. Kiyamov
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  3. N. M. Yakupov
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Correspondence to S. N. Yakupov, H. G. Kiyamov or N. M. Yakupov.

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(Submitted by D. A. Gubaidullin)

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Yakupov, S.N., Kiyamov, H.G. & Yakupov, N.M. Modeling a Synthesized Element of Complex Geometry Based upon Three-Dimensional and Two-Dimensional Finite Elements. Lobachevskii J Math 42, 2263–2271 (2021). https://doi.org/10.1134/S1995080221090316

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