Advances in Computational Design

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Finite element modeling of multiplyconnected three-dimensional areas

  • Polatov, Askhad M. (Department of Mathematics, National University of Uzbekistan) ;
  • Ikramov, Akhmat M. (Department of Mathematics, National University of Uzbekistan) ;
  • Razmukhamedov, Daniyarbek D. (Turin Polytechnic University in Tashkent)
  • Received : 2019.01.18
  • Accepted : 2019.12.20
  • Published : 2020.07.25
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Abstract

This article describes the technology for constructing of a multiply-connected three-dimensional area's finite element representation. Representation of finite-element configuration of an area is described by a discrete set that consist of the number of nodes and elements of the finite-element grid, that are orderly set of nodes' coordinates and numbers of finite elements. Corresponding theorems are given, to prove the correctness of the solution method. The adequacy of multiply-connected area topology's finite element model is shown. The merging of subareas is based on the criterion of boundary nodes' coincidence by establishing a simple hierarchy of volumes, surfaces, lines and points. Renumbering nodes is carried out by the frontal method, where nodes located on the outer edges of the structure are used as the initial front.

Keywords

Acknowledgement

The authors would like to express their appreciations to the administration of National University of Uzbekistan for their financial and overall support and assistance in software package development. The authors also express their appreciation to Prof. Kurmanbaev B. for valuable advices given during analysis of the calculation results. We also acknowledge the valuable assistance of Associate Prof. Gaynazarov S. with computational experiments, of Associate Prof. N. Kadirova for the preparation of articles for publication, F. Polatov, M.Sc., for article translation and edition.

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