NUMERICAL SIMULATION OF THE STRESS-STRAIN STATE OF METAL STRUCTURES USING GEOMETRIC INTERPOLANTS

Evgeny Konopatskiy; Oksana Shevchuk

doi:doi:10.30987/2658-6436-2022-2-61-71

UDC 004.94

NUMERICAL SIMULATION OF THE STRESS-STRAIN STATE OF METAL STRUCTURES USING GEOMETRIC INTERPOLANTS

Published в Automation and modeling in design and management · Volume 2022, Issue 2, 2022 · Pages 61–71 · Rubrics: Mathematical modeling, numerical methods and program complexes

DOI 10.30987/2658-6436-2022-2-61-71

Received: 22.06.2022 Accepted: 30.06.2022 Published: 30.06.2022

Authors

Evgeny Konopatskiy ¹ iD · Oksana Shevchuk ²

1 Makeevka, Russian Federation

2 Donbas National Academy of Civil Engineering and Architecture (Department «Specialized Information Technologies and Systems», Assistant)
Makeevka, Ukraine

ABSTRACT

The work is devoted to carrying out multidimensional interpolation and approximation methods for the numerical solution of differential equations and computer model development of the stress-strain state of metal structures. The core of the work is a fundamental computational algorithm for the numerical solution of differential equations using geometric interpolants on regular and irregular networks. On its basis, computational experiments are carried out on numerical simulation of the stress-strain state of operated reservoirs for storing petroleum products, which form a software package implemented in the Maple interpreter. At the same time, the differential equation for modelling the stress-strain state of an elastic cylindrical shell under axisymmetric loading is improved for the numerical analysis of the stress-strain state of a cylindrical reservoir with geometric imperfections. Also a new approach is proposed to take into consideration the initial conditions of the differential equation, which consists of parallel transfer of the numerical solution to the point, its coordinates correspond to the initial conditions. The advantage of the proposed approach for the numerical solution of differential equations using geometric interpolants is that it eliminates the need to coordinate geometric information in the process of interaction between CAD and FEA systems, by analogy with the isogeometric method.

KEYWORDS

computer model geometric interpolant differential equation numerical solution stress-strain state metal structures

Information References

Authors:

1. Makeevka, Russian Federation

2. Donbas National Academy of Civil Engineering and Architecture (Department «Specialized Information Technologies and Systems», Assistant)

Makeevka, Ukraine

Type:

Article

Pages:

from 61 to 71

Status:

Published

Subject area:

UDC 004.94

Language:

Russian

Keywords:

computer model, geometric interpolant, differential equation, numerical solution, stress-strain state, metal structures

References

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NUMERICAL SIMULATION OF THE STRESS-STRAIN STATE OF METAL STRUCTURES USING GEOMETRIC INTERPOLANTS

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