Development of a procedure for calculating problems in the mechanics of elastomers based on the open modeling language

Authors

DOI:

https://doi.org/10.15587/1729-4061.2025.326219

Keywords:

moment finite element scheme, variational principle of Lagrange, mathematical model of elastomeric structures

Abstract

The object of the study is the stress-strain state of elastomeric structures. When solving practical problems in elastomer mechanics, the issue of selecting an effective computational scheme based on computational mathematics methods arises. However, due to the insufficient number of studies, it is difficult to assess the optimality of a particular methodology, which necessitates an analysis of computational algorithms followed by a comparison of their advantages and disadvantages.

In the design of elastomeric structures, the numerical analysis of their stress-strain state is a relevant issue. One of the key characteristics is the compressibility of the material, which is not taken into account by equations for incompressible media. In thin-layer rubber elements, this effect becomes more pronounced as the ratio of one of the geometric dimensions to the thickness of the structure increases.

The use of the finite element method in displacements, despite its convenience, encounters computational errors. When the Poisson's ratio approaches 0.5, numerical instabilities arise, complicating the attainment of reliable computational results.

This study proposes a new approach to organizing computational schemes in specialized automated design systems, which ensures more accurate modeling of the stress-strain state of structures. The foundation is the use of Open Modeling Language, which simplifies the description of mechanics problems and corresponding numerical schemes within a unified variational framework.

The key result is the derivation of universal formulas for determining the potential energy of the system based on the moment finite element scheme. The proposed approach eliminates the “false shear” effect and improves the accuracy of numerical calculations for weakly compressible materials, which is confirmed by numerical analysis and experimental data

Author Biographies

Volodymyr Lavrik, Kyiv National University of Technologies and Design

PhD

Department of Information and Computer Technologies

Ihor Bohdanov, Berdyansk State Pedagogical University

Doctor of Pedagogical Sciences, Professor, Corresponding Member of the National Academy of Educational Sciences of Ukraine, Honored Worker of Science and Technology of Ukraine

Rector

Department of Professional Education, Labor Training and Technologies

Hanna Alieksieieva, Berdyansk State Pedagogical University

PhD, Associate Professor

Department of Computer Technologies and Computer Science

Oleksandr Antonenko, Berdyansk State Pedagogical University

PhD, Associate Professor

Department of Computer Technologies and Computer Science

Oleksandr Ovsyannikov, Berdyansk State Pedagogical University

PhD, Associate Professor

Department of Computer Technologies and Computer Science

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Development of a procedure for calculating problems in the mechanics of elastomers based on the open modeling language

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Published

2025-04-29

How to Cite

Lavrik, V., Bohdanov, I., Alieksieieva, H., Antonenko, O., & Ovsyannikov, O. (2025). Development of a procedure for calculating problems in the mechanics of elastomers based on the open modeling language. Eastern-European Journal of Enterprise Technologies, 2(7 (134), 23–32. https://doi.org/10.15587/1729-4061.2025.326219

Issue

Vol. 2 No. 7 (134) (2025): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2025 Volodymyr Lavrik, Ihor Bohdanov, Hanna Alieksieieva, Oleksandr Antonenko, Oleksandr Ovsyannikov

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