Application of Transition Finite Elements in hpq-Adaptive Modeling and Analysis of Machine Elements

Magdalena Zielińska

Uniwersytet Warmińsko-Mazurski w Olszynie
https://orcid.org/0000-0002-8702-6558

Grzegorz Zboiński

University of Warmia and Mazury in Olsztyn, Institute of Fluid Flow Machinery, Polish Academy of Sciences, Gdańsk
https://orcid.org/0000-0001-7775-2436


Abstract

This paper concerns the modeling and analysis of machine elements using the adaptive finite element method. The adaptation used is of hpq type, which means that the finite element dimension h and element transverse q and longitudinal p approximation order may be different in each element. These parameters are determined automatically by the program to obtain modeling and approximation error levels not higher than the assumed admissible level of the errors. The presented paper focuses on the use of transition elements between basic elements corresponding to the three-dimensional theory of elasticity and the first-order shell model. Three applied transition elements differ in their assumptions regarding the continuity of the displacement, strain, and stress fields between the basic models. The effectiveness of the application of transition elements was assessed in terms of the removal of the internal boundary layer at the boundary between the models and the convergence of adaptive solutions taking into account these models.


Keywords:

finite element method, adaptivity, transition models, modeling, analysis, machine elements


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Published
2024-04-12

Cited by

Zielińska, M., & Zboiński, G. (2024). Application of Transition Finite Elements in hpq-Adaptive Modeling and Analysis of Machine Elements. Technical Sciences, 27(27), 33–53. https://doi.org/10.31648/ts.9545

Magdalena Zielińska 
Uniwersytet Warmińsko-Mazurski w Olszynie
https://orcid.org/0000-0002-8702-6558
Grzegorz Zboiński 
University of Warmia and Mazury in Olsztyn, Institute of Fluid Flow Machinery, Polish Academy of Sciences, Gdańsk
https://orcid.org/0000-0001-7775-2436



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