Open AccessStereometry of compressed conoids and physical adequacy of q8 element bases
Author(s) -
A. N. Khomchenko,
Olena Lytvynenko,
Oleh Dudchenko,
Ігор Олександрович Астіоненко
Publication year - 2021
Publication title -
sistemnì tehnologìï
Language(s) - English
Resource type - Journals
eISSN - 2707-7977
pISSN - 1562-9945
DOI - 10.34185/1562-9945-3-134-2021-05
Subject(s) - serendipity , trigonometry , finite element method , element (criminal law) , computer science , trigonometric functions , spectrum (functional analysis) , popularity , theoretical computer science , calculus (dental) , mathematics , algorithm , mathematical analysis , structural engineering , geometry , engineering , law , epistemology , physics , medicine , philosophy , dentistry , quantum mechanics , political science
The paper considers new models of bases of serendipity finite elements (FE) Q8. The standard element Q8 has been used in the finite element method (FEM) for more than 50 years despite the physical inadequacy of the spectrum of equivalent nodal loads.In recent years, the library of serendipity finite elements has been significantly replen-ished with non-standard (alternative) models. The reasons for the inadequacy of the spectrum were identified and "recipes" were proposed to eliminate this shortcoming of standard serendipity models. New approaches to modeling bases with the help of hierarchical forms force to abandon conoids - linear surfaces that are associated with intermediate nodes of standard elements. According to the authors, these Catalan surfaces (1843) are insufficiently studied and deserve the attention of modern researchers. Therefore, research is being conducted today, and it is not necessary to give up conoids. The paper shows how by compressing the surface of the conoid it is possible to obtain a mathematically sound and physically adequate spectrum of nodal loads. It is interesting that such capabilities are embedded in trigonometric functions, the popularity of which in the FEM is growing steadily.The purpose of the research is to constructively prove the existence of mathematically substantiated and (most importantly) physically adequate models of serendipity elements Q8 with the help of trigonometric bases.Trigonometric models of the finite element Q8 once again confirmed that serendipity elements are an inexhaustible source of important and interesting information. It should be noted that today it is not necessary to give up conoids for the sake of physical adequacy of the model. Conoids are also of "historical" importance to FEM. The first bases of serendipity FEs were constructed from conoids (1968).Taylor's elegant method (1972) is also based on conoids. New results show that trigo-nometric bases are able to preserve conoids and ensure the physical adequacy of the models.