Open AccessDevelopment of a Finite Element Method and Its Application in a CAD
Author(s) -
А. N. Soloviev,
R. V. Kirichevsky
Publication year - 2022
Publication title -
vestnik novosibirskogo gosudarstvennogo universiteta. seriâ: informacionnye tehnologii/vestnik novosibirskogo gosudarstvennogo universiteta. seriâ: informacionnye tehnologii v obrazovanii
Language(s) - English
Resource type - Journals
eISSN - 2410-0420
pISSN - 1818-7900
DOI - 10.25205/1818-7900-2021-19-4-67-84
Subject(s) - finite element method , cartesian coordinate system , discretization , dissipative system , computer science , coordinate system , software , mechanical engineering , mathematics , structural engineering , mathematical analysis , geometry , engineering , physics , artificial intelligence , quantum mechanics , programming language
The presented review of existing domestic and foreign CAD systems showed that the use of FEM in their structure remains quite relevant before other methods in the speed of calculations, sufficient accuracy and software implementation in the CAD structure. To solve the problems of mechanics of elastomers and composites based on them, an over-view of the developed domestic software MIRELA+ is presented in more detail. This complex solves many problems of solid mechanics: it has a special focus on solving problems of dissipative heating, parameters of fracture mechanics of massive elastomeric structural elements and thin-layer rubber-metal elements with cracks with changing physical, mechanical and thermophysical parameters under cyclic deformation. Not many of the domestic programs can implement this, and licenses for foreign programs cost tens of thousands of dollars. This paper also presents methods of discretization by finite elements and an algorithm for constructing a system of re-solving equations used in MIRELA+, expressions for determining the components of the coordinate transformation tensor, the strain tensor at the FE centers in a Cartesian coordinate system. Examples of visual representation in a three-dimensional image using a color picture are given, where each shade or color corresponds to a certain range of numerical values of the corresponding function.