Special Features of Using Mathematical Modeling for the Study of Tetrahedral Elements
Year: 2024
Type: conference-paper
Abstract: In this scientific work, mathematical modeling of tetrahedron elements in the finite element method is presented, which includes the determination of geometric shape, shape functions, and material properties. Unknown fields such as displacement vectors, strain, and stress tensors are considered. The methodology of applying the principle of virtual work and equilibrium equations is described, allowing the derivation of a system of differential equations to describe the behavior of the tetrahedral element. Integration over the volume and consideration of boundary conditions help reduce the equations to a system of linear algebraic equations for numerical solution using the finite element method. It was found that modeling tetrahedral elements with a specific given radius (for example, R=0.3 mm) involves stages such as geometry determination, element generation, shape function formation, stiffness matrix computation, and solving a system of linear equations. The radius R of tetrahedral elements is taken into account at all stages, ensuring accuracy and reliability in tetrahedra modeling. The research also focuses on the fact that the occurrence of minor errors in iterative processes may result from several factors, including iteration step, the number of iterations, stopping criteria, linear or nonlinear material behavior, solution method selection, the presence of geometric inhomogeneities, and element size.
DOI: 10.4028/p-dbbwy3
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4402379426