ESTUDO DO REFINAMENTO DE MALHAS DE ELEMENTOS FINITOS COM ELEMENTO FINITO Q4-ISOPARAMÉTRICO LINEAR

Abstract

Due to the complex shape and variable loading conditions of most structures studied in engineering, it is impossible to perform calculations on structures with traditional analytical methods. Therefore, it is necessary to resort to approximate solutions to solve this problem. Thus, the finite element method (FEM) is used. This research focused on showing the mesh refinement of FEM using the Q4 – Isoparametric element. Thus, the program Finite Element Method, divided into 5 functions, being, function of reading the structure, function of degrees of freedom of the whole structure, creation of the matrix of rigidity of the structure, function for assembling the vector of external forces of the structure and function for the determination of nodal displacements. Then, the refinement was carried out gradually, in which the displacement value was calculated using the FEM and compared with its analytical solution, when possible. As a result, the three cases studied, beam, frame and 2D torus, show that the better the mesh refinement, in terms of quantity and especially the positioning of finite elements in the mesh, the closer the displacement value is to the exact solution. In this way, with the FEM, despite having an error percentage, it is possible to obtain results very close to the exact solution.