Método dos elementos finitos utilizando funções de forma de alta ordem aplicadas em estruturas em estado plano de tensão

Abstract

Since its popularization, the Finite Element Method (FEM) has received several approaches, with different levels of detail. One of these approaches, the constant strain triangle (CST) is very widespread in the academic environment, mainly for Plane State of Stress (PSS) problems due to its simplicity of application and good approximation of real solutions. However, in structural projects, due to the commitment to performance and security, new approaches were used to reduce the error without increasing the computational cost, such as the application of interpolation functions of higher orders. Therefore, this work sought to approach the FEM for structures submitted to an EPT using high order form functions for triangular elements, built through the concept of tensor product between unidimensional functions using modal bases with Jacobi’s orthogonal polynomials. The algorithm was developed in the Python programming language with the aid of the Jupyter Notebook platform, and the stress and displacement results obtained were compared with commercial software. The use of functions shape of a high order to the method was successful in being equal to the results of specific software without the need to refine the meshes of the studied geometries.