Isometric Boundary Element Method for 2D analysis of elastostatic structural issues

Resumo

In structural engineering, there is a growing trend towards using elements that better conform to geometric characteristics. This is particularly true when leveraging surface (or line, in 2D cases) generation in CAD environments, directly benefiting from more precise geometry. In this context, the need for Isogeometric elements arises. Through their utilization, the analysis of more complex stress and strain distributions is conducted with greater accuracy. This paper presents an alternative for analyzing the structural behavior of elastostatic structural cases through 2D modeling, employing an approximate method with Isogeometric elements. A computational implementation of the Boundary Element Method (BEM) was developed using the Python programming language. The "2D BEM" code was adapted, employing Kelvin's fundamental solution with the use of continuous and discontinuous linear elements, as well as higher-order elements, for more accurate boundary discretization. The formulation of BEM thus enables the modeling of the domain, in this case, the analysis of 2D bodies in the presence of mechanical damage, with iterative monitoring. The behavior is assessed through the displacements obtained for the boundary and internal points, as well as the stresses, conveniently evaluated in graphical representations. Applications are presented to test the implemented modeling and to provide an alternative for analyzing an important area within structural systems in civil construction projects, among others.