Interactive Modeling of NURBS for Isogeometric Analysis

Resumo

Isogeometric Analysis (IGA) is a numerical analysis method for structures that arises with the proposal of unification between design and simulation, allowing the creation of computational models that preserve the exact geometry of the problem. This approach is possible by a class of mathematical functions called NURBS (Non-Uniform Rational B-Splines), widely used in CAD (Computer Aided Design) systems for modeling curves and surfaces. In isogeometric analysis, the same functions representing the geometry approximate the field variables. In this context, this work was developed to provide a tool within the scope of computational mechanics for two-dimensional isogeometric analysis of linear elasticity problems, including the steps of modeling, analysis, and visualization of results. The system consists of two software programs: FEMEP (Finite Element Method Educational Computer Program), developed in Python and responsible for the geometric modeling stage, and FEMOOLab (Finite Element Method Object Oriented Laboratory), a MATLAB software for analysis and display of results. The proposed tool features a graphical user interface (GUI) that allows intuitive visualization and manipulation of NURBS curves with advanced modeling features such as curve intersection and region recognition features that streamline and simplify the process. The open-source system allows collaboration and continuous development by the community of users and developers.