Isogeometric analysis with interactive modeling of multi-patches NURBS

Resumo

Isogeometric analysis (IGA) is an innovative method of numerical analysis of structures that seeks to
unite design and simulation, allowing the creation of computational models that preserve the exact geometry of
the problem. This approach uses mathematical functions known as NURBS (Non-Uniform Rational B-Splines),
widely used in CAD systems to model curves and surfaces. In the context of the IGA, these same functions that
define the geometry are used to approximate the field variables. This work aims to provide a computational tool
for two-dimensional isogeometric analysis, covering the stages of modeling, analysis, and visualization of the
results. It is worth mentioning that the visualization of results is still a prototype under development. The system
consists of two software: FEMEP (Finite Element Method Educational Computer Program), developed in Python,
responsible for geometric modeling, and FEMOOLab (Finite Element Method Object-Oriented Laboratory), a
MATLAB software used for analysis and display of results. The proposed tool presents an intuitive graphical user
interface (GUI) to facilitate the visualization and manipulation of NURBS curves, providing advanced modeling
features. The device also includes features for the automatic intersection of curves and region recognition to
simplify and streamline the modeling process. In addition, the modeling software is also responsible for managing
attributes such as material properties and natural and essential boundary conditions. A relevant aspect of this work
is to provide open-source code, allowing the user and developer community to collaborate and contribute to the
continuous development of the tool. This open-source approach encourages innovation and shared growth,
fostering an environment for collaboration and mutual learning. This tool aims to make isogeometric analysis
accessible even to users with basic programming knowledge, expanding its scope and enabling its application in
various projects and engineering studies.