Development of computational tools for Isogeometric Analysis (IGA) - Ribeiro, Carlos Fernando Morgado (2014)
A few years ago drawings were made in the drawing boards and using pencils on vellum. There were no computers helping the designers in the parts modeling. After designing the object, the design was passed to the analysts. The designers and analysts were in constant communication. Nowadays, the designers used Computer Aided Design (CAD) tools in the parts modeling. For application the analysis at the geometries, initially a mesh to approximate the geometries is generated. After this, on the mesh the Finite Element Method (FEM) was applied. In complex engineering design, the generation and manipulation of meshes in FEA was estimated to take over 80% of the overall analysis time. The form to break down the barriers between engineering design and the analysis is with reconstruction the entire process, but at the same time maintaining compatibility with existing practices. Create only one geometric model is the focus of reconstruction process. This geometric model is used in the representation of the geometry, as well as in the analysis, and this concept is designated by Isogeometric Analysis (IGA). In this present work the development of the tools for generate the CAD and calculate the basis function for representation the object are proposed. Initially, the mathematical formulations for Bézier, B-Spline and NURBS, for curves and surfaces are presented. The algorithms developed to generate the curves and surfaces are demonstrated. The IGA and FEM formulation for tridimensional and bidimensional spaces are introduced. In this work, a development of a tools for application this method are proposed. The convergence of the results for FEM and IGA programs are studied and compared to the theoretical values and Abaqus comercial program. The results obtained with IGA formulation converge to the reference values.