Three-Dimensional Solid Structures Simulation on Isogeometric B-Rep Analysis

Isogeometric analysis (IGA) was devised to circumvent meshing step in the design process because it uses same basis functions as CAD packages: non-uniform rational B-splines (NURBS). That NURBS information is exchangeable via Initial Graphics Exchange Specification (IGES) files, which potentially can be extracted and read for analysis purpose in IGA context. However the utilization of NURBS domains proceeding directly from CAD for analysis purposes is still not fully developed. In particular, 3D solids IGES files contain a collection of faces forming the solid boundaries, but not the solid itself. Isogeometric B-Rep analysis (IBRA) allows to generate NURBS domains in an easy manner by trimming and coupling patches. A full description on IBRA applied for shells is given in [1], where they describe application of boundary conditions /coupling to trimmed edges and analysis-CAD integration. In this work we extend IBRA for three dimensional solid structures. Although the principles are the same than IBRA on shells, there are three aspects in solids that require extra development: interpretation of 3D solids IGES files, trimming surfaces definition and domain integration. We propose a methodology for the first item, which is based on the application of certain restrictions when the solid is modeled. Trimming surface definition is based on NURBS point projection form physical to parameter space. Domain integration is carried out in parameter space by Finite Cell Method [2]. Examples provided demonstrate the accuracy of the procedure and show that IBRA on three-dimensional solids is suitable for analysis – CAD integration on that kind of structures.