Implementation of improvements to Isogeometric Analysis for trimmed-coupled solids directly extracted from Computer Aided Design environment

Herrero Adan, Daniel

Abstract

This research provides an algorithm to analyse structures composed of solids that are directly extracted from Computer Aided Design (CAD) environment. The analysis assumes linear elastic material and small displacements, being the result the displacements field of the structure under a set of forces and constraints. Since the equation to obtain such displacements is not analytically solvable, the solution is approximated by a linear combination of the so-called basis functions. The use of domains from CAD in analysis without additional meshing is the original purpose of the Isogeometric Analysis (IGA). The basis functions used by IGA are Non-uniform Rational B-splines (NURBS). Since any model developed in CAD is geometrically defined by NURBS, it already comes discretized into NURBS, and can be used directly by IGA to obtain the displacement field without additional meshing.
Therefore this work is based on IGA techniques. Solids are defined in CAD as a set of faces that wrap their volume. This arrangement is valid for representation, but not for analysis as the solid itself does not exist (only the hollow volume). Therefore the first challenge that appears in this work is the generation of the solid enclosed by those faces, or solid parametrization. In addition, the solids can be trimmed by surfaces to achieve the final shape of the domain. The existence of such trimming surfaces presents two challenging aspects. Firstly, the discretization with NURBS as they come from CAD is not valid anymore, being necessary to find an alternative discretization scheme. Secondly, the trimming surfaces that bound the discretization are unknown in the discretization space, being necessary to approximate them. The domain may be formed by multiple solids that are coupled in a weak manner using Lagrange multiplier approach on the coupling interfaces. Apart from tackling these problems, two novel techniques have been implemented in this algorithm: a new triangulation technique for surfaces to allow the representation of results on the faces of the solids, and a new approach to calculate coordinates in the solid parameter space (point projection) that brings more robustness to the computation.
The first part of the algorithm is devised to read the content of the CAD files and transform into suitable data for analysis. This transformation includes the solid parametrization. Then the trimming surfaces are approximated to allow the accurate definition of the limits of the discretization, which is carried out by tetrahedral mesh. The application of constraints and coupling with Lagrange multiplier approach follows the process to end up in the analysis results, which are the displacements of the domain. The stresses are also computed by a post-processor developed in this work. The performance of this algorithm is proved by a set of examples at the rear of the thesis.
Although the trimmed solids need discretization different from NURBS, which vanishes partially the IGA original purpose, this thesis stands as another step forward in the IGA development towards the CAD-analysis integration for solids.

• Thesis Type: Thesis
• Deposit Date: Oct 12, 2020
• Publicly Available Date: Sep 9, 2021
• Public URL: https://uwe-repository.worktribe.com/output/6771957
• Award Date: Sep 9, 2021