Project Presentation
This website contains a summary of our HPC project carried out over the last few months. This project concerns NURBS Surfaces for Topology Optimization Problems, a specialized resource aimed at professionals, researchers, and enthusiasts in the fields of computational geometry, engineering design, and optimization. Non-Uniform Rational B-Splines (NURBS) are a mathematical model providing great flexibility and precision in representing both standard geometric shapes and complex free-form surfaces. This versatility makes NURBS an indispensable tool in the realm of topology optimization, where the goal is to find the most efficient material distribution within a given space, subject to certain constraints and performance criteria.
Topology optimization has become a cornerstone in various engineering disciplines, including aerospace, automotive, civil engineering, and biomechanics, to design components that are not only lighter and less costly but also mechanically and structurally more efficient. The integration of NURBS surfaces in this optimization process allows for the creation of smooth, highly refined geometries that traditional mesh-based approaches may struggle to accurately represent.
Our website offers an overview of the theory and application of NURBS in topological optimization problems.
Join us as we explore the intersection of mathematical modeling and engineering innovation through the prism of NURBS surfaces and topology optimization. Discover how these tools have enabled us engineering students to transition the computational aspects of a Topology Optimization software known as SANTO.
Many parts of this software, originally developed in Python within the I2M Laboratory, has been successfully migrated to C and parrallel implementation usi OpenMP was used to accelerate and optimize some computational hot spots in the code. For further details, go to the section Project-details.
.Main Applications of NURBS Surfaces
NURBS (Non-Uniform Rational B-Splines) surfaces are widely used in computer graphics and design due to their flexibility and precision. Here are some of their main applications:
- Computer-Aided Design (CAD): NURBS surfaces play a crucial role in CAD applications for representing and manipulating 3D geometry. They allow designers to create smooth and accurate surfaces for various objects and structures.
- Animation and Gaming: In the field of animation and gaming, NURBS surfaces are employed to model and animate characters, environments, and objects. Their ability to provide smooth and curved surfaces makes them suitable for realistic representations.
- Automotive Design: Automotive designers utilize NURBS surfaces to model car bodies and interior components. The smooth curves and surfaces achieved with NURBS aid in creating aesthetically pleasing and aerodynamically efficient designs.
- Aerospace Industry: NURBS surfaces are extensively used in the aerospace industry for designing aircraft and spacecraft. They help in creating complex and streamlined shapes that meet specific performance and aerodynamic requirements.
- Medical Imaging: In medical applications, NURBS surfaces find use in representing and visualizing anatomical structures. They enable the creation of accurate 3D models from medical imaging data for surgical planning and educational purposes.
Example of a NURBS surface
Acknowledgements
We would first like to express a sincere thank you to our tutor ZERROUQ Salah-eddine who allowed us to obtain concepts on a subject until now very little known to all of us. Through his pedagogical sense and his passion, he was able to communicate to us and pass on his knowledge to us so that we can achieve our objectives.
Despite the fact that these objectives were not completely achieved due to time and parallel activities, we were able to successfully complete the main objective and had very satisfactory and conclusive results. These open a door for a potential continuation of this subject in the years to come