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Section: New Results

Geometry

From CAD to Engineering: Computing FEM on curved surfaces

Participants : Jean-Claude Paul, Kan-Le Shi, Yu-Shen Liu, Jin-San Cheng, Cheng-Lei Yang, Bruno Durand, Jun-Hai Yong.

In cooperation with Bruno Lévy (Inria)

The cooperation with EADS, based on our new B-Spline surface formulation, was very promising, for complex shape modelling. Our surfaces are very efficient in term of precision. Moreover, they avoid the control point explosion of NURBS surfaces. We propose our work in two directions: 1) to Improve the Modelling process for the user (it is a strategic point of the success of our new mathematical surface); 2) to take profit of the control points way of our surface to compute numerical simulation on this surface directly. In industry, Geometry design and Engineering employ a sequence of tools that are generally not well matched to each other. For example, the output of a computer aided geometric design system is typically not suitable as direct input for a finite-element modeler. This is usually addressed through intermediate tools such as mesh generators. Unfortunately, these are notoriously lacking in robustness. Even once a geometric model has been successfully meshed, the output of a finite-element simulation cannot be directly applied to the original geometric model, since there is no straightforward mapping back to the original design degrees of freedom. Additionally there is a need for a trade-off between the speed of analysis and the fidelity of the results. In the early stages of design, quick results are necessary, but approximate results are acceptable. In the later stages, highly precise results are required, and longer computation times are tolerated. Worse, different underlying models are required for each level of refinement. These difficulties make the design process cumbersome and inhibit rapid iteration over design alternatives. We plan to use FEA on Knot vectors surfaces directly (i.e. use the same function basis for the Geometric Modeling and the Numerical Simulation Process. We will apply this approach to fluids analysis: turbulence modeling (fluid-structure interaction). We think that our surface functions exhibiting higher-order continuity are an ideal candidate for approximating such flows. From the practical point of view, the main objectives of the study are to evaluate, in the scope of this application, the efficiency of such approach in term of simulation accuracy, simulation time and computational convergence. We also aim to evaluation how such approach deals with simulation accuracy/convergence according to CAD definition (quality/size of patches used to define the 3D shape).

From CAD to Manufacturing: Robustness tolerance and error control

Participants : Jun-Hai Yong, Yu-Shen Liu, Clara Issandou, Hai-Chuan Song, Lu Yang, Kang-Lai Qian, Jean-Claude Paul.

In cooperation with Dr. Nabil Anwer – ENS Cachan and the Tsinghua PLM Center (supported by Dassault System). Dr. Yi-Jun Yang (Shandong University), Dr. Xiao-Diao Chen (Zhejiang University)

Based on our theoretical contribution in Differential Geometry, especially about our $ϵ$-Geometry Continuity and our new geometric operators we proposed several elegant solutions to the most important challenges in Computer Aided Design (see Lees A Piegl. "Ten challenges in Computer-Aided-Design". Jal of CAD 2005. 37 (4): 461-470): robustness, tolerances, error control. During CAD processes one uses a myriad of tolerances, many of which are directly related to the actual manufacturing process. Some interesting questions here include: What are the most relevant machining tolerances? How to set the army of computational tolerances, e.g. those of systems of equations, to guarantee machining within the required accuracy? How tolerances in different spaces, e.g. in model space and in parameter space, are related. Numerical instabilities also account for the majority of computational errors in commercial CAD systems. The problems related to robustness haunt every programmer who has ever worked on commercial systems. Fixing numerical bugs can be very frustrating, and often times results in patching up the code simply because no solution exists to remedy the problem. We first plan for assisting the designer when specifying the functional tolerances of a single part included in a mechanism, without any required complex function analysis. The mechanism assembly is first described through a positioning table formalism. In order to create datum reference frames and to respect assembly requirements, an ISO based 3D tolerancing scheme will be proposed, thanks to a set of rules based on geometric patterns and TTRS (Technologically and Topologically Related Surfaces). Since it remains impossible to determine tolerance chains automatically, the designer must impose links between the frames. We want to develop proposes ISO based tolerance specifications to help ensure compliance with the designer's intentions, saving on time and eliminating errors.