Isogeometric Analysis of Anisotropic materials with Model Reduction and X_FEM – AMRIA

This research project is expected to last for two years. The project coordinator joined the ICA laboratory in Tarbes which is hosting all the research. The overall project is split in 5 different tasks which represents 3 quite independent projects once the first task is completed. An article will be prepared at the end of the projects and will be presented in national or international congresses. The project coordinator will work with Francisco Chinesta (GeM Nantes) and David Benson (UCSD San Diego) for this project.
A post-doctorate was recruited in April 2012 to help the project coordinator in this research and an other post-doc will be recruited soon. The project coordinator, recruited in September 2011 as Assistant Professor dedicates all his research time to the project.
Regular meetings are organized between the different collaborators, and David Benson involvement in the project is granted via email exchanges and a visit planned for next year.

Within this research project, the collaborators propose to develop a numerical method that bridges model reduction, X-FEM and isogeometric analysis. This would allow solving problems never solved until now in the domain of large composite structures including discontinuities. Aeronautic and spatial industry should be naturally concerned by this research. New shape optimization tools and invert strategies in real time are direct applications for this research project. This research should also show the efficiency of NURBS for simulating the forming process of structures. Isogeometric analysis represents also a major interest for Computer Aided Design industry because the functions used for the simulation are the same as the ones describing the geometry.

Future works could address contact issues in an isogeometric approach or non linear phenomenon with PGD methods.

Two to three scientific articles will be issued by the end of the project and presented in national and international conferences.

This research project takes place in the context of large composite structures and complex assembly.
Nowadays, numerical simulation has still a hard time computing large structures even with parallel computing and supercomputers.
Degenerated elements like shells fail in simulating the complexity though the thickness of composite panels.

Model reduction, introduced to overcome the curse of dimensionality (encountered in atomic scale models for example) is now used to simplify the modeling of shell structures like composite panels used more and more in aerospace industry. The key of such a success stands in variable separation; separation between space and time variables (LATIN Ladevèze 1985) and between in-plane/out-of-plane variables for thin structures. This kind of separation, introduced in PGD (proper generalized decomposition) enable taking advantage of the few magnitude order that exists in between the thickness ant the others dimensions while keeping a fine description through the thickness. Superiority of isogeometric analysis (Hughes 2005) in term of continuity allows to introduce shell formulations with a reduced number of degrees of freedom (Benson 2010) with higher order shape functions even for explicit dynamic computations. Coupling both the methods should lead to improved efficiency for the simulation of large composite panels, even for the forming process. Recent works on coupling different shells will enable considering complex geometries.

PGD efficiency allows to introduce material parameters as unknown in the formulation like layers orientations. The result is a relatively more complex problem to solve but only once in order to be particularized at low cost for a given set of parameters. Applications of this concept are huge, from optimizations of the mechanical behavior of a part considering the process to inverse identification of material properties, and this could represent a new paradigm in numerical simulation. PGD coupled with isogeometric analysis allows to introduce as well the geometry has unknown in the problem, for efficient shape optimization strategies.

Efficiency of X-FEM coupled with isogeometric analysis was proven during my post-doc at UC San-Diego, combining capabilities of both the methods:
possibility to model discontinuities,
description of the geometry without approximation,
higher order continuity introduced with the NURBS for robustness an efficiency in most the mechanical problems.
Optimal convergence up to 4th order was obtained and improve efficiency in term of degrees of freedom was shown compared to classical finite elements.

Coupling X-FEM and PGD within an isogeometric framework offers tremendous perspectives for the composite and aerospace industry.