Phd project: A novel immersed shell method for airplane concepts

Organisation/Company: ONERA

Research Field: Mathematics » Computational mathematics

Researcher Profile: First Stage Researcher (R1)

Positions: PhD Positions

Country: France

Application Deadline: 1 May 2025 - 18:00 (Europe/Paris)

Type of Contract: Temporary

Job Status: Full-time

Offer Starting Date: 1 Oct 2025

Is the job funded through the EU Research Framework Programme? Not funded by a EU programme

Is the Job related to staff position within a Research Infrastructure? No

Job Description

New wing or airplane models are typically first designed in CAD software. These CAD models are a composition of surfaces described by spline functions (2D curves in embedded 3D). To create a finite element model from this CAD geometry, these surface splines have to be discretized into surface meshes. This process is often error-prone and requires manual interventions because the resulting surface meshes require well-shaped triangles. Another disadvantage of this discretization process is the loss of the smooth surface representation.

In this thesis, we suggest developing a novel immersed finite element method in which we take the surface representation from CAD directly and embed it in a regular finite element mesh. The regular finite element mesh is then used to discretize the shell equations while keeping the surface description smooth.

This approach is challenging in two ways. Firstly, we need to develop a stabilization scheme to ensure the stability and accuracy of the finite element solutions and secondly, we need to develop an adapted shell model. In contrast to classical shell models in which local coordinates on the surfaces are used, we will develop a shell model based on projecting differential operators onto the surface.

All the theoretical developments will be accompanied by the development of a parallelized high-performance code in Python and C++ in the software package CutFEMx (https://github.com/sclaus2/CutFEMx).

Where to Apply

E-mail: susanne.claus@onera.fr

Requirements

Research Field: Mathematics » Computational mathematics

Education Level: Master Degree or equivalent

Skills/Qualifications: Experience in numerical methods for PDEs and an affinity to programming in Python and/or C++ is an advantage.

Specific Requirements: As the thesis may be co-financed by the DGA, candidates must be French nationals, or citizens of a European Union country, the UK, or Switzerland.