Background: IRT SystemX and the TOP project

Within the IRT SystemX, an interdisciplinary and multicultural environment (Alstom, Bull, EDF, Safran, Paris-Saclay University, Inria, Institut Mines Telecom, Kalray, OVH, Renault, Sherpa, Systematic Paris Region, …), you will contribute to the research project TOP (Topology Optimization Platform). This collaborative R&D project brings together industrial partners (software developers and end-users) and academics. The main objective is to provide the industrial R&D departments with innovative, robust design tools capable of handling complex engineering requirements for mechanical parts.
Work at IRT is based on two key aspects:

  • Synergy of talents: the institute brings together in one place all the partners of the project, thus creating a real melting pot of interactions between public and industrial research actors.
  • Pooling of skills and platforms: by reaching a critical mass, SystemX aims at constituting a platform thanks to the pooling of many skills and technological bricks.


Today, the engineering design departments are tasked with designing mechanical systems that must fulfill increasingly more demanding specifications. Topology optimization is one industrial tool that contributes to meeting this challenge. The topology optimization of a structure consists in obtaining the most efficient material distribution within a given design domain, while satisfying a set of functional requirements. In this context, the level set method is a promising alternative to the technologies at the heart of most commercially available software packages. In particular, it provides a precise and unambiguous representation of the interface of the mechanical part throughout the optimization process.
The scientific literature offers a large panel of applications of the level-set method to structural design problems whose mechanical models can be either linear (linear elasticity, frequency response, low coupling thermo-elasticity, etc.) or non-linear (contact, buckling, hyper elastic materials, etc.).

In particular, the optimization of contact problems has been recently considered however without optimizable contact areas and only for domains discretized by Cartesian fixed meshes.
Position characteristics

The internship will last approximately 6 months and will take place on the IRT SystemX campus located in Palaiseau. This internship is intended as a preliminary work to be followed by a PhD thesis in the same framework.

Missions and objectives

The objective of this internship is the development of a numerical method for the topology optimization of mechanical structures within the framework of the level set approach for 2D contact problems. The main task is to optimize the contact area (with and without friction) using adaptive remeshing tools. In particular, the intern will be tasked with the following missions:
• Getting familiar with the scientific literature dealing with topology optimization with the level set method, in particular with the application to the case of parts with contact zones.
• Proposing a numerical method to treat the case of an optimizable contact zone, relying on remeshing to fit the evolving interface.
• Developing a software prototype to deal with elementary academic test cases in 2D inspired by use cases representative of the needs of the industrial partners of the TOP project.

Candidate profile

Student from a research master (M2) in applied mathematics, a French engineering school, or an equivalent background.
Thanks to your education and work experience, you have acquired a solid knowledge of numerical simulation and engineering computational science. Ideally, you are also familiar with one or more of the following topics:

  • Numerical analysis of PDEs
  • Finite elements
  • Structural mechanics
  • Level set method
  • Numerical optimization
  • Scientific programming

Your personal competencies include:

  • Real appetite for research and interest in pursuing a PhD thesis
  • Analytical skills, autonomy and initiative
  • Ability to report work progress and to communicate (orally and in writing) in a synthetic manner
  • Good fluency in French or English (ideally both languages)


Reference: STAGE_2018_TOP
To apply:


[1] G. Allaire, F. Jouve & A.M. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, 194(1), pp. 363—393. 2004.

[2] A. Maury, G. Allaire & F. Jouve. “Shape optimisation with the level set method for contact problems in linearised elasticity. 2017. <hal-01435325v2>



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