LMA - Laboratoire de Mécanique et d’Acoustique

Theme Structures

This topic addresses the behavior of deformable structures by studying their static or dynamic behavior under different loads. These structures include rich models taking into account local or distributed nonlinearities, complex materials assemblies or uncertainties. This gives rise to a wide range of phenomena transcribed by studying the stability of the solutions and their bifurcations. Complexity in the model is managed by the development of model reduction and original calculation methods.

Scientific objectives

  • Nonlinear structures: definition, computation and promotion of the use of nonlinear vibration modes; development of original algorithms based on Taylor series for continuation and bifurcation analysis.
  • Modeling deployable flexible structures: model reduction, taking into account large displacements and/or large rotations, dynamic study including instabilities.
  • Structures based elastomers: modeling the dynamic behavior of dissipative elastomers (constitutive laws, fatigue damage models), development of specific numerical methods (model reduction, macro-models...).
  • Uncertain structures: development of methods to reduce computational costs; simultaneous consideration of nonlinearities and uncertainties.

Topics addressed

  • Nonlinear normal modes of structures with contact and gap.
  • Periodic solutions of musical instruments.
  • Irreversible energy transfer via dynamic absorbers: application in acoustics and mechanics.
  • Bifurcations detection by extracting singularities in the Taylor series.
  • Development of advanced structural models (models of beam with flexible thin section, application to the folding and deployment of structures based on tape measure), numerical simulation by the finite element method, stability study by the asymptotic numerical method.
  • Simulation of composite slender structures (laminated elastomeric metal).
  • Simulation of damping structures (frequency adapter).
  • Modeling damage due to mechanical fatigue.
  • Stability of uncertain systems (stochastic eigenvalue problem).
  • Frequency response of nonlinear uncertain systems.

Contribution to socio-economical aspects

Development of applications and studies specific to these fields

  • Space: design of deployable space structures and study of their stability, design of laminated high-tech parts.
  • Aviation: design laminated parts for helicopter rotors.
  • Energy: security of electricity production plants.

Development of free software


  • Academic: GdR Dynolin, IUSTI (Marseille), L3M (Metz), LMR (University of Tours), LOFIMS (INSA de Rouen).
  • National labs and industrial partners: EDF R&D (Clamart, France), Eurocopter, PSA Peugeot Citroën, Snecma, Thales Alenia Space.


Nassira Boulebbad-Gomez Stéphane BOURGEOIS Bruno COCHELIN Stéphane LEJEUNES Pernelle MARONE-HITZ Elia PICAULT Emmanuelle SARROUY Pierre SUQUET