Publications de François Marie Alain Demoures

Unified Discrete Multisymplectic Lagrangian Formulation for Hyperelastic Solids and Barotropic Fluids

We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction is the definition of discrete deformation gradients and discrete Cauchy-Green deformation tensors, which a ...

SPRINGER2022

Multisymplectic Variational Integrators for Fluid Models with Constraints

François Marie Alain Demoures

We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for barotropic and incomp ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

A multisymplectic integrator for elastodynamic frictionless impact problems

Mathieu Desbrun, Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures, Alejandro Marcos Aragon

We present a structure preserving numerical algorithm for the collision of elastic bodies. Our integrator is derived from a discrete version of the field-theoretic (multisymplectic) variational description of nonsmooth Lagrangian continuum mechanics, combi ...

Elsevier2017

Multisymplectic Variational Integrators For Nonsmooth Lagrangian Continuum Mechanics

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

This paper develops the theory of multisymplectic variational integrators for nonsmooth continuum mechanics with constraints. Typical problems are the impact of an elastic body on a rigid plate or the collision of two elastic bodies. The integrators are ob ...

Cambridge Univ Press2016

Multisymplectic variational integrators and space/time symplecticity

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

Multisymplectic variational integrators are structure-preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and spatial discrete evo ...

World Scientific Publ Co Pte Ltd2016

Discrete variational Lie group formulation of geometrically exact beams dynamics

Tudor Ratiu, François Gay-Balmaz, Yves Weinand, François Marie Alain Demoures

The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resultin ...

Springer2015

Multisymplectic Lie group variational integrator for a geometrically exact beam in R3

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

In this paper we develop, study, and test a Lie group multisymplectic integra- tor for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum ma ...

Elsevier2014

Lie Group and Lie Algebra Variational Integrators for Flexible Beam and Plate in R3

François Marie Alain Demoures

The purpose of this thesis is to develop variational integrators synchronous or asynchronous, which can be used as tools to study complex structures composed of plates and beams subjected to large deformations and stress. We consider the geometrically exac ...

EPFL2012

Flexible beam in R3 under large overall motions and Asynchronous Variational Integrators

Tudor Ratiu, François Gay-Balmaz, Yves Weinand, François Marie Alain Demoures

The theory of discrete variational mechanics has its roots in the optimal control literature of the 1960's. The past ten years have seen a major development of discrete variational mechanics and corresponding numerical integrators, due largely to pioneerin ...

IABSE ETH Zurich2011

AVI as a mechanical tool for studying dynamic and static beam structures

François Marie Alain Demoures

In this paper we study the dynamic behavior of an isotropic Kirchhoff- Love beam and investigate the equilibrium position of an Euler-Bernoulli beam. Using the discrete Euler-Lagrange and Lagrange-d’Alembert principles, we simulate the behavior by means of ...

Cruz (Ed.)2010