Skip to Main content Skip to Navigation
Journal articles

Multisymplectic variational integrators for nonsmooth lagrangian continuum mechanics

Abstract : 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 obtained by combining, at the continuous and discrete levels, the variational multisymplectic formulation of nonsmooth continuum mechanics with the generalized Lagrange multiplier approach for optimization problems with nonsmooth constraints. These integrators verify a spacetime multisymplectic formula that generalizes the symplectic property of time integrators. In addition, they preserve the energy during the impact. In the presence of symmetry, a discrete version of the Noether theorem is verified. All these properties are inherited from the variational character of the integrator. Numerical illustrations are presented.
Document type :
Journal articles
Complete list of metadata

Cited literature [112 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01385077
Contributor : Christian Cardillo <>
Submitted on : Thursday, October 27, 2016 - 10:54:10 AM
Last modification on : Tuesday, December 8, 2020 - 3:34:10 AM

File

Multisymplecitc variational in...
Files produced by the author(s)

Identifiers

Citation

Francois Demoures, Francois Gay-Balmaz, Tudor S Ratiu. Multisymplectic variational integrators for nonsmooth lagrangian continuum mechanics. Forum of Mathematics, Sigma, Cambridge University press, 2016, 4,e19, 54 p. ⟨10.1017/fms.2016.17⟩. ⟨hal-01385077⟩

Share

Metrics

Record views

274

Files downloads

443