Papers › A linearly-implicit energy-momentum preserving scheme for geometrically nonlinear...
A linearly-implicit energy-momentum preserving scheme for geometrically nonlinear mechanics based on non-canonical Hamiltonian formulations
Andrea Brugnoli, Denis Matignon, Joseph Morlier
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor. This framework is developed for von-K\'arm\'an nonlinearities in beams and plates, as well as geometrically nonlinear elasticity with Saint-Venant material behavior. In the case of plates, both negligible and non-negligible membrane inertia are considered. For the former case the two-dimensional elasticity complex is leveraged to express the dynamics in terms of the Airy stress function. The finite element discretization employs a mixed approach, combining a conforming approximation for displacement and velocity fields with a discontinuous stress tensor representation. A staggered, linear implicit time integration scheme is proposed, establishing connections with existing explicit-implicit energy-preserving methods. The stress degrees of freedom are statically condensed, reducing the computational complexity to solving a system with a positive definite matrix. The integration strategy preserves energy and angular momentum exactly. The methodology is validated through numerical experiments on the Duffing oscillator, a von-K\'arm\'an beam, and a column undergoing finite deformations. Comparisons with fully implicit energy-preserving method and the leapfrog scheme demonstrate that the proposed approach achieves superior accuracy while maintaining energy stability. Additionally, it enables larger time steps compared to explicit schemes and exhibits computational efficiency comparable to the leapfrog method.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections