PGD reduced-order modeling for structural dynamics applications

TL;DR

This paper introduces a PGD-based method for linear elastodynamics that emphasizes energy conservation and stability, comparing Lagrangian and Hamiltonian formulations through numerical examples.

Contribution

It develops weak formulations of PGD using Lagrangian and Hamiltonian mechanics, enhancing numerical stability and energy conservation in structural dynamics modeling.

Findings

Hamiltonian PGD offers better stability and energy conservation.

Both formulations effectively model dynamical behavior.

Numerical examples validate the proposed approach.

Abstract

We propose in this paper a Proper Generalized Decomposition (PGD) approach for the solution of problems in linear elastodynamics. The novelty of the work lies in the development of weak formulations of the PGD problems based on the Lagrangian and Hamiltonian Mechanics, the main objective being to devise numerical methods that are numerically stable and energy conservative. We show that the methodology allows one to consider the Galerkin-based version of the PGD and numerically demonstrate that the PGD solver based on the Hamiltonian formulation offers better stability and energy conservation properties than the Lagrangian formulation. The performance of the two formulations is illustrated and compared on several numerical examples describing the dynamical behavior of a one-dimensional bar.