The LATIN-PGD methodology to nonlinear dynamics and quasi-brittle materials for future earthquake engineering applications

TL;DR

This paper introduces a novel LATIN-PGD methodology combining model reduction and advanced time-integration techniques to efficiently solve nonlinear quasi-brittle dynamics problems relevant for earthquake engineering.

Contribution

It presents the first implementation of LATIN combined with PGD and TDGM for nonlinear low-frequency dynamics with damage models, improving computational efficiency.

Findings

Efficient solution of 3D bending beam nonlinear dynamics.

Comparison shows advantages over classical nonlinear solvers.

Framework enables future seismic risk uncertainty analysis.

Abstract

This paper presents a first implementation of the LArge Time INcrement (LATIN) method along with the model reduction technique called Proper Generalized Decomposition (PGD) for solving nonlinear low-frequency dynamics problems when dealing with a quasi-brittle isotropic damage constitutive relations. The present paper uses the Time-Discontinuous Galerkin Method (TDGM) for computing the temporal contributions of the space-time separate-variables solution of the LATIN-PGD approach, which offers several advantages when considering a high number of DOFs in time. The efficiency of the method is tested for the case of a 3D bending beam, where results and benchmarks comparing LATIN-PGD to classical time-incremental Newmark/Quasi-Newton nonlinear solver are presented. This work represents a first step towards taking into account uncertainties and carrying out more complex parametric studies imposed by seismic risk assessment.