Time integration with proper generalized decomposition for efficient time response analysis in nonlinear dynamical systems

Dae-Guen Lim; Gil-Yong Lee; Kang-Jae Park; Won-Ho Jung; Jun-Ho Kim; Yong-Hwa Park

doi:10.1117/12.3009750

9 May 2024 Time integration with proper generalized decomposition for efficient time response analysis in nonlinear dynamical systems

Dae-Guen Lim, Gil-Yong Lee, Kang-Jae Park, Won-Ho Jung, Jun-Ho Kim, Yong-Hwa Park

Author Affiliations +

Proceedings Volume 12951, Health Monitoring of Structural and Biological Systems XVIII; 129512F (2024) https://doi.org/10.1117/12.3009750
Event: SPIE Smart Structures + Nondestructive Evaluation, 2024, Long Beach, California, United States

Abstract

This paper presents a new framework that aims to improve the efficiency of time response analysis for nonlinear dynamical systems by combining conventional time integration methods with Proper Generalized Decomposition (PGD). The PGD approach utilizes low-dimensional subspaces of the time response to approximate the solution as a low-order separated representation of spatial and temporal components, with the Galerkin projection employed to formulate subproblems for each component. The subproblem for spatial basis is viewed as computing a reduced-order criterion, and the temporal problem projected to a subspace spanning this criterion uses time integration to obtain time coefficients. During the time integration, the spatial modes obtained from the calculation of the previous step are used as a reduced basis, and additional spatial modes are added until the residual of equations of motion satisfy the target tolerance. Numerical examples demonstrate that the proposed method allows significant computational savings compared to conventional time integration methods while accurately reflecting the nonlinear behavior.

Conference Presentation

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Dae-Guen Lim, Gil-Yong Lee, Kang-Jae Park, Won-Ho Jung, Jun-Ho Kim, and Yong-Hwa Park "Time integration with proper generalized decomposition for efficient time response analysis in nonlinear dynamical systems", Proc. SPIE 12951, Health Monitoring of Structural and Biological Systems XVIII, 129512F (9 May 2024); https://doi.org/10.1117/12.3009750

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available