Advanced
search

To read this content please select one of the options below:

Efficiency evaluation of structural nonlinear analysis method based on the Woodbury formula

Gang Li (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, China)
Shuo Jia (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, China)
Hong-Nan Li (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, China and School of Civil Engineering, Shenyang Jianzhu University, Shenyang, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 5 June 2019

Issue publication date: 5 June 2019

166

Abstract

Purpose

The purpose of this paper is to make a theoretical comprehensive efficiency evaluation of a nonlinear analysis method based on the Woodbury formula from the efficiency of the solution of linear equations in each incremental step and the selected iterative algorithms.

Design/methodology/approach

First, this study employs the time complexity theory to quantitatively compare the efficiency of the Woodbury formula and the LDLT factorization method which is a commonly used method to solve linear equations. Moreover, the performance of iterative algorithms also significantly effects the efficiency of the analysis. Thus, the three-point method with a convergence order of eight is employed to solve the equilibrium equations of the nonlinear analysis method based on the Woodbury formula, aiming to improve the iterative performance of the Newton–Raphson (N–R) method.

Findings

First, the result shows that the asymptotic time complexity of the Woodbury formula is much lower than that of the LDLT factorization method when the number of inelastic degrees of freedom (IDOFs) is much less than that of DOFs, indicating that the Woodbury formula is more efficient for local nonlinear problems. Moreover, the time complexity comparison of the N–R method and the three-point method indicates that the three-point method is more efficient than the N–R method for local nonlinear problems with large-scale structures or a larger ratio of IDOFs number to the DOFs number.

Originality/value

This study theoretically evaluates the efficiency of nonlinear analysis method based on the Woodbury formula, and quantitatively shows the application condition of the comparative methods. The comparison result provides a theoretical basis for the selection of algorithms for different nonlinear problems.

Keywords

Acknowledgements

Funding for authors was provided by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (2018YFD1100404), the National Natural Science Foundation of China (Grant No. 51878112), the Fundamental Research Funds for the Central Universities (DUT17ZD220) and Dalian High Level Talent Innovation Support Program (2017RD04, 2015R044). The opinions, findings and conclusions expressed in this paper are those of the authors and do not necessarily reflect the views of those acknowledged here.

Citation

Li, G., Jia, S. and Li, H.-N. (2019), "Efficiency evaluation of structural nonlinear analysis method based on the Woodbury formula", Engineering Computations, Vol. 36 No. 4, pp. 1082-1100. https://doi.org/10.1108/EC-09-2018-0393

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited

Related articles

Manage cookies

We’re listening — tell us what you think

Join us on our journey