Nonlinear dynamic reanalysis of structures by combined approximations

A major difficulty in non-linear dynamic reanalysis by mode superposition is the need to repeat the eigenproblem solutions. This study shows how the combined approximations approach can be used to overcome this difficulty. The approach is based on the integration of several concepts and methods, inc...

Full description

Saved in:
Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2006-07, Vol.195 (33-36), p.4420-4432
Main Authors: Kirsch, U., Bogomolni, M., Sheinman, I.
Format: Article
Language:English
Subjects:
Approximate reanalysis
Computational techniques
Dynamic analysis
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Nonlinear analysis
Physics
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A major difficulty in non-linear dynamic reanalysis by mode superposition is the need to repeat the eigenproblem solutions. This study shows how the combined approximations approach can be used to overcome this difficulty. The approach is based on the integration of several concepts and methods, including matrix factorization, series expansion and reduced basis. The advantage is that efficient local approximations and accurate global approximations are combined to achieve an effective solution procedure. In the procedure developed for material non-linearity, improved basis vectors are introduced using the concepts of Gram–Schmidt orthogonalizations and shifts. Numerical examples show that accurate approximations are achieved efficiently for very large changes in the design variables.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2005.09.013