Inverse mass matrix for isogeometric explicit transient analysis via the method of localized Lagrange multipliers

A variational framework is employed to generate inverse mass matrices for isogeometric analysis (IGA). As different dual bases impact not only accuracy but also computational overhead, several dual bases are extensively investigated. Specifically, locally discontinuous biorthogonal basis functions a...

Full description

Saved in:
Bibliographic Details
Published in:International journal for numerical methods in engineering 2019-03, Vol.117 (9), p.939-966
Main Authors: González, José A., Kopačka, J., Kolman, R., Cho, S. S., Park, K. C.
Format: Article
Language:English
Subjects:
Accuracy
Basis functions
Boundary conditions
Boundary element method
Bézier extraction
Computation
Continuity (mathematics)
explicit transient analysis
Finite element method
free vibration
inverse mass matrix
isogeometric analysis
Lagrange multiplier
localized Lagrange multipliers
Mass matrix
Mathematical analysis
Parameterization
Splines
Transient analysis
Vibration analysis
Vibration control
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 variational framework is employed to generate inverse mass matrices for isogeometric analysis (IGA). As different dual bases impact not only accuracy but also computational overhead, several dual bases are extensively investigated. Specifically, locally discontinuous biorthogonal basis functions are evaluated in detail for B‐splines of high continuity and Bézier elements with a standard C0 continuous finite element structure. The boundary conditions are enforced by the method of localized Lagrangian multipliers after generating the inverse mass matrix for completely free body. Thus, unlike inverse mass matrix methods without employing the method of Lagrange multipliers, no modifications in the reciprocal basis functions are needed to account for the boundary conditions. Hence, the present method does not require internal modifications of existing IGA software structures. Numerical examples show that globally continuous dual basis functions yield better accuracy than locally discontinuous biorthogonal functions, but with much higher computational overhead. Locally discontinuous dual basis functions are found to be an economical alternative to lumped mass matrices when combined with mass parameterization. The resulting inverse mass matrices are tested in several vibration problems and applied to explicit transient analysis of structures.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5986