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

0502781 - ÚT 2020 RIV GB eng J - Journal Article
Gonzáles, J.A. - Kopačka, Ján - Kolman, Radek - Cho, S.S. - Park, K.C.
Inverse mass matrix for isogeometric explicit transient analysis via the method of localized Lagrange multipliers.
International Journal for Numerical Methods in Engineering. Roč. 117, č. 9 (2019), s. 939-966. ISSN 0029-5981. E-ISSN 1097-0207
R&D Projects: GA MŠMT(CZ) EF15_003/0000493; GA ČR(CZ) GA17-22615S; GA ČR GA17-12925S; GA ČR(CZ) GA16-03823S
Institutional support: RVO:61388998
Keywords : Bezier extraction * explicit transient analysis * free vibration * inverse mass matrix * isogeometric analysis * localized Lagrange multipliers
OECD category: Applied mechanics
Impact factor: 2.866, year: 2019
Method of publishing: Limited access
https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5986

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 Bezier elements with a standard C-0 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.
Permanent Link: http://hdl.handle.net/11104/0298220