Inverse mass matrix via the method of localized lagrange multipliers

0486539 - ÚT 2019 RIV GB eng J - Journal Article
González, J.A. - Kolman, Radek - Cho, S.S. - Felippa, C.A. - Park, K.C.
Inverse mass matrix via the method of localized lagrange multipliers.
International Journal for Numerical Methods in Engineering. Roč. 113, č. 2 (2018), s. 277-295. ISSN 0029-5981. E-ISSN 1097-0207
R&D Projects: GA MŠMT(CZ) EF15_003/0000493; GA ČR GA17-22615S
Institutional support: RVO:61388998
Keywords : explicit time integration * inverse mass matrix * localized Lagrange multipliers * partitioned analysis
OECD category: Applied mechanics
Impact factor: 2.746, year: 2018
https://onlinelibrary.wiley.com/doi/10.1002/nme.5613

An efficient method for generating the mass matrix inverse of structural dynamic problems is presented, which can be tailored to improve the accuracy of target frequency ranges and/or wave contents. The present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces and constructs the free-free inverse mass matrix using the standard FEM procedure. The various boundary conditions are realized by the the method of localized Lagrange multipliers. In particular, the present paper constructs the kernel inverse matrix by using the standard FEM elemental mass matrices. It is shown that the accuracy of the present inverse mass matrix is almost identical to that of a conventional consistent mass matrix or a combination of lumped and consistent mass matrices. Numerical experiments with the proposed inverse mass matrix are conducted to validate its effectiveness when applied to vibration analysis of bars, beams, and plain stress problems.
Permanent Link: http://hdl.handle.net/11104/0283565