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A general mass lumping scheme for the variants of the extended finite element method
Author(s) -
Asareh Iman,
Song JeongHoon,
Mullen Robert L.,
Qian Yu
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6308
Subject(s) - degrees of freedom (physics and chemistry) , mass matrix , finite element method , spurious relationship , kinetic energy , matrix (chemical analysis) , mathematics , benchmark (surveying) , energy (signal processing) , mixed finite element method , algorithm , mathematical analysis , physics , classical mechanics , chemistry , quantum mechanics , statistics , geodesy , chromatography , neutrino , thermodynamics , geography
Summary A new strategy for the mass matrix lumping of enriched elements for explicit transient analysis is presented. It is shown that to satisfy the kinetic energy conservation, the use of zero or negative masses for enriched degrees of freedom of lumped mass matrix may be necessary. For a completely cracked element, by lumping the mass of each side of the interface into the finite element nodes located at the same side and assigning zero masses to the enriched degrees of freedom, the kinetic energy for rigid body translations is conserved without transferring spurious energy across the interface. The time integration is performed by adopting an explicit‐implicit technique, where the regular and enriched degrees of freedom are treated explicitly and implicitly, respectively. The proposed method can be viewed as a general mass lumping scheme for the variants of the extended finite element methods because it can be used irrespective of the enrichment method. It also preserves the optimal critical time step of an intact finite element by treating the enriched degrees of freedom implicitly. The accuracy and efficiency of the proposed mass matrix are validated with several benchmark examples.