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Partitioned formulation of contact‐impact problems with stabilized contact constraints and reciprocal mass matrices
Author(s) -
González José A.,
Kopačka Ján,
Kolman Radek,
Park KwangChun
Publication year - 2021
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.6739
Subject(s) - lagrange multiplier , substructure , penalty method , finite element method , mass matrix , mathematics , mathematical optimization , stiffness matrix , scaling , stiffness , reciprocal , stability (learning theory) , numerical stability , numerical analysis , computer science , mathematical analysis , structural engineering , engineering , geometry , physics , machine learning , nuclear physics , neutrino , linguistics , philosophy
This work presents an efficient and accuracy‐improved time explicit solution methodology for the simulation of contact‐impact problems with finite elements. The proposed solution process combines four different existent techniques. First, the contact constraints are modeled by a bipenalty contact‐impact formulation that incorporates stiffness and mass penalties preserving the stability limit of contact‐free problems for efficient explicit time integration. Second, a method of localized Lagrange multipliers is employed, which facilitates the partitioned governing equations for each substructure along with the completely localized contact penalty forces pertaining to each free substructure. Third, a method for the direct construction of sparse inverse mass matrices of the free bodies in contact is combined with the localized Lagrange multipliers approach. Finally, an element‐by‐element mass matrix scaling technique that allows the extension of the time integration step is adopted to improve the overall performance of the algorithm. A judicious synthesis of the four numerical techniques has resulted in an increased stable explicit step‐size that boosts the performance of the bipenalty method for contact problems. Classical contact‐impact numerical examples are used to demonstrate the effectiveness of the proposed methodology.