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Consideration of constraints within the finite element method by means of matrix operators
Author(s) -
Mechnik RalphPeter
Publication year - 1991
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.1620310507
Subject(s) - finite element method , mathematics , matrix (chemical analysis) , mixed finite element method , element (criminal law) , extended finite element method , algebra over a field , mathematical optimization , calculus (dental) , computer science , pure mathematics , structural engineering , engineering , materials science , political science , law , composite material , medicine , dentistry
The following paper describes the incorporation of different constraints into a finite element system by means of matrix operators in conjunction with consecutive corresponding transformations. Instead of increasing the number of equations‐as e.g. the Lagrange Multiplier Method 10, 14 does‐the Matrix Operator Method yields a set of reduced magnitude which can be solved more efficiently. The method will be developed for two classes of constraints: (i) stiff coupling of previously known subdomains and (ii) contact problem between two bodies. The assembly rules to obtain the system matrices are deduced. An application is given by a three‐dimensional example of structural analysis in mechanical engineering.