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Unified finite element analysis
Author(s) -
Mikhailov Mikhail Dimitrov
Publication year - 1983
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.1620191008
Subject(s) - finite element method , gauss , mathematics , matrix (chemical analysis) , boundary value problem , extension (predicate logic) , mixed finite element method , extended finite element method , class (philosophy) , mathematical analysis , calculus (dental) , algebra over a field , computer science , pure mathematics , engineering , structural engineering , physics , medicine , materials science , dentistry , quantum mechanics , composite material , programming language , artificial intelligence
A special matrix is introduced, the elements of which are zero or first‐order differential operators. This matrix is used to define a boundary value problem which covers a wide class of engineering applications. An equivalent variational formulation is found using an extension of the Gauss theorem. From this variational principle the equations of the elements are derived. The unified formulae presented here can be useful for educational purposes and for the design of a finite element system for total analysis.