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Stiffness matrix of the four‐node quadrilateral element in closed form
Author(s) -
Griffiths D. V.
Publication year - 1994
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.1620370609
Subject(s) - quadrilateral , direct stiffness method , stiffness matrix , finite element method , scalar (mathematics) , matrix (chemical analysis) , subroutine , stiffness , node (physics) , mathematics , fortran , gaussian elimination , gaussian , computer science , structural engineering , geometry , engineering , physics , materials science , composite material , operating system , quantum mechanics
The stiffness matrix of a plane four‐node quadrilateral finite element is given in closed form. When expressed as a FORTRAN subroutine and compared with the classical method of forming the stiffness matrix using Gaussian integration, the approach gives a CPU time speed‐up of the order of 2–3 on a vector machine and of the order of 4–5 on a scalar machine. The technique used to generate the terms of the stiffness matrix made use of a computer algebra system which could clearly be extended to generate the matrices for other elements types.