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A numerical integration scheme for finite element method based on symbolic manipulation
Author(s) -
Yagawa G.,
Ye G.W.,
Yoshimura S.
Publication year - 1990
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.1620290711
Subject(s) - numerical integration , finite element method , stiffness matrix , numerical analysis , scheme (mathematics) , mixed finite element method , mathematics , extended finite element method , simple (philosophy) , computer science , mathematical analysis , structural engineering , engineering , philosophy , epistemology
This paper is concerned with the improvement of the efficiency and accuracy of the usual numerical integration procedures for the finite element method. A modified numerical integration scheme based on both the symbolic manipulation system and the numerical integration formula is proposed. Its efficiency for the integration of complicated rational or irrational expressions is demonstrated through several numerical examples. To verify its effectiveness in the calculation of the finite element stiffness matrix, a simple numerical example is also presented.