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The application of symbolic computing to the hierarchical finite element method
Author(s) -
Bardell N. S.
Publication year - 1989
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.1620280513
Subject(s) - finite element method , computer science , stiffness , mixed finite element method , variety (cybernetics) , elasticity (physics) , brick , mathematics , structural engineering , computational science , engineering , physics , artificial intelligence , thermodynamics , civil engineering
One difficulty associated with the hierarchical finite element method is that of accurately determining the integrals necessary to establish the stiffness and mass matrices of arbitrarily high order elements. This paper describes how such integrals can be calculated exactly using symbolic computing. Results are presented which permit the construction of high order hierarchical finite elements applicable to a variety of problems involving two‐dimensional elasticity, and plate and shell bending. Three‐dimensional solid or brick elements are not considered.