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Shape functions and integration formulas for three‐dimensional finite element analysis
Author(s) -
Bedrosian G.
Publication year - 1992
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.1620350106
Subject(s) - quadrilateral , hexahedron , finite element method , numerical integration , mathematics , tetrahedron , integration by parts , pyramid (geometry) , degenerate energy levels , base (topology) , brick , mathematical analysis , geometry , structural engineering , engineering , physics , civil engineering , quantum mechanics
Shape functions and numerical integration formulas for three‐dimensional finite element analysis as found in most finite element reference books are incomplete. For example, shape functions and integration formulas for a pyramid with a quadrilateral base are missing. It is also difficult to find symmetric higher‐order integration formulas for triangular and tetrahedral elements. In general, these shape functions and integration formulas cannot be satisfactorily derived as degenerate cases of shape functions and integration formulas for hexahedral (brick) elements. In this paper we present C °‐continuous quadrilateral pyramid elements and integration formulas for two‐ and three‐dimensional elements.