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Integration of triangular finite elements containing corrective rational functions
Author(s) -
Katz I. Norman
Publication year - 1977
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.1620110111
Subject(s) - rational function , mathematics , elliptic rational functions , class (philosophy) , numerical integration , quadrature (astronomy) , order (exchange) , pure mathematics , degree (music) , algebra over a field , mathematical analysis , computer science , engineering , quarter period , physics , finance , elliptic curve , artificial intelligence , acoustics , electrical engineering , economics
Rational corrective functions are often supplemented to complete polynomials in order to create conforming triangular finite elements for plate bending. Although such elements containing complete polynomials of degree 3 or 4 have long been known, conforming triangular elements for plate bending, which contain complete polynomials of arbitrary degree p ⩽ 5 and new corrective rational functions, have been given only recently. Integration of rational functions usually requires numerical quadrature. It is shown here that these new corrective rational functions fall into two classes. For those in one class, explicit closed form integration formulas are available. For those in the other class, integration can be performed very efficiently by summing series whose general term is O( k d ) for large k , where d ⩽ 5. These formulas also apply to the older third and fourth order elements.