Finite Element Method Application For Nonlinear Mechanical Response Of Three-Dimensonal Beams Using Mathematica

Yıl 2019, , 961 - 966, 01.12.2019

Hakan Tanrıöver

https://doi.org/10.2339/politeknik.439546

Öz

Mechanical behavior of beams under large rotations and
displacements was investigated. Using co-rotational approach given by
Crisfield, three dimensional beam finite elements was modeled in Mathematica
environment. The symbolic process of Mathematica provides keeping the
parameters in the model as variables and beams having different geometries can
be modelled easily. The yielding non-linear equation system was solved by
utilizing Newton-Raphson technique. Dynamic balance equations and numerical
time integration method were introduced, the solution process was left as a
future work, however. Comparisons with the results of ANSYS and those of the
works from the literature are accomplished.

Anahtar Kelimeler

Three-dimensional beams, Mathematica, nonlinear analysis

Üç Boyutlu Kirişlerin Doğrusal Olmayan Mekanik Davranışı için Mathematica Kullanarak Sonlu Elemanlar Yöntemi Uygulaması

Öz

Kirişlerin büyük
dönmeler ve yer değiştirmeler altında mekanik davranışı incelendi. Crisfield
tarafından verilen eş-dönüşlü formülasyon yardımıyla üç boyutlu kiriş sonlu
elemanları Mathematica yazılımı içerisinde modellendi. Mathematica yazılımının
sembolik işlemcisi sayesinde modele ait parametreler değişken tutulabilir ve
değişik geometrilerdeki kirişler kolayca modellenebilir. Doğrusal olmayan
denklem takımları Newton-Raphson yöntemi ile çözüldü. Dinamik hareket denklemi
ve sayısal zaman integrasyon yöntemi ortaya konuldu yalnız çözümlemeler ileriki
çalışmalara bırakıldı. Literatürdeki çalışmaların ve ANSYS programının
sonuçlarıyla karşılaştırmalar yapıldı.

Anahtar Kelimeler

Üç boyutlu kiriş, Mathematica, Doğrusal Olmayan analiz

Kaynakça

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