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

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

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

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.

Keywords:

Three-dimensional beams, Mathematica, nonlinear analysis,

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