Vol.11, No 1, 2013 pp. 1 -12
UDC 624.01+531;519.6
MODELING OF PIEZOELECTRIC SMART STRUCTURES BY IMPLEMENTATION OF A USER DEFINED SHELL FINITE ELEMENT
Tamara Nestorović1, Somu Shabadi1, Dragan Marinković2,3, Miroslav Trajkov1
1Ruhr Univerisität Bochum, Germany
2Institut für Mechanik, TU Berlin, Germany
3Faculty of Mechanical Engineering, University of Niš, Serbia
In this paper, the nine node piezoelectric shell element developed in [1] has been implemented in the commercial FE software ABAQUS. In comparison with our previous work [2], the application has been extended to modeling of arbitrary thin walled structures also with complex geometries, whereby the automated mesh generation has been achieved by developing a Python based interface for meshing procedure. In order to be able to perform the post processing, special adaptation of the user element has to be performed for visualization purposes. The implemented element regards the piezoelectric thin layers polarized in the thickness direction and it is based on the e31 piezoelectric effect. It is also shown that this biquadratic nine node element based on degenerated shell approach is less prone to locking effects and more suitable for implementation with curved structures. Through several examples the accuracy of the implemented user defined shell element as well as of the Python mesh generator has been demonstrated, along with the possibilities for post processing. Meshing the structures with the nine node user element is not third party software dependent.
Key words: User Element, Piezoelectric Shell Element, ABAQUS, Piezoelectric Active Structures
MODELIRANJE PIEZOELEKTRIČNIH AKTIVNIH STRUKTURA POMOĆU KORISNIČKOG KONAČNOG ELEMENTA TIPA LJUSKE
U ovom radu piezoelektrični element tipa ljuske sa devet čvorova razvijen u [1] implementiran je u okviru komercijalnog softvera konačnih elemenata ABAQUS. U poređenju sa našim prethodnim radom [2] proširili smo primenu na modeliranje tankozidnih struktura proizvoljno kompleksnih geometrija, pri čemu je automatsko generisanje mreže realizovano putem interfejsa zasnovanog na Pythton kodu. U cilju sprovođenja postprocesiranja izvršena je posebna adaptacija korisničkog elementa radi vizualizacije rezultata. Implementirani korisnički element tretira tanke piezoelektrične slojeve koji su polarizovani u pravcu debljine i zasniva se na e31 piezoelektričnom efektu. Takođe je pokazano da je ovaj bikvadratni element sa devet čvorova zasnovan na pristupu degenerisane ljuske manje podložan loking efektu i da je prikladniji za primene na zakrivljenim strukturama. Na nekoliko primera potvrđena je tačnost implementiranog korisničkog elementa tipa ljuske, i generatora mreže zasnovanog na Python kodu, kao i mogućnost postprocesiranja. Generisanje mreže pomoću ovog korisničkog elementa sa devet čvorova nije uslovljeno primenom nekog eksternog softvera.
Ključne reči: korisnički element, piezoelektrični element tipa ljuske, ABAQUS, piezoelektrične aktivne strukture