Ιδρυματικό Αποθετήριο
Πολυτεχνείο Κρήτης
Πολυτεχνείο Κρήτης
EN
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EL
| URI: | http://purl.tuc.gr/dl/dias/F0AA16FB-65BB-4FFE-B731-7E3234EEE43A | ||
| Έτος | 2009 | ||
| Τύπος | Δημοσίευση σε Περιοδικό με Κριτές | ||
| Άδεια Χρήσης |
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| Βιβλιογραφική Αναφορά | J. R. Fernández, R. Martínez ,G. E. Stavroulakis ," Numerical analysis of an elasto-piezoelectric problem with damage ," Intern. j. for num. meth. in engineering,vol. 77,no.2 ,pp. 261-284, 2008.doi: 10.1002/nme.2408 https://doi.org/10.1002/nme.2408 | ||
| Εμφανίζεται στις Συλλογές |
In this paper, we analyze an algorithm for the quasistatic evolution of the mechanical state of an elasto-piezoelectric body with damage. Both damage, caused by the development and the growth of internal microcracks, and piezoelectric effects, are included in the model. The mechanical problem is expressed as an elliptic system for the displacement field coupled with a non-linear parabolic partial differential equation for the damage field and a linear partial differential equation for the electric potential. The variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential, and a non-linear parabolic variational equation for the damage field. The existence of a unique weak solution is stated. Then, a fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, some numerical simulations are performed, in one, two and three dimensions, to demonstrate the accuracy of the scheme and the behaviour of the solution
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