Vol.2, No 10, 2000 pp. 1253-1261
UDC 537.226.86(045)
VARIATIONAL
THEORY
FOR NONLINEAR
PIEZOELECTRICITY
Ji-Huan He
Shanghai University, Shanghai Institute
of Applied Mathematics and Mechanics, Shanghai 200072, P.R. China
Abstract. The present paper concentrates
on the construction of a generalized variational principle (non Gurtin-type
and not involving convolutions) for nonlinear piezoelectricity. By the
semi-inverse method proposed by He, a family of variational principles
is established directly from the field equations and boundary conditions.
Present theory provides a more complete theoretical basis for the finite
element applications, variational-based meshless method(element-free method),
and the other direct variational methods such as Ritz's , Trefftz's and
Kantorovitch's methods.
VARIJACIONA
TEORIJA ZA NELINEARNU PIEZOELEKTRIKU
Rad je usresređen na konstruisanje generalizovano
varijacionog principa (koji nije Gurtin-ovog tipa i koji ne obuhvata konvolucije)
za nelinearnu piezoelektriku. Pomoću semi-inverzne metode koju je predložio
He, ustanovljena je familija varijacionih principa direktno iz jednačina
polja i graničnih uslova. Ova teorija obezbedjuje kompletniju teorijsku
osnovu za primenu konačnih elemenata, meshless metoda (metoda bez elementa)
zasnovanog na varijaciji i drugih direktnih varijacionih metoda kao što
su Ritz-ova, Treffty-ova i Kantorovitch-ov metoda.
