Issue 42

J.-M. Nianga et alii, Frattura ed Integrità Strutturale, 42 (2017) 280-292; DOI: 10.3221/IGF-ESIS.42.30 284 0 i u on   (28)   0 i i u N onC  (29) 0 on    (30)   0 on C   (31) , , , 1 1 2 ( ) ( ) ( ) ijkl k l j kij k j ijkl k l j kij k j NNkl k l kNN k i a u n e E n a u n e E n a u e E N on C       (32) , 0 NNkl k l kNN k a u e E on C   (33) 1 2 0 i i i i D n D n on C    (34) where N and n represent the unit normal to C, outer to its side 1, see (Fig. 2), and the unit outer normal to the open domain , C C     respectively. Figure 2 : Representation of the fissured piezoelectric structure C  . These relations express a compression on C according to (33), as well as the normality of the force which acts; with an opposition between the action and the reaction, according to (32). Consequently, the variational formulation (FVP) for the problem of such a fissured piezoelectric structure can be stated as follows: Problem (FVP): Find * * ( , ) u u inV V    such that: * * ( , ) ( , ) 0 ( , ) ( , ) 0 u a u v u b v u v V c d u V                         (35) where   1 ( ); ( ); 0 u i i C i V u u u H u       (36)     * ( ); ; 0 u u i i i i V u u u V u N     (37)   1 ; ( ); 0 C V H          (38)