Internal Loads of Beam and Wall

As a matter of course, the virtual work needs to be independent of the description. Thus, equating Eqs. (8.1) allows us to associate the internal mechanical as well as electric loads of beam L x,t) and wall L x, s,t)  

The constitutive relation of an adaptive laminated composite shell is given in Eq. (6.6). Being considered for the thin wall of the beam, the lines, respectively columns, associated with the cross-sectional strain component °(x, s) and bending curvature Ks x,s) can be dropped in accordance with Remark 7.4. To comply with the specification of a prismatic beam in Remark 7.1, also with regard to the material properties, the latter need to be constant along the lengthwise direction and thus the constitutive matrix lK(s) only depends on the cross-sectional coordinate. The constitutive relation of the wall and the corresponding formulation for the beam with the constitutive matrix P then 

Insertion of these constitutive relations into the virtual work of internal loads of the wall SU t) and of the beam SU t) as expressed by Eqs. (8.1) results in 

For the lower line, use has been made again of the relation between strain and electric field strength measures of wall and beam provided by Eq. (7.33). Similarly, the constitutive matrix of the beam may be identified  

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