Geometry of a laminate with K layers

2 Laminates with Groups of Electrically Paralleled Laminae 

The above representation is identical to classical lamination theory just that the matrix dimensions are extended by virtue of the included electrostatic fields. But the so-far utilized analogous assumptions for the latter need to be thought over, as the effect of the electrodes on the electrostatic field distribution within the individual layer and the parallel connection of electrode pairs of several layers is not yet considered. 

Remark 6.3. The electric field strength is assumed to be constant across the thickness of the individual laminae and to be identical in all laminae with paralleled electrode pairs with respect to absolute values. 

While a linear through thickness variation of mechanical strains is considered, the electroding by groups of piezoelectric layers results in a piecewise 

When the laminate resultants are formed by through thickness integration as in Eqs. (6.3), then the electrostatic fields of every group with connected electrodes have to be considered separately. Thus, individual rows and columns are introduced in the coefficient matrix of the laminate constitutive relation. Explicitly written out for two groups denoted by the letters c and d, the constitutive relation may be formulated as 

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