Negligence of Strain and Stress Components

Here the consequences of typical assumptions for the employment of the described shells as thin walls of a beam will be demonstrated. 

Remark 6.7. Membrane response dominates the structural behavior and forces acting along the curved coordinate direction are negligible. 

The reasons for these assumptions are illustrated within the context of the theory of thin-walled beams in the following chapter. The first part of Remark 6.7 demands negligence of the shell bending and twisting curvatures, while the second part sets the internal forces along the s-direction to zero  

These equations are to be applied to the constitutive relation of Eq. (6.6), exemplarily for two groups of electrically paralleled laminae. By virtue of Eqs. (6.20a), the associated columns and lines are eliminated, while the condensation due to Eq. (6.20b) on top leads to an additional term in every remaining component of the constitutive matrix  

It needs to be noted that those components responsible for the direct electric interaction between laminae groups are modified from 0, see Eq. (6.6), to -A24A24/A22. As the electrostatic fields of both groups have been coupled to the considered mechanical fields, the condensation of the latter has converted the indirect coupling to a virtually direct one. 

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