Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd Edition

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B.11.2 Plane-Strain Conditions

Plane-strain conditions are used in the analysis of structures that are very thick in the z-direction. The z-direction strain is assumed zero $({\epsilon }_{zz}=0)$. Also zero are the shear strains ${\epsilon }_{yz}=0$ and ${\epsilon }_{zx}=0$. Hence, the 3-D elasticity relations (39) that express stresses in terms of strains are reduced to

$\begin{array}{l}{\sigma }_{xx}=\frac{E}{(1+\nu )}\hfill \end{array}$