An initially flat plate is defined by its reference domain Ω:

$\Omega =\left\{\left({X}_{1},{X}_{2},Z\right)\in {R}^{3}/Z\in \left(-\frac{t}{2},\frac{t}{2}\right),\left({X}_{1},{X}_{2}\right)\in M\subset {R}^{2}\right\}$

(6.41)

where t is the constant thickness of the plate, Z is the transverse coordinate orthogonal to the undeformed mid-plane $M$ identified by Z = 0 and (X_{1},X_{2}) are mid-plane (or simply in-plane) reference coordinates.

The following displacement field is assumed for the plate:

$v\left({X}_{1},{X}_{2},Z\right)=u\left({X}_{1},{X}_{2}\right)+Z\phi \left({X}_{1},{X}_{2}\right)+{Z}^{2}\psi \left({X}_{1},{X}_{2}\right)$

(6.42)

where u = {u_{1},u_{2},u_{3}}^{T} represents the displacement ...

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