Strain measures and compatibility equations in the linear high-order shell theories

General Equations of Anisotropic Plates and Shells Including Transverse Shear Deformations, Rotary Inertia and Initial Curvature Effects

“…In order to obtain such formulation, it is necessary to "rst develop the compatibility equations associated with the strain}displacement relationships. In order to obtain such equations, the reader may follow the procedures described by Sanders [10] and Brull and Librescu [168].…”

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“…T33 = (r+1) ^3 (^ = 0^) constitute the nth-order strain measures. However, alongside with (62), several other variants of the strain-measures may be defined (see in this sense [32]).…”

“…The basic field equations derived in Sections 6.1-6.5 may easily be specialized for this case. Some results pertaining to this theory are reported in [25,5,32,[40][41][42][43]. Moreover, a large diversity of high-order theories may result through various selection of ^in (14).…”