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The shell theory used is based on a degeneration of 3-D elasticity using the following three assumptions
Assumption (1) is equivalent to taking into account the effect of transverse shear deformation and it has been widely used in recent years both in the context of linear and nonlinear analysis of shells. On the other hand, assumption (2) is the typical plane stress condition, traditionally used in plate and shell theory. This condition, namely plane stress hypothesis, is then used to reduce the three-dimensional constitutive relations to surface ones. Finally, assumption (3) implies that the thickness of the shell, measured along the fiber direction, at each point does not change in different deformed configurations of the shell, which implies zero strain along the fiber direction. This last assumption, namely fiber inextensibility condition, is essential for an adequate kinematic description of the large rotations of the fiber directions.
- Normals to the shell middle surface before deformation remain straight, but not necessarily normal to the middle surface after deformation.
- The normal stress, in the thickness direction, is zero.
- The shell thickness remains constant during the deformation
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