Reinforced shells

Abstract

As above we accept in this case the assumptions about line contact and the rigid coupling of the ribs with the skin. The eccentricity of the stringers arrangement is taken into account. We consider the middle surface of the skin as the basic surface [143], so that the rib rigidity depends on its arrangement. The corresponding system of equilibrium equations for the stringer cylindrical shell has the form:

$${L_{01}}(\mathop U\limits^ - ) \equiv {L_1}(\mathop U\limits^ - ) + {q_1}\Phi (\eta )\left[ {1 + \beta \Phi (\eta )} \right]u,\xi \xi + 0.5(1 - v){u_{,\eta \eta }} + 0.5(1 + v){v_{,\eta \xi }} - v{w_{,\xi }} + \gamma \Phi (\eta ){w_{,\xi \xi \xi }} = $$

$${L_2}(\mathop U\limits^ - ) \equiv {v_{,\eta \eta }} + 0.5(1 - v){v_{,\xi \xi }} + 0.5(1 + v){u_{,\eta \xi }} - {w_{,\eta }} = {\mathop q\limits^ - _y},]$$

((6.1))

$${L_{03}}(\mathop U\limits^ - ) \equiv {L_3}(\mathop U\limits^ - ) + {q_3}\Phi (\eta ) \equiv (1 + {a^2}{\nabla ^4})w - {v_{,\eta }} - v{u_{,\xi }} + {(\alpha {w_{,\xi }} + \gamma u)_{,\xi \xi \xi }}\Phi (\eta ) = {\mathop q\limits^ - _z}.$$

.