Variable Thickness Shell and Continuity Conditions

Equation set (6.30) applies to a plain or holed shallow shell provided the only condition for the shearing force is Qz = qr/2 [cf. (6.27)] where the load is either q = 0 or q = constant. In order to determine the flexure of a variable thickness shell, we will consider a shell made of several concentric ring elements of constant thickness that are continuously linked together and where the normal thickness of each of them is varied by small increments.

6.3.1 Shell Relations for a Constant Thickness Ring Element

The five unknowns C1 to C5 in set (6.30) require use of five relations which determine the boundary conditions at center and edge of a constant thickness shell either in a plain or ring form. These five relations are hereafter chosen as the normal displacement, slope, radial bending moment, radial tension, and tangential elongation. From sets (6.30) and (6.3), we obtain respectively displac. w = f ( £ Ci y + C5 )

i=i dw dYi

0 0