2.12.12 Buckling of Shells

If a circular cylindrical shell is uniformly compressed in the axial direction, buckling symmetrical with respect to the axis of the cylinder (Figure 2.128) may occur at a certain value of the compressive load. The critical value of the compressive force Ncr per unit length of the edge of the shell can be obtained by solving the differential equation d4w

d2w dx2

where a is the radius of the cylinder and h is the wall thickness.

Alternatively, the critical force per unit length may also be obtained by using the energy method. For a cylinder of length L, simply supported at both ends, one obtains i2p2 EhL2 \

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