999.
We consider the plane-strain buckling of a cylindrical shellof arbitrary thickness which is made of a Varga material andis subjected to an external hydrostatic pressure on its outersurface. The WKB method is used to solve the eigenvalue problemthat results from the linear bifurcation analysis. We show thatthe circular cross-section buckles into a non-circular shapeat a value of µ
1 which depends on
A1/
A2 and a mode number,where
A1 and
A2 are the undeformed inner and outer radii, andµ
1 is the ratio of the deformed inner radius to
A1. Inthe large mode number limit, we find that the dependence ofµ
1 on
A1/
A2 has a boundary layer structure: it is constantover almost the entire region of 0 <
A1/
A2 < 1 and decreasessharply from this constant value to unity as
A1/
A2 tends tounity. Our asymptotic results for
A1 1 = O(1) and
A1 1 = O(1/
n) are shown to agree with the numerical resultsobtained by using the compound matrix method.
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