薄肉筒の彈性安定に就て

抄録

The object of this investigation is to study mathematically and experimentally the problems of elastic stability of the thin walled cylinder with any form of periphery and compressed along its axis.
For this purpose the author introduced the simplified equation of equilibrium (15)& (16),
∇⁴Φ-(1-σσ²)/R²K∂⁴w/∂Z⁴=0 (15)
Φ=-DR²(∇⁴w+P₀/_??_∂∂²w/∂ZZ²) (16)
For the circular cylinder the radius of curvature at any point on its periphery is constant, but generally it changes with its position on the periphery; then it is difficult to slove the differential equation (15) & (16). The radius of curvature at any point R₂ is the function of periphery length. To solve (15) & (16) the author expressed R₂ and normal deflection w as function of s.
When R₂ is expressed with a rapidly convergent infinite series of cosks, the equations (15) & (16) is used, but for bad convergent series the author used the strain energy method. This method is very convenient, for instance in the case of rectangular cylinder.
All the results are compared with the extreme cases and for elliptic cylinder with experimental results.