A Study of the Effect of Imperfections on Buckling Capability in Thin Cylindrical Shells Under Axial Loading

Lauren Kougias

Objective

To study the effect of ovalization of a thin cylindrical shell on load carrying capability under an axial compressive load Evaluate buckling capabilities for several values of e

FEA Modeling and Part Dimensions Thin cylindrical shell modeled using shell elements AMS 4829 (Ti 6-4) properties used at 70°F

Cylinder Dimensions R = 40” L = 80” t = 0.15”

Symmetry Boundary Conditions Along Edge

Axial Load Applied andSimply Supported Along Edge

Buckling Capability: Theoretical Solution Theoretical solution for perfect (e = 0”) cylinder: 1,455,952 lb

E = Young’s Modulus v = Poisson’s Ratio t = wall thickness R = radius

Solution based on experimental data: 420,736 lb kc = buckling coefficient

Methodology

Used eigenvalue buckling solution to perform mesh density study to find appropriate element size for analysis for perfect cylinder (e = 0). Eigenvalue buckling solution used to create

imperfections in model for nonlinear buckling. Nonlinear buckling analysis performed using Riks

modified method for perfect cylinder (e = 0). Riks method is a solution method in Abaqus that

models postbuckling behavior of a structure. Nonlinear buckling analysis performed for several

ovalized cylinders (e = 0%-100% of shell thickness)

Eigenvalue Buckling Solution

Eigenvalue buckling mode four best represents ovalized shape

Mesh density study resulted in element size of 2” to yield an accurate solution.

Nonlinear Buckling Results, e = 50%

Summary of Nonlinear Buckling Results

Effect of Ovalization on Buckling Capability for a Thin Cylindrical Shell

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Distance Out of Round (in)

Bu

ck

ling

Lo

ad

Ca

pa

bili

ty (

lb)

Theoretical Solution

Load vs. Displacement Curves Typical behavior of a structure undergoing collapse (on left). Behavior of structure with e = 50% closely matches predicated

curve.

Conclusion

Adding imperfections in the form of ovalization significantly reduced the load carrying capability of the structure.

Further studies that take other types of imperfections into account must be addressed

Only addresses isotropic materials and the results should not be assumed to be the same for a composite structure