## *IMPERFECTION command

## *IMPERFECTION command

(OP)

I have to perform a postbuckling analysis on a compressed cylinder. I've made a buckling analysis (linear) to find the eigenvalues, then I would like to use the *imperfection command to introduce imperfection modes in the cylinder. I set up a Static, Riks analysis with the command written as:

*imperfection,file=buckling-mode,step=1,inc=1

but nothing happened....

Results are the same with or without the *imperfection command. Why doesn't the processor take the command into account?

Thanks a lot

Tommy

*imperfection,file=buckling-mode,step=1,inc=1

but nothing happened....

Results are the same with or without the *imperfection command. Why doesn't the processor take the command into account?

Thanks a lot

Tommy

## RE: *IMPERFECTION command

1.2.6 Buckling of an imperfection-sensitive cylindrical shell

Product: ABAQUS/Standard

This example serves as a guide to performing a postbuckling analysis using ABAQUS for an imperfection-sensitive structure. A structure is imperfection sensitive if small changes in an imperfection change the buckling load significantly. Qualitatively, this behavior is characteristic of structures with closely spaced eigenvalues. For such structures the first eigenmode may not characterize the deformation that leads to the lowest buckling load. A cylindrical shell is chosen as an example of an imperfection-sensitive structure.

Geometry and model

The cylinder being analyzed is depicted in Figure 1.2.6–1. The cylinder is simply supported at its ends and is loaded by a uniform, compressive axial load. A uniform internal pressure is also applied to the cylinder. The material in the cylinder is assumed to be linear elastic. The thickness of the cylinder is 1/500 of its radius, so the structure can be considered to be a thin shell.

The finite element mesh uses the fully integrated S4 shell element. This element is based on a finite membrane strain formulation and is chosen to avoid hourglassing. A full-length model is used to account for both symmetric and antisymmetric buckling modes. A fine mesh, based on the results of a refinement study of the linear eigenvalue problem, is used. The convergence of the mesh density is based on the relative change of the eigenvalues as the mesh is refined. The mesh must have several elements along each spatial deformation wave; therefore, the level of mesh refinement depends on the modes with the highest wave number in the circumferential and axial directions.

Solution procedure

The solution strategy is based on introducing a geometric imperfection in the cylinder. In this study the imperfections are linear combinations of the eigenvectors of the linear buckling problem. If details of imperfections caused in a manufacturing process are known, it is normally more useful to use this information as the imperfection. However, in many instances only the maximum magnitude of an imperfection is known. In such cases assuming the imperfections are linear combinations of the eigenmodes is a reasonable way to estimate the imperfect geometry (Arbocz, 1987).

Determining the most critical imperfection shape that leads to the lowest collapse load of an axially compressed cylindrical shell is an open research issue. The procedure discussed in this example does not, therefore, claim to compute the lowest collapse load. Rather, this example discusses one approach that can be used to study the postbuckling response of an imperfection-sensitive structure.

The first stage in the simulation is a linear eigenvalue buckling analysis. To prevent rigid body motion, a single node is fixed in the axial direction. This constraint is in addition to the simply supported boundary conditions noted earlier and will not introduce an overconstraint into the problem since the axial load is equilibrated on opposing edges. The reaction force in the axial direction should be zero at this node.

The second stage involves introducing the imperfection into the structure using the *IMPERFECTION option. A single mode or a combination of modes is used to construct the imperfection. To compare the results obtained with different imperfections, the imperfection size must be fixed. The measure of the imperfection size used in this problem is the out-of-roundness of the cylinder, which is computed as the radial distance from the axis of the cylinder to the perturbed node minus the radius of the perfect structure. The scale factor associated with each eigenmode used to seed the imperfection is computed with a FORTRAN program. The program reads the results file produced by the linear analysis and determines the scale factors so that the out-of-roundness of the cylinder is equal to a specified value. This value is taken as a fraction of the cylinder thickness.

The final stage of the analysis simulates the postbuckling response of the cylinder for a given imperfection. The primary objective of the simulation is to determine the static buckling load. The modified Riks method is used to obtain a solution since the problem under consideration is unstable. The Riks method can also be used to trace the unstable and stable solution branches of a buckled structure. However, with imperfection-sensitive structures the first buckling mode is usually catastrophic, so further continuation of the analysis is usually not undertaken. When using the *STATIC, RIKS option, the tolerance used for the force residual convergence criteria may need to be tightened to ensure that the solution algorithm does not retrace its original loading path once the limit point is reached. Simply restricting the maximum arc length allowed in an increment is normally not sufficient.