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1、Note: This workshop provides instructions in terms of the ABAQUS Keywords interface. If you wish to use the ABAQUS GUI interface instead, please see the “Interactive” version of these instructions.Please complete either the Keywords or Interactive version of this workshop.Goals Learn the technique u
2、sed for postbuckling analysis. Use the *NODE FILE option to save eigenmodes for use in a later postbuckling investigation. Learn how to “seed” a perfect geometry with imperfections based on previously extracted eigenmodes. Use ABAQUS/Viewer to create load-displacement curves for postbuckling results
3、 evaluation.IntroductionThis workshop is a follow-up to Workshop1. The model is a two-dimensional, thin elastic ring that is subject to external pressure. Numerical results can be compared to a theoretical solution, which is a critical buckling pressure ofwhere E is Youngs modulus, I is the moment o
4、f inertia, and R is the mean radius of the ring. For this problem there is a critical buckling pressure of 0.05171 MPa, or 7.5 lb/in2.In Workshop 1 it sufficed to mesh a 45 segment of the ring and to use a combination of symmetric and antisymmetric boundary conditions. Here a 90 model should be used
5、. This workshop consists of the following steps: 1. Run an eigenvalue buckling analysis of a 90 model.2. Run a postbuckling analysis on “perturbed” geometry based on the perfect ring geometry and the eigenvalues calculated in Step 1.3. Evaluate the results.The model is shown below:ABAQUS simulation1
6、. Enter the working directory for this workshop:./buckling/keywords/workshop22. Run the eigenvalue buckling problem to obtain the basic eigenmodes using the input file postbuckle1.inp.3. Open the postbuckle2.inp in a text editor and find the *IMPERFECTION option. The *IMPERFECTION option automatical
7、ly perturbs the perfect geometry of a model with an imperfection based on previously generated eigenvalue buckling results.In the eigenvalue buckling analysis (postbuckle1.inp) the *NODE FILE option is used to save the eigenmodes to the results (.fil) file for use by the *IMPERFECTION option. When p
8、erturbing a mesh, you choose which eigenmodes will be used and the magnitudes of the perturbations generated from each eigenmode. This decision requires judgment and experience. For structural problems (beams and shells) perturbations of 0.01 to 0.1 of the cross-section or thickness dimension are ty
9、pically used. It is also typical to use a few modes to ensure that the dominant imperfection is present in the model. 4. Run the postbuckling analysis postbuckle2.inp. 5. Once the analysis completes, study the results in ABAQUS/Viewer. Recall that in a Riks step the load magnitude is found as part o
10、f the solution. The load proportionality factor (output variable LPF) is written to the output database (.odb) file as history data.6. Try running a few cases: Mode 1 used for the imperfection alone, Mode 2 used for the imperfection alone, Mode 3 used for the imperfection alone, and a combination of
11、 these modes. You will observe results such as the following figure:7. Try running the problem with very tight convergence controls and limiting the maximum arc length increment that the program is allowed to take. Increase the maximum number of increments allowed in the step so that the analysis do
12、es not end before buckling occurs.CommentsThis workshop problem really does not require the use of the Riks procedure. As shown in the above figure, the postbuckling response is stable (retains a positive slope). You may wish to try the analyses again without the RIKS parameter on the *STEP option.
13、We use this problem in the workshop to demonstrate the importance of selecting appropriate imperfections for “seeding” otherwise geometrically perfect models of structures. It would have been preferable to use a doubly curved shell model; but, to be meaningful, such models are rather large and impra
14、ctical for use in a workshop such as this. Review benchmark problem Buckling of a cylindrical shell under uniform axial pressure and example problems Laminated composite shells: buckling of a cylindrical panel with a circular hole and Buckling of an imperfection sensitive cylindrical shell for additional details and examples of postbuckling analysis with ABAQUS.