1. Collapse of Frame Workshop Thirteen REFERENCE: Training Manual Geometric Instability (9-74)

2. Workshop Supplement September 30, 2001 Inventory #001492 W13-2 Workshop Thirteen: Collapse of Frame Arc-Length Method Purpose Analyze the post-buckling response of a L-shaped frame. Goal Use the arc-length method to capture the post-buckling response Model Description BEAM189 elements meshed on an L-shaped frame, simply supported at ends. A concentrated force is applied near the left edge.

3. Workshop Supplement September 30, 2001 Inventory #001492 W13-3 1.Read in the input file named “ANL_W13_PostCollapse.inp” Use the GUI menu method: –Utility Menu > File > Read Input From… Select the file “ANL_W13_PostCollapse.inp” Click on [OK] or Command Input method: –/INPUT,ANL_W13_PostCollapse,inp Notes: This will read in an input file which will generate the geometry, loads, and boundary conditions for the current exercise. We will have a mesh of quadratic BEAM189 elements. The current database will be erased, and the jobname will be changed to “Exercise_13”. The graphics and other settings will also be set to be consistent with these slides. Workshop Thirteen: Collapse of Frame … Arc-Length Method

4. Workshop Supplement September 30, 2001 Inventory #001492 W13-4 Before continuing with the exercise, you can also examine the mesh and the boundary conditions on the model to become more familiar with it. The model is comprised of 3D quadratic BEAM189 elements. Because we will be assuming that the response is 2D, out-of-plane rotations and translations will be constrained for the entire mesh. The material properties are linear elastic. A nodal force of 500 units is applied in the downward direction near the left edge. The arc-length method will be used to capture the post-buckling response of this frame structure. Simply Supported Ends Applied Nodal Force Workshop Thirteen: Collapse of Frame … Arc-Length Method

5. Workshop Supplement September 30, 2001 Inventory #001492 W13-5 2.Verify the element options for BEAM189 (3-node quadratic beam with 4th node for orientation) Use the GUI menu method: –Main Menu > Preprocessor > Element Type > Add/Edit/Delete … Select “Type 1 BEAM189” Click on [Options] Verify element options, then click on [OK] Select [Close] or Command Input method: –/PREP7 –ETLIST Notes: Element type 1 will use BEAM189. The default element options will be used. KEYOPT(1), warping DOF, is important for open cross-sections which have significant warping. KEYOPT(2), cross-section scaling, is considered for finite-strain analyses. Workshop Thirteen: Collapse of Frame … Arc-Length Method

6. Workshop Supplement September 30, 2001 Inventory #001492 W13-6 3.Specify solution options for nonlinear analysis Use the GUI menu method: –Main Menu > Solution > -Analysis Type- Sol’n Control … –Solution Control > Basic tab Select “Large Displacement Static” under “Analysis Options” Specify “20” for number of substeps Select “Write every substep” for “Frequency” Do NOT select [OK] yet. or Command Input method: –/SOLU –NLGEOM,ON –OUTRES,ALL,ALL –NSUBST,20 Notes: This will be a large-deflection nonlinear analysis. All intermediate results will be saved for postprocessing purposes. Additional Notes: Only the initial number of substeps (20) has been specified. Recall that, for the arc-length method, automatic time stepping is not used since the arc-length method has its own time- stepping routine. Hence, we do not specify an ending time (TIME) or the min and max number of substeps. Workshop Thirteen: Collapse of Frame … Arc-Length Method

7. Workshop Supplement September 30, 2001 Inventory #001492 W13-7 4.Specify arc-length solution options Use the GUI menu method: –Solution Control > Advanced NL tab Turn on arc-length method by selecting “Activate arc-length method” checkbox. Enter “10” for “Max multiplier” and “1e-7” for “Min multiplier” Select [OK] to close the dialog box. or Command Input method: –ARCLEN,ON,10,1e-7 Notes: The min and max arc-length multipliers act in an analogous fashion to the min and max substeps for the Newton-Raphson method. That is why we only specify an initial number of substeps only (to calculate the initial arc-length radius), as noted in the previous slide. Usually, a termination criteria is set to end the analysis after a certain DOF limit is reached. However, for this case, we will run the analysis to completion of the applied load. Workshop Thirteen: Collapse of Frame … Arc-Length Method

8. Workshop Supplement September 30, 2001 Inventory #001492 W13-8 5.Specify monitor options Use the GUI menu method: –Main Menu > Solution > Unabridged Menu … –Main Menu > Solution > -Load Step Opts- Nonlinear > Monitor + Select the upper-left node (Node #2). Click on [OK]. In the dialog box, select “Variable 2” and “UX”. Click on [OK] to close the dialog box. Repeat for same node (Node #2), this time selecting “Variable 3” and “UY”. or Command Input method: –MONITOR,2,2,UX –MONITOR,3,2,UY Notes: We will monitor the DOF at the upper corner, near where the applied load is. We expect that this node will have the maximum response of the structure, so we have chosen UX and UY DOF of this node to monitor. The output will be in the monitor file (jobname.mntr). Workshop Thirteen: Collapse of Frame … Arc-Length Method

9. Workshop Supplement September 30, 2001 Inventory #001492 W13-9 6.Solve the nonlinear analysis Use the GUI menu method: –Main Menu > Solution > -Solve- Current LS After reviewing the status window, close it by selecting “File > Close” To start the analysis, click on [OK] or Command Input method: –SOLVE Notes: Review the status window before executing the solution. Nonlinear geometric effects are on. Initial number of substeps is 20. The arc-length method is activated. All intermediate results will be saved for postprocessing. The solution may take a few minutes to solve, depending on your hardware. Workshop Thirteen: Collapse of Frame … Arc-Length Method

10. Workshop Supplement September 30, 2001 Inventory #001492 W13-10 Open the monitor file (Exercise_13.mntr) in any text editor. Part of the output is shown below: SOLUTION HISTORY INFORMATION FOR JOB: Exercise_13.mntr ANSYS RELEASE 6.0 02:22:54 09/23/2001 LOAD SUB- NO. NO. TOTL INCREMENT TOTAL VARIAB 1 VARIAB 2 VARIAB 3 STEP STEP ATTMP ITER ITER TIME/LFACT TIME/LFACT MONITOR MONITOR MONITOR CPU UX UY 1 1 1 2 2 0.48944E-01 0.48944E-01 0.65625 0.22944E-02 -.23146E-02 1 2 1 4 6 0.90943E-01 0.13989 1.5781 0.22473E-01 -.22748E-01 1 3 1 4 10 0.76080E-01 0.21597 2.5312 0.63474E-01 -.72339E-01 1 4 1 4 14 0.91617E-01 0.30758 3.4062 0.16821 -.23311 1 5 1 4 18 0.92267E-01 0.39985 4.2969 0.41644 -.73368 1 16 1 4 62 0.27438E-01 0.82562 13.969 21.825 -45.130 1 17 1 4 66 0.25638E-01 0.85126 14.891 25.431 -49.854 1 18 1 4 70 0.22776E-01 0.87404 15.766 29.342 -54.356 1 19 1 4 74 0.18562E-01 0.89260 16.688 33.549 -58.540 1 20 1 4 78 0.12848E-01 0.90545 17.578 38.026 -62.300 1 21 1 5 83 0.57865E-02 0.91123 18.688 42.730 -65.540 1 22 1 4 87 -.21070E-02 0.90912 19.641 47.601 -68.198 1 23 1 4 91 -.99948E-02 0.89913 20.625 52.566 -70.260 1 24 1 4 95 -.17115E-01 0.88201 21.578 57.570 -71.765 1 25 1 4 99 -.23011E-01 0.85900 22.516 62.578 -72.795 1 26 1 4 103 -.27578E-01 0.83143 23.422 67.570 -73.444 1 27 1 4 107 -.30956E-01 0.80047 24.266 72.539 -73.801 1 28 1 4 111 -.33383E-01 0.76709 25.094 77.479 -73.942 1 29 1 3 114 -.35096E-01 0.73199 25.750 82.387 -73.926 1 30 1 4 118 -.36399E-01 0.69559 26.641 87.260 -73.791 1 31 1 3 121 -.37348E-01 0.65824 27.297 92.091 -73.569 1 32 1 4 125 -.38225E-01 0.62002 28.203 96.874 -73.267 Workshop Thirteen: Collapse of Frame … Arc-Length Method

11. Workshop Supplement September 30, 2001 Inventory #001492 W13-11 There are two useful things to note from the monitor file, as shown on the previous page: The “Increment Time/LFACT” shows the timestep during the course of the analysis. The “Total Time/LFACT” shows the current time (i.e., load multiplier). –If the time increment starts decreasing, then it is usually a good indication that ANSYS may be encountering some change in the response. A negative time increment usually means that the response is going through a post-buckling phase (“negative” slope of 1D force-deflection curve). –In the excerpt from earlier, we can see that the total time peaks at around TIME=0.90 (90% of applied load). Then, the applied load is decreased gradually in the post-bucking region. The VARIAB 2 & 3 columns indicate the DOF we are monitoring from Step 5. In this case, we are looking at UX and UY of Node 2. –The monitoring of DOF helps to determine what is occurring during the analysis. In this case, despite the fact that the load is decreasing, our DOF at Node 2 is still increasing. This is what we would expect during post-buckling response. –Sometimes, if there is a sharp bifurcation point (or any sudden change in the response), the arc- length method will go backwards in the force-deflection curve. By monitoring the UX and UY at a given node, if these DOF are decreasing as the load is decreased, this may give an indication that the load is simply being reversed, and the post-buckling response is not captured. In this case, the analysis can be terminated instead of running to completion. Including geometric imperfections, as discussed in the lecture notes of Chapter 9, will help prevent the existence of a sharp bifurcation point. Workshop Thirteen: Collapse of Frame … Arc-Length Method

12. Workshop Supplement September 30, 2001 Inventory #001492 W13-12 7.Postprocess the response at Node 2 Use the GUI menu method: –Main Menu > TimeHist Postpro > Variable Viewer... Select the results file “Exercise_13.rst”. Click on [OK] The Time-History calculator will appear, as shown on the right. Click on the “+” (Add Data) icon. Select “Solution Summary > Arc Length Items > Total load factor”. Click on [OK] Do NOT close the Time-History Calculator yet. or Command Input method: –/POST26 –SOLU,2,ALLF Notes: We will plot the response at Node 2 as load-factor vs. displacement. Variable #2 will be the total load factor. Workshop Thirteen: Collapse of Frame … Arc-Length Method

13. Workshop Supplement September 30, 2001 Inventory #001492 W13-13 Postprocess the response at Node 2 (cont’d) Use the GUI menu method: –Variable Viewer Click on the “+” (Add Data) icon. Select “Nodal Solution > DOF Solution > X- Component of displacement”. Click on [OK] Select Node #2 (upper-left corner). Click on [OK]. Repeat for UY at Node 2. Click on [Cancel] to finish. Do not close the Time-History calculator yet. or Command Input method: –NSOL,3,2,U,X –NSOL,4,2,U,Y Notes: We have added UX and UY of Node 2 as variables to plot. Workshop Thirteen: Collapse of Frame … Arc-Length Method

14. Workshop Supplement September 30, 2001 Inventory #001492 W13-14 Postprocess the response at Node 2 (cont’d) Use the GUI menu method: –Variable Viewer Click on “X-Axis” for UX_3 Highlight (select) ALLF_2 Click on the “Graph data” icon (circled in figure on right) The plot of load factor vs. x-displacement at node 2 will be shown in the Graphics Window Repeat procedure, this time using UY_4 as the “X-Axis” variable. or Command Input method: –XVAR,3 –PLVAR,1 –XVAR,4 –PLVAR,1 Notes: You have just plotted load factor vs. x- and y- displacement at node 2. Note that the response is very complex. Workshop Thirteen: Collapse of Frame … Arc-Length Method

15. Workshop Supplement September 30, 2001 Inventory #001492 W13-15 You can change the look of graphs under “Utility Menu > PlotCtrls > Style > Graphs”. The UX and UY response at Node 2 are shown together below. (In this case, UY values are switched to positive, so the displacement represents absolute values.) Can you explain why the response curves look like this? (See animation on next page for help) Workshop Thirteen: Collapse of Frame … Arc-Length Method

16. Workshop Supplement September 30, 2001 Inventory #001492 W13-16 Animations of response, generated in the “General Postprocessor” (Utility Menu > PlotCtrls > Animate) also help in evaluating the response. By comparing both animations and x-y plots, better insight of the structural behavior can be obtained. Workshop Thirteen: Collapse of Frame … Arc-Length Method