1. 實驗力學研究室 1 Solving the Model

2. 實驗力學研究室 2 Multiple Load and Constraint Cases Option 1. Results from multiple load cases in a single run may be combined. Option 2. Results from multiple runs in the same database may be combined. Option 3. Results from the above two scenarios and from multiple databases may be combined. Final Model Checks

3. 實驗力學研究室 3 Free Node Check In a structural analysis, a free node will typically result in an insufficiently constrained error. In a modal analysis, free nodes will manifest themselves in a zero frequency mode. Regardless of analysis type, free nodes should be avoided. Model Continuity Check Discontinuity is least likely in a single volume, automeshed solids, and the probability of discontinuity increases as transitional and manual meshing are used with greater frequency.

4. 實驗力學研究室 4 Sanity Checks I.Material Properties II.Boundary Conditions First, if multiple load and constraint sets have been defined, verify that the proper boundary conditions are in the proper set. Second, visually check the boundary condition icons. Finally, perform a load resultant check to provide the sum total of external loads. III.Mass

5. 實驗力學研究室 5 IV.System Resources Number of elements and type Number of nodes Number of degrees of freedom Type of solution Run time Disk usage RAM usage Machine name and type Machine RAM V.Element Check

6. 實驗力學研究室 6 When the Solution Fails I.Insufficient System Resources Use the following techniques with caution to reduce model size. Symmetry. Clean up questionable features. Use local refinement. Manual mesh. A manual mesh can often be 30% smaller than an automesh.

7. 實驗力學研究室 7 II.Insufficiently Constrained Models 1.Solve Model for First Mode The first mode of a structure is the shape of minimum stiffness. If a portion of the model is unconstrained or poorly constrained, it will result in a zero or nearly zero mode. While this may be a time- consuming solve, it is usually sufficient to identify unattached portions of the mesh. A follow-up modal run is recommended after fixing the mistake. 2.Abrupt Change in Stiffness This error is typically created in transitional meshing of dissimilar elements. Additional sources of failure may be the wrong element choice for a particular solution or poorly defined material models.

8. 實驗力學研究室 8 Convergence

9. 9 The process of successive mesh refinement to produce the optimal results is called convergence. Understanding Convergence Rectangle method for determining the area under a curve.

10. 實驗力學研究室 10 Area estimate improves with the resolution of the rectangles.

11. 實驗力學研究室 11 As the number of nodes increases, the flexibility of the structure increase because it becomes less rigid. Consequently, for a given load, the model will undergo greater deformation or strain. Hence, for a given load, stress will continue to rise as the mesh density increases. The degrees of convergence can best be expressed by the percent change in the result of interest between the two most recent mesh refinements or convergence passes.

12. 實驗力學研究室 12

13. 實驗力學研究室 13 Total uncertainty can be defined by Uncertainty versus Error Error estimates attempt to quantify the convergence of a model by calculating the relative change in output between adjacent nodes or elements.

14. 實驗力學研究室 14

15. 實驗力學研究室 15 The reported error for Node 5 might be (1,129-223)1,229, or 80.25%. Convergence in regions of negligible stress is inconsequential and should be reported as such. Eq. 10.2 is the normalized present maximum difference method, The probable error method,

16. 實驗力學研究室 16 Relating Error Estimates to Convergence

17. 實驗力學研究室 17

18. 實驗力學研究室 18 P-elements versus H-elements While convergence in an h-element mesh involves adding more nodes to capture high strain gradients, p-elements can represent similar behavior with a smaller number of elements using a more powerful mathematical definition. Element Quality versus Convergence The shape of individual has a direct impact on the accuracy of local data and the resulting convergence.

19. 實驗力學研究室 19 Displaying and Interpreting Results

20. 實驗力學研究室 20 Method for Viewing Results

21. 實驗力學研究室 21 I.Displacement Results Animation Regardless of the animation display method you chose, the first question you should ask yourself is whether the component is deforming as you expected. If the animation does not mask sense to you, changes are your boundary conditions should be modified and the analysis rerun before you proceed. Magnitude of Deformed Shape Are the resulting displacements so large that the linear assumption should be questioned?

22. 實驗力學研究室 22

23. 實驗力學研究室 23 II.Stress Results Fringe Quality Examine unaveraged, noncontinuous tone results and verify that the stress contour is relatively smooth. Convergence 1.Refining the mesh in problem areas should help the model converge. 2.Redefining poorly shaped elements resulting from high aspect ratios or edge or face angles that are either too small, will also improve results.

24. 實驗力學研究室 24 3.Deletion and recreation of areas of poor convergence will typically take less time than modifying these areas in an attempt to correct them. Stress Magnitude Globally high or low stress magnitudes could be caused by incorrect values of the model’s loads and/or elemental properties.