1. 實驗力學研究室 1 Finite Element Model Building

2. 實驗力學研究室 2 Setting Up the Model Should a thin-walled part be modeled with shells? Should a planar idealization be used? Grouping and Layering Grouping will help organize a model into logical sections. The various parts of an assembly model should be organized in separate groups to assist in model building. Such organization will also facilitate results viewing because each component can be displayed individually.

3. 實驗力學研究室 3 Resource Requirements The time to think about memory and disk requirements is before the modeling starts, not when it is finished. Due to the speed of today’s systems, it is often more convenient to overmesh than to take the time to be judicious. However, when you know you might be running into a resource crunch, you can utilize mesh control to focus the mesh density where you need it.

4. 實驗力學研究室 4 Element Selection Modern preprocessors will default to quadrilateral elements or a quad-dominate mesh for a shell model and triangular tetrahedrons for a solid model. The former choice is made for accuracy, and the latter for convenience. Rectangular elements provide a linear strain distribution across the edged or volume. First order triangular elements only capture a single strain value; they are often called constant strain elements. Therefore, you will need many more triangular elements relative to quads to capture a high gradient. Second order element or parabolic tetrahedrons can capture more complex local strain gradients and provide reasonable results with proper convergence methods.

5. 實驗力學研究室 5 In the case of a nonlinear solution, it might be prudent to take the time to model in more accurate bricks for the run time savings alone. A fair estimate is that you will need five tetrahedrons for every brick element in a model to get the same results. Because nonlinear runs generally tend to be more time consuming, a smaller model may allow you to make more design iterations within the time allotted.

6. 實驗力學研究室 6 Manual versus Automatic Meshing 1.If accuracy and speed were equal, few design analysts or even analysis specialists would dispute that automeshing is the way to go. The goal of FEA is not to be build a mesh but to get performance data. 2.Given the power of today’s preprocessors, the need to manual mesh a shell model should never arise. If a surface model can be developed in either a CAD system or the FEM tool, a little preparation can allow you to automesh nearly the entire model.

7. 實驗力學研究室 7 3.The issue of manual versus automatic arises most often in the context of solid models. Even in solid models, a typical solid “manual” mesh consists of revolving or extruding automatic or semi-automatic surface meshes. The real task is in planning the extrusions or revolutions so that the mesh matches up at the seams between the different steps.

8. 實驗力學研究室 8 The key differences between equivalent automeshed and manual meshed solid models are discussed below. 1.Modeling Speed Manual meshing is very time consuming on even moderately complex solid parts. Automeshing, or the other hand is the hands-down speed champion. However, while an automesh might get you to the run button faster, the excess of elements required to achieve the same degree of accuracy might cause the solution to take far longer.

9. 實驗力學研究室 9 2.Solution Speed Total modeling and solution time must be considered, which also means considering how many times a model must be remeshed and how many times a particular mesh must be solved. 3.Accuracy I.For a given mesh density, a brick will provide more accurate answers closer to the converged solution than a second order tetrahedral mesh. II.A linear tet mesh should always be considered inaccurate unless the time is taken in test models to confirm that the stress change is gradual enough to allow linear tets to converge correctly.

10. 實驗力學研究室 10 III.However, properly converged second order tets can provide the same accuracy as a linear brick mesh. IV.One accuracy issue is the fact that many geometric simplifications are required to obtain a brick mesh and the simplifications require to build a brick mesh cancel out any element accuracy issues when compared to a second order tet mesh with little or no simplification.

11. 實驗力學研究室 11 4.Convergence While run times for the manual mesh may be faster, the time required to modify it might be prohibitively long. The truth is that if convergence is difficult or time consuming, most design analysts will not invest the necessary time. 5.Perception In any industry or specialty, you must put in a minimum amount of work to gain credibility. If you are willing to simply accept automesh results, you are not living up to your responsibility as an FEA user.

12. 實驗力學研究室 12 Manual and Automatic Mixed Meshes If you wish to mix the two to take advantage of the best of both worlds, you will need to break your geometry into parts. In most cases, you will have to transition these two dissimilar meshes with rigid links or multi-point constraints. P-elements and H-elements P-elements are excellent for capturing high stress gradients. For areas of gradual stress transition or away from any area of interest, h-elements are more efficient. H-elements can capture most stress conditions if enough degrees of freedom are placed in the area.

13. 實驗力學研究室 13 However, when the option is available, choose to use the best element in the best location. Refer to your software’s documentation to confirm that the option of mixing h and p elements is available and for information on specific usage techniques.

14. 實驗力學研究室 14 Meshing Beam Models 1.The best and easiest way to construct a beam model is to prepare CAD wireframe at the neutral axis of all beams. Take the time to split the wireframe at every joint or connection of two beams. 2.One guideline typically appearing in FEA reference is that the length of the beam should be about ten times the maximum cross-sectional dimension. 3.The best guideline for determining the applicability of a beam model is that if it looks like beams, or if a 2D or 3D wireframe representation conveys most of the structure with little ambiguity, then a beam model is probably appropriate.

15. 實驗力學研究室 15 Meshing Shell Models Building a shell model requires mid-plane surfaces in one form or another. However, the model must be constructed with just the right features to allow this to happen. A good technique for starting shell models is to sketch the part first to identify the sky features required in the model.

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22. 實驗力學研究室 22 Element Shape Quality 1.The ideal shape for a triangular element or face is an equilateral triangle and the ideal shape for a quadrilateral element or face is a square. 2.H-elements should have an aspect ratio as less than 5:1, whereas p-elements can produce good results with an aspect ratio as high as 20:1.

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24. 實驗力學研究室 24 Mapped Meshing Mapped Meshing refers to specifying or forcing a particular mesh pattern by indicating the number of nodes on all the edges of a surface or volume. If all surfaces were perfectly rectangular, mapped meshing would not be as much of as issue, because most h-element meshers will fill a rectangle with uniformly shaped elements. However, meshing an irregular surface with a fixed nominal element size can yield unpredictable results.

25. 實驗力學研究室 25 Biasing a Mesh Mesh biasing is a means of forcing smaller elements near an area of interest, while allowing larger elements in regions with a more gradual stress gradient.

26. 實驗力學研究室 26 Transitioning Mesh Densities The technique is to use automeshing of surfaces with the geometry broken into patches. A good rule of thumb for minimizing occurrence of high aspect-ratio elements is to limit transitions to ratios of 2:1 or less. In (a) the mesh transitions from a 0.05 nominal element size to a 0.50 nominal element size without control of the transition. The mesh in (b) uses a series of regions to effect the transition.

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28. 實驗力學研究室 28 Controlling a P-element Mesh P-element automeshers will attempt to fill the model with the largest elements possible, within a default or user-specified aspect ratio and edge or face angle tolerances, for solution efficiency. However, p- element solvers are not immune to element distortion. Tightening the element creation tolerances is the simplest way to improve the general mesh quality in a p-element mesh.

29. 實驗力學研究室 29 Boundary Conditions

30. 實驗力學研究室 30 “Boundary conditions” is calculating the loads and constraints that each component or system of components experiences in its working environment.

31. 實驗力學研究室 31 A Simple Example… The legs are rigid in compression and do not add any substantial component to the vertical deformation. The legs are rigid in bending and force the chair bottom, local to the interface, to remain perfectly horizontal. Any sliding of the legs on the floor due to side load components resulting from the seat bending will be neglected; legs are bolted to the floor or friction is sufficient to resist side loading. The load can be modeled as being uniformly distributed both at the instant of its application and time thereafter.

32. 實驗力學研究室 32 Types of Boundary Conditions Boundary conditions are applied as constrains and loads. 1.Typically, loads are used to represent inputs to the system of interest. These can be in the form of forces, moments, pressures, temperatures, or accelerations. 2.Constraints, on the other hand, are typically used as reactions to the applied loads. Constraints can resist translational or rotational deformation induced by these loads.

33. 實驗力學研究室 33 3.In a linear static analysis, the boundary conditions must be assumed constant from application to final deformation of the system. In a dynamic analysis, the boundary condition can vary with time and, in a nonlinear analysis, the orientation and distribution of the boundary conditions can vary as the displacement of the structure is calculated.

34. 實驗力學研究室 34 Boundary Conditions and Accuracy 1.An overly stiff model due to poorly applied constraints is typically called overconstrained. 2.The second is that of an underconstrained model, which simply has too few constraints to prevent rigid body motion.

35. 實驗力學研究室 35 In many cases, redundant constraints will have no effect on the overall behavior of the model. For example, if all nodes of a shell element are constrained in its normal direction, constraining their rotations about either of its parallel axes would be redundant. In general, however, the application of redundant constraints suggests a poorly constructed constraint scheme. Overconstrained Models I.Redundant Constraints II.Excessive Constraints Excessive constraints result both from a poor understanding of the actual supporting structure being represented by them and insufficient planning of the total boundary condition scheme.

36. 實驗力學研究室 36 Each point should be fixed vertically, and horizontal constraints should be selectively applied so that in-plane spatial rotation and rigid body translation is removed without causing excessive constraints.

37. 實驗力學研究室 37 Constraining the center point of Patch 1 in all three translational DOFs. Constraining x and y translations of the center point of Patch 2. Constraining z and y translations of the center point of Patch 3. Constraining just the y translations of the center point of Patch 4.

38. 實驗力學研究室 38 III.Coupled Strain Effects Strain or material deformation in one direction is dependent on deformation, or the freedom to deform, in other directions. This coupled effect is governed by the Poisson’s ratio of the material and must be considered in the application of constraints in shell, solid, or planar models.

39. 實驗力學研究室 39 Fig (a) fixes only the x DOF on the left vertical edge and the y DOF on the bottom edge. Fig(b) has both the x and y DOFs constrained on all nodes of the left vertical edge. It is important to node that this vertical restriction on the left edge actually reduces the horizontal deformation by 5%.

40. 實驗力學研究室 40 Understiffened Models I.The most common underconstrained modeling errors stem from neglecting one or more spatial degrees of freedom. II.Insufficient Part Stiffness Many parts are stiffened considerably by attached components, even if they are not rigidly attached in all directions. Because loads impart no stiffness in a linear analysis, replacing an attached component with an equivalent load could allow the modeled part to have much greater flexibility than it should.

41. 實驗力學研究室 41 Bracketing Boundary Conditions When the optimum or correct boundary conditions scheme is hard to model or determine, consider bracketing the system with conditions that take into account the various options you are considering. Bracketing the boundary conditions of a chair analysis, using (a) infinite friction and (b) no friction.

42. 實驗力學研究室 42 Loads 1.Magnitude 2.Orientation 3.Distribution 4.Time dependence I.Units In defining loads, you must always verify use of a set units consistent with the rest of your model.

43. 實驗力學研究室 43 II.Load Distribution i.Uniform ii.Per unit length or area iii.Interpolated, or functionally defined. III.Load Orientation In most cases, the orientation of an applied load will be defined by specifying the load components in the directions of the active coordinate system.

44. 實驗力學研究室 44 IV.Nonlinear Forces If the surface or edge on which a load is applied deforms so much that an update to the load orientation is required, a nonlinear, large displacement analysis is probably warranted. Another type of nonlinear force is called a follower force. Follower forces are loads defined with respect to local nodes or elements, not a fixed coordinate system. As the part deforms locally, the load orientation changes. If follower forces are required, large displacement effects should also be solved for.

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46. 實驗力學研究室 46 V.Types of load a.Forces and Moments b.Pressure Loads c.Acceleration Loads d.Temperature Loads VI.Checking Applied Loads