1. Finite-Element Analysis
Lecture Slides
Chapter 19
Finite-Element Analysis
The McGraw-Hill Companies © 2012

2. Chapter Outline
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3. Model of a Connecting Rod
Meshed model
Stress contours
Fig. 19–1
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4. Errors in Finite Element Method
Numerical technique that discretizes domain of continuous structure
Two error categories
Computational errors
Discretization errors
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5. Structural Problem Finite-element model Idealized model Fig. 19–2
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6. Special-purpose elements
Element Geometries
Element categories
Line elements
Surface elements
Solid elements
Special-purpose elements
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7. Sample Finite-Element Library
Table 19–1
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8. Sample Finite-Element Library
Table 19–1
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9. Sample Finite-Element Library
Table 19–1
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10. Sample Finite-Element Library
Table 19–1
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11. Finite-Element Solution Process
Fig. 19–3
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12. Finite-Element Solution Process
Fig. 19–4
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13. Example 19–1
Fig. 19–5
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14. Example 19–1
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15. Example 19–1
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16. Example 19–1
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17. Example 19–1
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18. Network of elements and nodes is called a mesh
Mesh Generation
Network of elements and nodes is called a mesh
Mesh density increases as more elements are placed within a given region
Mesh refinement is when the mesh is modified from one analysis to the next to yield improved results
Results generally improve when mesh density is increased in areas of high stress gradients
Mesh generation techniques
Manual
Semiautomatic
Fully automated
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19. Automatic Meshing
Fig. 19–6
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20. Loads are applied at the nodes
Load Application
Loads are applied at the nodes
Element loads such as weight, thermal effects, surface pressure, etc. are automatically converted to equivalent nodal loads
The results very near the nodal forces may be unrealistic
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21. Constraints at the nodes can be placed to model boundary conditions
Typical boundary conditions include fixed, simply supported, and constrained in one direction.
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22. Computing speeds are sufficient to allow for dense meshes
Modeling Techniques
CAD packages and automatic mesh generators make model creation relatively painless
Computing speeds are sufficient to allow for dense meshes
The model only needs to be as detailed as needed
For example, five beam elements can provide deflections and slopes at the nodes of the shaft shown.
Fig. 19–7
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23. Results from Five-Element Model
Fig. 19–7
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24. Detailed Solid Model of Stepped Shaft
Close-up of stress contours at shoulder
Fig. 19–8
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25. Plate with end temperatures maintained at 0ºF and 100ºF
Thermal Stresses
Plate with end temperatures maintained at 0ºF and 100ºF
Steady-state temperature contours
Thermal stress contours where initial plate temperature was 0ºF
Fig. 19–9
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26. Critical Buckling Load
Buckled can with deflections greatly exaggerated
FEM model of thin-walled aluminum can under vertical load
Fig. 19–10
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27. First free vibration mode of stepped beam
Vibration Analysis
First free vibration mode of stepped beam
20-element beam model, f1 = 322 Hz
element brick and tetrahedron model, f1 = 316 Hz
Fig. 19–11
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28. Second free vibration mode of stepped beam
Vibration Analysis
Second free vibration mode of stepped beam
20-element beam model, f2 = 1296 Hz
element brick and tetrahedron model, f2 = 1249 Hz
Fig. 19–12
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