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Finite-Element Analysis
Lecture Slides Chapter 19 Finite-Element Analysis The McGraw-Hill Companies © 2012
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Chapter Outline Shigley’s Mechanical Engineering Design
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Model of a Connecting Rod
Meshed model Stress contours Fig. 19–1 Shigley’s Mechanical Engineering Design
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Errors in Finite Element Method
Numerical technique that discretizes domain of continuous structure Two error categories Computational errors Discretization errors Shigley’s Mechanical Engineering Design
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Structural Problem Finite-element model Idealized model Fig. 19–2
Shigley’s Mechanical Engineering Design
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Special-purpose elements
Element Geometries Element categories Line elements Surface elements Solid elements Special-purpose elements Shigley’s Mechanical Engineering Design
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Sample Finite-Element Library
Table 19–1 Shigley’s Mechanical Engineering Design
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Sample Finite-Element Library
Table 19–1 Shigley’s Mechanical Engineering Design
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Sample Finite-Element Library
Table 19–1 Shigley’s Mechanical Engineering Design
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Sample Finite-Element Library
Table 19–1 Shigley’s Mechanical Engineering Design
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Finite-Element Solution Process
Fig. 19–3 Shigley’s Mechanical Engineering Design
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Finite-Element Solution Process
Fig. 19–4 Shigley’s Mechanical Engineering Design
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Example 19–1 Fig. 19–5 Shigley’s Mechanical Engineering Design
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Example 19–1 Shigley’s Mechanical Engineering Design
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Example 19–1 Shigley’s Mechanical Engineering Design
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Example 19–1 Shigley’s Mechanical Engineering Design
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Example 19–1 Shigley’s Mechanical Engineering Design
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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 Shigley’s Mechanical Engineering Design
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Automatic Meshing Fig. 19–6 Shigley’s Mechanical Engineering Design
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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 Shigley’s Mechanical Engineering Design
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Constraints at the nodes can be placed to model boundary conditions
Typical boundary conditions include fixed, simply supported, and constrained in one direction. Shigley’s Mechanical Engineering Design
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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 Shigley’s Mechanical Engineering Design
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Results from Five-Element Model
Fig. 19–7 Shigley’s Mechanical Engineering Design
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Detailed Solid Model of Stepped Shaft
Close-up of stress contours at shoulder Fig. 19–8 Shigley’s Mechanical Engineering Design
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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 Shigley’s Mechanical Engineering Design
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Critical Buckling Load
Buckled can with deflections greatly exaggerated FEM model of thin-walled aluminum can under vertical load Fig. 19–10 Shigley’s Mechanical Engineering Design
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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 Shigley’s Mechanical Engineering Design
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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 Shigley’s Mechanical Engineering Design
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