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

Chapter Outline Shigley’s Mechanical Engineering Design

Model of a Connecting Rod Meshed model Stress contours Fig. 19–1 Shigley’s Mechanical Engineering Design

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

Structural Problem Finite-element model Idealized model Fig. 19–2 Shigley’s Mechanical Engineering Design

Special-purpose elements Element Geometries Element categories Line elements Surface elements Solid elements Special-purpose elements Shigley’s Mechanical Engineering Design

Sample Finite-Element Library Table 19–1 Shigley’s Mechanical Engineering Design

Sample Finite-Element Library Table 19–1 Shigley’s Mechanical Engineering Design

Sample Finite-Element Library Table 19–1 Shigley’s Mechanical Engineering Design

Sample Finite-Element Library Table 19–1 Shigley’s Mechanical Engineering Design

Finite-Element Solution Process Fig. 19–3 Shigley’s Mechanical Engineering Design

Finite-Element Solution Process Fig. 19–4 Shigley’s Mechanical Engineering Design

Example 19–1 Fig. 19–5 Shigley’s Mechanical Engineering Design

Example 19–1 Shigley’s Mechanical Engineering Design

Example 19–1 Shigley’s Mechanical Engineering Design

Example 19–1 Shigley’s Mechanical Engineering Design

Example 19–1 Shigley’s Mechanical Engineering Design

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

Automatic Meshing Fig. 19–6 Shigley’s Mechanical Engineering Design

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

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

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

Results from Five-Element Model Fig. 19–7 Shigley’s Mechanical Engineering Design

Detailed Solid Model of Stepped Shaft Close-up of stress contours at shoulder Fig. 19–8 Shigley’s Mechanical Engineering Design

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

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

First free vibration mode of stepped beam Vibration Analysis First free vibration mode of stepped beam 20-element beam model, f1 = 322 Hz 56 384-element brick and tetrahedron model, f1 = 316 Hz Fig. 19–11 Shigley’s Mechanical Engineering Design

Second free vibration mode of stepped beam Vibration Analysis Second free vibration mode of stepped beam 20-element beam model, f2 = 1296 Hz 56 384-element brick and tetrahedron model, f2 = 1249 Hz Fig. 19–12 Shigley’s Mechanical Engineering Design