Finite Element Primer for Engineers: Part 3

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• Finite Element Primer for Engineers Part 3
• Mike Barton S. D. Rajan

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Contents

• Introduction to the Finite Element Method (FEM)
• Steps in Using the FEM (an Example from Solid
  Mechanics)
• Examples
• Commercial FEM Software
• Competing Technologies
• Future Trends
• Internet Resources
• References

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Information Available from Various Types of FEM
Analysis

• Static analysis
• Deflection
• Stresses
• Strains
• Forces
• Energies
• Dynamic analysis
• Frequencies
• Deflection (mode shape)
• Stresses
• Strains
• Forces
• Energies

• Heat transfer analysis
• Temperature
• Heat fluxes
• Thermal gradients
• Heat flow from convection faces
• Fluid analysis
• Pressures
• Gas temperatures
• Convection coefficients
• Velocities

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Example FEM Application Areas

• Automotive industry
• Static analyses
• Modal analyses
• Transient dynamics
• Heat transfer
• Mechanisms
• Fracture mechanics
• Metal forming
• Crashworthiness

• Aerospace industry
• Static analyses
• Modal analyses
• Aerodynamics
• Transient dynamics
• Heat transfer
• Fracture mechanics
• Creep and plasticity analyses
• Composite materials
• Aeroelasticity
• Metal forming
• Crashworthiness

• Architectural
• Soil mechanics
• Rock mechanics
• Hydraulics
• Fracture mechanics
• Hydroelasticity

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Variety of FEM Solutions is Wide and Growing Wider

• The FEM has been applied to a richly diverse
  array of scientific and technological problems.
• The next few slides present some examples of the
  FEM applied to a variety of real-world design and
  analysis problems.

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• This example shows an intravenous pump modeled
  using hexahedral elements.

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Car tires require sophisticated analysis because
of their complex geometry, large deformations,
nonlinear material behavior, and varying contact
conditions. Brick elements are used to represent
the tread and steel bead, while shell elements
are used in the wall area. Membrane elements are
used to represent the tire cords.
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This forging example is a simulation of a bulk
forming process with multiple stages. This
axisymmetric analysis begins with a cylinder of
metal meshed very simply.
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A 3-D finite element model of an instrumented
canine cervical spine. The model consisted of
four vertebrae (C3-C6), a titanium alloy plate,
and two screws attached to the back of two
vertebrae (C4-C5).
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Finite element analysis works on the premise that
a complex structure like the helicopter shown
here can be simulated on a computer screen so
that the helicopter's physical properties can be
studied to determine how well the design will
perform under real-world conditions. The computer
models permit the design team to examine a wide
range of options and to detect design flaws long
before the prototype stage.
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This guitar features two strips of graphite
running the length of the neck. This FEM model
was used to study how much the neck moved when
string forces were applied and moisture content
changed. Using the FEM calculations,
designers could try different reinforcement
scenarios to increase neck stability.
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The boats hull consists of a thick core material
sandwiched between two thinner layers of plys
oriented in different directions. The initial
analysis work focused on maximizing the hull's
overall stiffness by examining different
core-material densities and varying the ply
thickness and orientations.
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Dynamic analysis of a tuning fork, to find it's
first eight modes of vibration.
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Contents

• Introduction to the Finite Element Method (FEM)
• Steps in Using the FEM (an Example from Solid
  Mechanics)
• Examples
• Commercial FEM Software
• Competing Technologies
• Future Trends
• Internet Resources
• References

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Commercially Available FEM Software Suites

• Here we present a survey of some of the
  better-known integrated FEM software packages.
  These integrated systems allow users to perform
  all facets of FEM analysis, including modeling,
  meshing, solution and post-processing.
• The Internet provides a vast new resource for
  individuals interested in the FEM. See the
  Reference section of this paper for interesting
  FEM links to start your Internet research.
• In addition to the integrated FEM packages
  listed below, many vendors offer dedicated
  software for solid modeling, mesh generation, FE
  equation generation and solution, and
  post-processing.

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Commercially Available FEM Software Suites
(cont.)(partial list)
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Contents

• Introduction to the Finite Element Method (FEM)
• Steps in Using the FEM (an Example from Solid
  Mechanics)
• Examples
• Commercial FEM Software
• Competing Technologies
• Future Trends
• Internet Resources
• References

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Technologies That Compete With the FEM

• Other numerical solution methods
• Finite differences
• Approximates the derivatives in the differential
  equation using difference equations.
• Useful for solving heat transfer and fluid
  mechanics problems.
• Works well for two-dimensional regions with
  boundaries parallel to the coordinate axes.
• Cumbersome when regions have curved boundaries.
• Weighted residual methods (not confined to a
  small subdomain)
• Collocation
• Subdomain
• Least squares
• Galerkins method
• Variational Methods (not confined to a small
  subdomain)
• Denotes a method that has been used to
  formulate finite element solutions.

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Technologies that Compete With the FEM (cont.)

• Prototype Testing
• Reliable. Well-understood.
• Trusted by regulatory agencies (FAA, DOT, etc.)
• Results are essential for calibration of
  simulation software.
• Results are essential to verify modeled results
  from simulation.
• Non destructive testing (NDT) is lowering costs
  of testing in general.
• Expensive, compared to simulation.
• Time consuming.
• Development programs that rely too much on
  testing are increasingly less competitive in
  todays market.
• Faster product development schedules are
  pressuring the quality of development test
  efforts.
• Data integrity is more difficult to maintain,
  compared to simulation.

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Contents

• Introduction to the Finite Element Method (FEM)
• Steps in Using the FEM (an Example from Solid
  Mechanics)
• Examples
• Commercial FEM Software
• Competing Technologies
• Future Trends
• Internet Resources
• References

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Future Trends in the FEM and Simulation

• The FEM in particular, and simulation in
  general, are becoming integrated with the entire
  product development process (rather than just
  another task in the product development process)
• FEM cannot become the bottleneck.
• A broader range of people are using the FEM
• Not just hard-core analysts.
• Increased data sharing between analysis data
  sources (CAD, testing, FEM software, ERM
  software.)
• FEM software is becoming easier to use
• Improved GUIs, automeshers.
• Increased use of sophisticated shellscripts and
  wizards.

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Future Trends in the FEM and Simulation (cont.)

• Enhanced multiphysics capabilities are coming
• Coupling between numerous physical phenomena.
• Ex Fluid-structural interaction is the most
  common example.
• Ex Semiconductor circuits, EMI and thermal
  buildup vary with current densities.
• Improved life predictors, improved service
  estimations.
• Increasing use of non-deterministic analysis and
  design methods
• Statistical modeling of material properties,
  tolerances, and anticipated loads.
• Sensitivity analyses.
• Faster and more powerful computer hardware.
  Massively parallel processing.
• Decreasing reliance on testing.
• FEM and simulation software available via
  Internet subscription.

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Contents

• Introduction to the Finite Element Method (FEM)
• Steps in Using the FEM (an Example from Solid
  Mechanics)
• Examples
• Commercial FEM Software
• Competing Technologies
• Future Trends
• Internet Resources
• References

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Selected FEM Resources on the Internet

• The internet offers virtually unlimited resources
  to persons interested in the FEM.
• The following links are a small sample of FEM
  sites on the Internet which the author has found
  useful. Thousands more (at least!) are readily
  available.
• Most commercial FEM developers have extensive
  presence on the Internet, with web pages that
  include company histories, descriptions of
  software products, and example FEM solutions.
• Other good FEM resources on the web originate
  with academia, government, and discussion and
  user groups.

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Selected FEM Resources on the Internet (cont.)

• http//www.engineeringzones.com - A website
  created to educate people in the latest
  engineering technologies, manufacturing
  techniques and software tools. Exellent FEM
  links, including links to all commercial
  providers of FEM software.
• http//www.comco.com/feaworld/feaworld.html -
  Extensive FEM links, categorized by analysis type
  (mechanical, fluids, electromagnetic, etc.)
• http//femur.wpi.edu - Extensive collection of
  elementary and advanced material relating to the
  FEM.
• http//www.engr.usask.ca/7Emacphed/finite/fe_res
  ources/fe_resources.html - Lists many public
  domain and shareware programs.
• http//sog1.me.qub.ac.uk/dermot/ferg/ferg.htmlFi
  nite - Home page of the the Finite Element
  Research Group at The Queen's University of
  Belfast. Excellent set of FEM links.
• http//www.tenlinks.com/cae/ - Hundreds of links
  to useful and interesting CAE cited, including
  FEM, CAE, free software, and career information.
• http//www.geocities.com/SiliconValley/5978/fea.ht
  ml - Extensive FEM links.
• http//www.nafems.org/ - National Agency for
  Finite Element Methods and Standards (NAFEMS).

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Contents

• Introduction to the Finite Element Method (FEM)
• Steps in Using the FEM (an Example from Solid
  Mechanics)
• Examples
• Commercial FEM Software
• Competing Technologies
• Future Trends
• Internet Resources
• References

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References
Cashman, J., 2000. Future of Engineering
Simulation, ANSYS Solutions, Vol. 2, No. 1, pp.
3-4. Chandrupatla, T. R. and Ashok D. Belegundu,
1997. Introduction to Finite Elements in
Engineering, Prentice Hall, Upper Saddle River,
New Jersey. Kardestuncer, H., 1987. Finite
Element Handbook, McGraw-Hill, New York. Krouse,
J., 2000. Physical Testing Gets a Bum Rap,
ANSYS Solutions, Vol. 2, No. 2, p. 2. Lentz, J.,
1994. Finite Element Analysis Cross Training,
unpublished lecture notes, Honeywell Engines and
Systems, Phoenix, Az. Nikishkov, G.V., 1998.
Introduction to the Finite Element Method,
unpublished lecture notes, University of Arizona,
Tucson, Az. Rajan, S.D., 1998. Finite Elements
for Engineers, unpublished lecture notes, Arizona
State University, Tempe, Az. Segerlind, L. J.,
1984. Applied Finite Element Analysis, John Wiley
and Sons, New York.