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Fin ite Element Primer fo r 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 (modeshape)
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 appliedto 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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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-knownintegratedFEM software packages. These integratedsystems allow users to perform all facets of FEM analysis,including modeling, meshing, solution and post-processing.
The Internet provides a vast new resource for individualsinterested in the FEM. See the Reference section of thispaper for interesting FEM links to start your Internetresearch.
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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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 ofdevelopment 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 (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 theInternet which the author has found useful. Thousands more(at least!) are readily available.
Most commercial FEM developers have extensive presenceon the Internet, with web pages that include companyhistories, descriptions of software products, and example FEMsolutions.
Other good FEM resources on the web originate withacademia, government, and discussion and user groups.
S l t d FEM R th I t t ( t )
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Selected FEM Resources on the Internet (cont.)
http://www.ansys.nethttp://www.engineeringzones.com- A website created to educate people in the latestengineering technologies, manufacturing techniques and software tools. Exellent FEMlinks, including links to all commercial providers of FEM software.
http://www.comco.com/feaworld/feaworld.html - Extensive FEM links, categorizedby analysis type (mechanical, fluids, electromagnetic, etc.)
http://www.engr.usask.ca/%7Emacphed/finite/fe_resources/fe_resources.html-Lists many public domain and shareware programs.
http://sog1.me.qub.ac.uk/- Home page of the the Finite Element Research Group atThe 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.gorni.eng.br/- Extensive FEM links.
http://www.nafems.org/- National Agency for Finite Element Methods and Standards(NAFEMS).http://www.6dof.com/
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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
References
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References
Cashman, J., 2000. Future of Engineering Simulation,ANSYSSolutions, Vol. 2, No. 1, pp. 3-4.
Chandrupatla, T. R. and Ashok D. Belegundu, 1997. Introduction toFinite 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,ANSYSSolutions, 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.