Lying by Approximation: The Truth about Finite Element Analysis

116 Pages·2017·6.06 MB·English

by  Vincent C. Prantil

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S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G I
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P LYING BY APPROXIMATION
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Stephen F. Barrett, D
SERIES EDITOR: O
University of Wyoming P
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LYING BY APPROXIMATION L
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• The Truth about Finite Element Analysis
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The Truth about Finite Element Analysis S
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Vincent C. Prantil,
Milwaukee School of Engineering
Christopher Papadopoulos,
University of Puerto Rico, Mayag Ÿez
Paul D. Gessler,
Graduate Student, Marquette University
In teaching an introduction to the finite element method at the
undergraduate level, a prudent mix of theory and applications
L
is often sought. In many cases, analysts use the finite elementmethod to perform parametric Y
I
N
G
studies on potential designs to size parts, weed out less desirabledesign scenarios, and predict B
Y
system behavior under load. In this book, we discuss common pitfalls encountered by many finite A
P
element analysts, in particular, students encountering the method for the first time. We present a P
R
O
variety of simple problems in axial, bending, torsion, and shearloading that combine the students’ X
I
M
knowledge of theoretical mechanics, numerical methods, and approximations particular to the A
T
I
finite element method itself. We also present case studies inwhich analyses are coupled with O
N

experiments to emphasize validation, illustrate where interpretations of numerical results can
be misleading, and what can be done to allay such tendencies. Challenges in presenting the
necessary mix of theory and applications in a typical undergraduate course are discussed. We also
discuss a list of tips and rules of thumb for applying the method in practice. Vincent C. Prantil
Christopher Papadopoulos
ABOUT SYNTHESIS
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This volume is a printed version of a work that appears in the Synthesis Digital
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Paul D. Gessler
Library of Engineering and Computer Science. Synthesis Lectures provide R
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concise, original presentations of important research and development topics,
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published quickly, in digital and print formats. For more information visit N
www.morganclaypool.com &

C S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G
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ISBN: 978-1-62705-235-1 A
90000 Y
P
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w w w. m o r g a n c l a y p o o l . c o m O Stephen F. Barrett,
9 781627 052351 SERIES EDITOR
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Lying by Approximation
eTruthaboutFiniteElementAnalysis

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LyingbyApproximation:eTruthaboutFiniteElementAnalysis
VincentC.Prantil,ChristopherPapadopoulos,andPaulD.Gessler
www.morganclaypool.com
ISBN:9781627052351 paperback
ISBN:9781627052368 ebook
DOI10.2200/S00503ED1V01Y201305ENG023
APublicationintheMorgan&ClaypoolPublishersseries
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Lying by Approximation
eTruthaboutFiniteElementAnalysis
Vincent C. Prantil
MilwaukeeSchoolofEngineering
Christopher Papadopoulos
UniversityofPuertoRicoMayagüez
Paul D. Gessler
GraduateStudent,MarquetteUniversity
SYNTHESISLECTURESONENGINEERING#23
M
&C Morgan &cLaypool publishers
ABSTRACT
In teaching an introduction to the finite element method at the undergraduate level, a prudent
mix of theory and applications is often sought. In many cases, analysts use the finite element
methodtoperformparametricstudiesonpotentialdesignstosizeparts,weedoutlessdesirable
designscenarios,andpredictsystembehaviorunderload.Inthisbook,wediscusscommonpit-
fallsencounteredbymanyfiniteelementanalysts,inparticular,studentsencounteringthemethod
for the first time. We present a variety of simple problems in axial, bending, torsion, and shear
loadingthatcombinethestudents’knowledgeoftheoreticalmechanics,numericalmethods,and
approximations particular to the finite element method itself. We also present case studies in
whichanalysesarecoupledwithexperimentstoemphasizevalidation,illustratewhereinterpre-
tations of numerical results can be misleading, and what can be done to allay such tendencies.
Challengesinpresentingthenecessarymixoftheoryandapplicationsinatypicalundergraduate
coursearediscussed.Wealsodiscussalistoftipsandrulesofthumbforapplyingthemethodin
practice.
KEYWORDS
finite element method, finite element analysis, numerical methods, computational
analysis,engineeringmechanics,mathematicalmodeling,modelingapproximation