Lying by Approximation

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 method to perform parametric studies on potential designs to size parts, weed out less desirable design scenarios, and predict system behavior under load. In this book, we discuss common pitfalls encountered by many finite element analysts, in particular, students encountering the method for the first time. We present a variety of simple problems in axial, bending, torsion, and shear loading that combine the students' knowledge of theoretical mechanics, numerical methods, and approximations particular to the finite element method itself. We also present case studies in which analyses are coupled with 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. Table of Contents: Preface / Acknowledgments / Guilty Until Proven Innocent / Let's Get Started / Where We Begin to Go Wrong / It's Only a Model / Wisdom Is Doing It / Summary / Afterword / Bibliography / Authors' Biographies
About the Author: Vincent C. Prantil earned his B.S., M.S., and Ph.D. in Mechanical Engineering from Cornell University where he was awarded the Sibley Prize in Mechanical Engineering and held an Andrew Dickson White Presidential Fellowship. He was a Senior Member of Technical Staff at Sandia National Laboratories California in the Applied Mechanics and Materials Modeling Directorates for eleven years. He joined the faculty in the Department of Mechanical Engineering at the Milwaukee School of Engineering in September 2000 where he presently specializes infinite element model development, numerical methods, and dynamic systems modeling. Since joining academia, he has become interested in the use of animation to both engage students and as a suggestive tool for students to use as a mnemonic device to enhance long-lasting learning. In addition to working with Tim Decker in Milwaukee, he has teamed up with colleagues at Northern Illinois University and Rutgers University in their efforts to showcase the power of video simulation for teaching undergraduate engineering concepts in dynamic modeling and controls theory. Christopher Papadopoulos earned B.S. degrees in Civil Engineering and Mathematics in 1993 at Carnegie Mellon University, and his Ph.D. in Theoretical and Applied Mechanics in 1999 at Cornell University, where he was a National Science Foundation Graduate Research Fellow. He is currently a member of the faculty of the Department of Engineering Science and Materials at the University of Puerto Rico, Mayaguez (UPRM), where he has worked since 2009. He was previously a member of the faculty in the Department of Civil Engineering and Mechanics at the University of Wisconsin-Milwaukee from 2001-2008. Chris is currently the principal investigator of two NSF projects, one in appropriate technology and engineering ethics, and the other in mechanics education. He has additional research interests in nonlinear structural mechanics and biomechanics. Chris currently serves as Secretary and Executive Board Member of the ASEE Mechanics Division and he is the chair of the Mechanics Committee in his department. He is also a member of a campus committee that arranged for an art exhibit honoring the life of Roberto Clemente to be donated to the UPRM campus from the Smithsonian Museum. Chris is a passionate educator and advocate for humanitarian uses of technology. In his free time he enjoys swimming, cycling, running, cooking, and learning the languages of the Caribbean. Paul D. Gessler is currently a graduate student pursuing his M.S. in the Mechanical Engineering Department at Marquette University in Milwaukee, Wisconsin. He earned his B.S. in Mechanical Engineering from the Milwaukee School of Engineering in 2012. Paul's main interests are using modeling and simulation at an appropriate abstraction level to improve the product design and systems engineering process. He has experience with a wide variety of commercial FEA/CFD codes and has written several bespoke codes for fluid, structural, and thermal system analysis. Paul hopes to be a proponent of model-based design practices in industry throughout his career.