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
In teaching an introduction to transport or systems dynamics modeling at the undergraduate level, it is possible to lose pedagogical traction in a sea of abstract mathematics. What the mathematical modeling of time-dependent system behavior offers is a venue in which students can be taught that physical analogies exist between what they likely perceive as distinct areas of study in the physical sciences. We introduce a storyline whose characters are superheroes that store and dissipate energy in dynamic systems. Introducing students to the overarching conservation laws helps develop the analogy that ties the different disciplines together under a common umbrella of system energy. In this book, we use the superhero cast to present the effort-flow analogy and its relationship to the conservation principles of mass, momentum, energy, and electrical charge. We use a superhero movie script common to mechanical, electrical, fluid, and thermal engineering systems to illustrate how to apply the analogy to arrive at governing differential equations describing the systems' behavior in time. Ultimately, we show how only two types of differential equation, and therefore, two types of system response are possible. This novel approach of storytelling and a movie script is used to help make the mathematics of lumped system modeling more approachable for students.