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Lying by Approximation

Book Description

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

Table of Contents

  1. Preface
    1. What This Book Is Intended to Be
    2. Pedagogical Approach
    3. What This Book Is Not Intended to Be
    4. Outline of Book
  2. Acknowledgments
  3. Guilty Until Proven Innocent
    1. Guilty Until Proven Innocent
    2. What a Minimal Requisite Skill Set Looks Like
    3. The Ten Most Common Mistakes
    4. Man vs. Machine
    5. Putting it Together: Toward a New FEA Pedagogy
  4. Let's Get Started
    1. Qualitative Concepts of Mechanics of Materials
    2. The Stress Tensor
    3. Idealized Structural Responses
      1. Axial Response
      2. Lateral Shear Response
      3. Bending Response
      4. Torsional Response
    4. What Dimension Are You In?
      1. The Limit of the Thin (Plane Stress and Pressure Vessels)
      2. The Limit of the Thick (Plane Strain)
      3. Analogy of Plane Stress and Plane Strain
      4. The Limit of the Round (Axisymmetry)
    5. St. Venant's Principle
    6. Combined Loading
    7. A Closing Remark and Look Ahead
  5. Where We Begin to Go Wrong
    1. Exceptions to the Rule
    2. The Lines in the Sand
      1. A Stepped Axial Rod
      2. A Short, Stubby Beam
      3. A Thick-Walled Pressure Vessel
    3. Utility of the Finite Element Method
  6. It's Only a Model
    1. The Expectation Failure
    2. Philosophy of Mathematical Modeling
    3. The Art of Approximation
    4. What Are We Approximating? (1/3)
    5. What Are We Approximating? (2/3)
    6. What Are We Approximating? (3/3)
    7. Lessons Learned
  7. Wisdom Is Doing It
    1. Preliminary Analysis
    2. Pre-processing
      1. The Cast of Element Characters
      2. Good and Bad Elements
      3. Applying Boundary Constraints
      4. Applying External Loads
    3. Post-processing
    4. Further Rules to Live By in Practice
    5. Solution Validation
    6. Verification
  8. Summary
  9. Afterword
  10. Bibliography
  11. Authors' Biographies