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The Finite Element Method, 2nd Edition

Book Description

Written for practicing engineers and students alike, this book emphasizes the role of finite element modeling and simulation in the engineering design process. It provides the necessary theories and techniques of the FEM in a concise and easy-to-understand format and applies the techniques to civil, mechanical, and aerospace problems. Updated throughout for current developments in FEM and FEM software, the book also includes case studies, diagrams, illustrations, and tables to help demonstrate the material.



  • Plentiful diagrams, illustrations and tables demonstrate the material
  • Covers modeling techniques that predict how components will operate and tolerate loads, stresses and strains in reality
  • Full set of PowerPoint presentation slides that illustrate and support the book, available on a companion website

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. Biography
  7. Preface to the First Edition
  8. Chapter 1. Computational Modeling
    1. 1.1 Introduction
    2. 1.2 Physical problems in engineering
    3. 1.3 Computational modeling using FEM
    4. 1.4 Solution procedure
    5. 1.5 Results visualization
    6. Reference
  9. Chapter 2. Briefing on Mechanics for Solids and Structures
    1. 2.1 Introduction
    2. 2.2 Equations for three-dimensional solids
    3. 2.3 Equations for two-dimensional solids
    4. 2.4 Equations for truss members
    5. 2.5 Equations for beams
    6. 2.6 Equations for plates
    7. 2.7 Remarks
    8. 2.8 Review questions
    9. References
  10. Chapter 3. Fundamentals for Finite Element Method
    1. 3.1 Introduction
    2. 3.2 Strong and weak forms: problem formulation
    3. 3.3 Hamilton’s principle: A weak formulation
    4. 3.4 FEM procedure
    5. 3.5 Static analysis
    6. 3.6 Analysis of free vibration (eigenvalue analysis)
    7. 3.7 Transient response
    8. 3.8 Remarks
    9. 3.9 Review questions
    10. References
  11. Chapter 4. FEM for Trusses
    1. 4.1 Introduction
    2. 4.2 FEM equations
    3. 4.3 Worked examples
    4. 4.4 High order one-dimensional elements
    5. 4.5 Review questions
    6. References
  12. Chapter 5. FEM for Beams
    1. 5.1 Introduction
    2. 5.2 FEM equations
    3. 5.3 Remarks
    4. 5.4 Worked examples
    5. 5.5 Case study: resonant frequencies of micro-resonant transducer
    6. 5.6 Review questions
    7. References
  13. Chapter 6. FEM for Frames
    1. 6.1 Introduction
    2. 6.2 FEM equations for planar frames
    3. 6.3 FEM equations for space frames
    4. 6.4 Remarks
    5. 6.5 Case study: finite element analysis of a bicycle frame
    6. 6.6 Review questions
    7. References
  14. Chapter 7. FEM for Two-Dimensional Solids
    1. 7.1 Introduction
    2. 7.2 Linear triangular elements
    3. 7.3 Linear rectangular elements
    4. 7.4 Linear quadrilateral elements
    5. 7.5 Elements for axisymmetric structures
    6. 7.6 Higher order elements—triangular element family
    7. 7.7 Rectangular Elements
    8. 7.8 Elements with curved edges
    9. 7.9 Comments on Gauss integration
    10. 7.10 Case study: Side drive micro-motor
    11. 7.11 Review questions
    12. References
  15. Chapter 8. FEM for Plates and Shells
    1. 8.1 Introduction
    2. 8.2 Plate elements
    3. 8.3 Shell elements
    4. 8.4 Remarks
    5. 8.5 Case study: Natural frequencies of the micro-motor
    6. 8.6 Case study: Transient analysis of a micro-motor
    7. 8.7 Review questions
    8. References
  16. Chapter 9. FEM for 3D Solid Elements
    1. 9.1 Introduction
    2. 9.2 Tetrahedron element
    3. 9.3 Hexahedron element
    4. 9.4 Higher order elements
    5. 9.5 Elements with curved surfaces
    6. 9.6 Case study: Stress and strain analysis of a quantum dot heterostructure
    7. 9.7 Review questions
    8. References
  17. Chapter 10. Special Purpose Elements
    1. 10.1 Introduction
    2. 10.2 Crack tip elements
    3. 10.3.3 Coupling of FEM and the boundary element method
    4. 10.5 Strip element method
    5. 10.6 Meshfree methods
    6. 10.7 S-FEM
    7. References
  18. Chapter 11. Modeling Techniques
    1. 11.1 Introduction
    2. 11.2 CPU time estimation
    3. 11.3 Geometry modeling
    4. 11.4 Meshing
    5. 11.5 Mesh compatibility
    6. 11.6 Use of symmetry
    7. 11.6.4 Repetitive symmetry
    8. 11.7 Modeling of offsets
    9. 11.8 Modeling of supports
    10. 11.9 Modeling of joints
    11. 11.10 Other applications of MPC equations
    12. 11.11 Implementation of MPC equations
    13. 11.12 Review questions
    14. References
  19. Chapter 12. FEM for Heat Transfer Problems
    1. 12.1 Field problems
    2. 12.2 Weighted residual approach for FEM
    3. 12.3 1D heat transfer problem
    4. 12.4 2D heat transfer problem
    5. 12.5 Summary
    6. 12.6 Case study: Temperature distribution of heated road surface
    7. 12.7 Review questions
    8. References
  20. Chapter 13. Using FEM Software Packages
    1. 13.1 Introduction
    2. 13.2 Basic building block: keywords and data lines
    3. 13.3 Using sets
    4. 13.4 ABAQUS input syntax rules
    5. 13.5 Defining a finite element model in ABAQUS
    6. 13.6 General procedures
    7. 13.7 Remarks (example using a GUI: ANSYS)
    8. References
  21. References
  22. Index