2nd Edition

What Every Engineer Should Know about Computational Techniques of Finite Element Analysis

By Louis Komzsik Copyright 2009
    350 Pages 68 B/W Illustrations
    by CRC Press

    Finite element analysis (FEA) has become the dominant tool of analysis in many industrial fields of engineering, particularly in mechanical and aerospace engineering. This process requires significant computational work divided into several distinct phases. What Every Engineer Should Know About Computational Techniques of Finite Element Analysis offers a concise, self-contained treatment of FEA and all of the tools needed for efficient use and practical implementation.

    This book provides you with a walk-through of the process from the physical model to the computed solution. Based on the author's thirty years of practical experience in finite element analysis in the shipbuilding, aerospace, and automobile industries, it describes the transformation of the physical problem into a mathematical model, reduction of the model to a more efficient, numerically solvable form, and the solution of the problem using specific computational techniques. The author discusses time and frequency domain solutions as used in practice, as well as the representation of the computed results.

    What Every Engineer Should Know About Computational Techniques of Finite Element Analysis serves as a to-the-point guide to using or implementing FEA for both beginners and everyday users who must apply the finite element method to your daily work. The techniques can be easily executed in most available FEA software packages.

    CRC Press Authors Speak

    Louis Komzsik introduces you to two books that share a common mathematical foundation, the finite element analysis technique. Watch the video.

    NUMERICAL MODEL GENERATION
    Finite Element Analysis
    Solution of Boundary Value Problems
    Finite Element Shape Functions
    Finite Element Basis Functions
    Assembly of Finite Element Matrices
    Element Matrix Generation
    Local to Global Coordinate Transformation
    A Quadrilateral Finite Element
    References
    Finite Element Model Generation
    Spline Approximation
    Geometric Modeling Objects
    Geometric Model Discretization
    Delaunay Mesh Generation
    References
    Modeling of Physical Phenomena
    Lagrange's Equations of Motion
    Continuum Mechanical Systems
    Finite Element Analysis of Elastic Continuum
    A Tetrahedral Finite Element
    Equation of Motion of Mechanical System
    Transformation to Frequency Domain
    References
    Constraints and Boundary Conditions
    The Concept of Multi-Point Constraints
    The Elimination of Multi-Point Constraints
    The Axial Bar Element
    The Concept of Single Point Constraints
    The Elimination of Single Point Constraints
    References
    Singularity Detection of Finite Element Models
    Local Singularities
    Global Singularities
    Massless Degrees of Freedom
    Industrial Case Studies
    References

    COMPUTATIONAL REDUCTION TECHNIQUES
    Matrix Factorization and Linear System Solution
    Finite Element Matrix Reordering
    Sparse Matrix Factorization
    Multifrontal Factorization
    Linear System Solution
    Distributed Factorization and Solution
    Factorization Case Study
    References
    Static Condensation
    Single Level, Single Component Condensation
    Computational Example
    Single Level, Multiple Component Condensation
    Multiple Level Static Condensation
    Static Condensation Case Study
    References
    Spectral Computations
    Spectral Transformation
    Lanczos Reduction
    Generalized Eigenvalue Problem
    Eigenvalue Computation
    Distributed Eigenvalue Computation
    Normal Modes Analysis Case Study
    Complex Spectral Computations
    Complex Modes Analysis Case Study
    Dense Eigenvalue Analysis
    Householder Reduction Techniques
    Tridiagonal Reduction
    Reduction to Hessenberg Form
    References
    Dynamic Reduction
    Single Level, Single Component Dynamic Reduction
    Accuracy of Dynamic Reduction
    Computational Example
    Single Level, Multiple Component Dynamic Reduction
    Multiple Level Dynamic Reduction
    Multibody Analysis Application
    References
    Component Modal Synthesis
    Single Level, Single Component Modal Synthesis
    Mixed Boundary Component Mode Reduction
    Computational Example
    Single Level, Multiple Component Modal Synthesis
    Multiple Level Modal Synthesis
    Component Modal Synthesis Case Study
    References

    ENGINEERING SOLUTION COMPUTATIONS
    Modal Solution Technique
    Modal Reduction
    Truncation Error in Modal Reduction
    The Method of Residual Flexibility
    The Method of Mode Acceleration
    Coupled Modal Solution Application
    References
    Transient Response Analysis
    The Central Difference Method
    The Newmark Method
    Starting Conditions and Time Step Changes
    Stability of Time Integration Techniques
    Transient Solution Case Study
    References
    Frequency Domain Analysis
    Direct Frequency Response Analysis
    Reduced Order Frequency Response Analysis
    Accuracy of Reduced Order Solution
    Frequency Response Case Study
    References
    Nonlinear Analysis
    Introduction to Nonlinear Analysis
    Newton-Raphson Methods
    Quasi-Newton Iteration Techniques
    Convergence Criteria
    Computational Example
    Nonlinear Dynamics
    References
    Sensitivity and Optimization
    Design Sensitivity
    Design Optimization
    Planar Bending of the Bar
    Computational Example
    Eigenfunction Sensitivities
    Variational Analysis
    References
    Engineering Result Computations
    Displacement Recovery
    Stress Calculation
    Nodal Data Interpolation
    Level Curve Computation
    Engineering Results Case Study
    References
    Closing Remarks
    Annotation
    Index

    Biography

    Dr. Louis Komzsik is the chief numerical analyst in the Office of Architecture and Technology at Siemens PLM Software.

    "It is an excellent presentation really of what engineers should know about computational techniques in FEA. The descriptions of the various subjects are very clear and transparently expose the facts.

    "I hope engineers are interested to learn these lectures, which give them the opportunity to take a critical position in their doing.

    "This is necessary because
    - computing uses floating point models while classical theories use inductive and deductive models
    - computing is essentially finite while mathematics is the science of infinite
    - computing sometimes promotes logical mistakes

    "Also in view of these more or less philosophical aspects your book will sharpen the thinking about limitations of application of the FE technique."
    -Dr. Otto Gartmeier, Manager, NVH Optimization, Daimler Chrysler Corporation

    " I wish this book had been published earlier! …If you use NASTRAN on a daily basis as the Number 1 Code, you will find that Dr. Komzsik's book is unique and outstanding, compared to all other Finite Element books. Look at the real life examples. It shows that Dr. Komzsik studied mathematics and then was, for over 20 years, one of the team leaders at MSC developing and maintaining NASTRAN. All of the important features in real life applications are explained in a few sentences and illustrated if necessary…
    "I highly recommend this excellent book for every engineer. Even for students, it is very affordable and should be used as a standard reference whenever a Finite Element code is applied."
    -Dr. Ortwin Ohtmer, Professor of Mechanical Engineering, California State University, Long Beach, USA