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

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.

Table of Contents:
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