Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a "mesh." The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same time advancing adaptive refinement procedures.
These improvements are made possible due to a change in notation that embeds knowledge of solid continuum mechanics into the equations used to formulate the stiffness matrices; this allows the modeling characteristics of individual elements to be identified by visual inspection. The ability to visually relate the equations involved in element formulation to the physical process they represent is like having an x-ray of the inner workings of the finite element method; it is similar is to the effect that Graphical User Interfaces or GUI's had on computing. As a result, students at any level of finite element study are provided with an understanding of the capabilities and limitations of this powerful analytic tool.
Preface
Chapter 1 : Introduction
Chapter 2 : An Overview of Finite Element Modeling Characteristics
Chapter 2A : Elements of Two-Dimensional Modeling
Chapter 2B : Exact Solutions for Two Longitudinal Bar Problems
Chapter 3 : Identification of Finite Element Strain Modeling Capabilities
Chapter 4 : The Source and Quantification of Discretization Errors
Chapter 5 : Modeling Inefficiency in Irregular Isoparametric Elements
Chapter 6 : Introduction to Adaptive Refinement
Chapter 7 : Strain Energy-Based Error Estimators - The Z/Z Error Estimator
Chapter 7A : Gauss Points, Super Convergent Strains, and Chebyshev Polynomials
Chapter 7B : An Unsuccessful Example of Adaptive Refinement
Chapter 8 : A High Resolution Point-Wise Residual Error Estimator
Chapter 9 : Modeling Characteristics and Efficiencies of Higher Order Elements
Chapter 10 : Formulation of a 10-Node Quadratic Strain Element
Chapter 10A : A Numerical Example for a 10-Node Stiffness Matrix
Chapter 10B : MATLAB Formulation of the 10-Node Element Stiffness Matrix
Chapter 11 : Performance-Based Refinement Guides
Chapter 12 : Summary and Research Recommendations
Index
