The Essentials of Finite Element Modeling and Adaptive Refinement: For Beginning Analysts to Advanced Researchers in Solid Mechanics
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.This groundbreaking text extends the usefulness of finite element analysis for both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method and 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 physically interpretable notation allows the modeling characteristics of individual elements to be identified by visual inspection--an ability akin to having an x-ray of the inner workings of the finite element method. This capability simplifies the understanding and application of the finite element method in the same way the introduction of Graphical User Interfaces or GUI's extended the audience and capabilities of computing. This classroom tested book presents: * A simplified approach for forming finite element analysis that renders isoparametric elements obsolete. * A physically interpretable notation expressed in terms of rigid body motions and strain quantities that allows the modeling capabilities of individual elements to be evaluated visually. * A proof that the inter-element jumps in strain quantify the point-wise failure of the finite element solution to satisfy the governing differential equation representation of the problem being solved. * The identification of a common basis for the finite element and the finite difference methods that breathes new life into the finite difference method and allows new types of practical error estimators and refinement guides to be developed. * New point-wise error estimators that identify errors in terms of quantities of direct interest in solid mechanics so the termination criteria can be related to material failure models.
