By John Otto Dow
This can be the 3rd ebook in a sequence designed to make the finite aspect process and adaptive refinement extra available. the 1st publication, A Unified method of the Finite aspect process and mistake research systems, laid the theoretical heritage for simplifying and lengthening the finite aspect and finite distinction tools by means of introducing using a bodily interpretable notation. This notation simplifies and extends computational mechanics by means of reversing the standard mathematical process of abstracting the notation utilized in the improvement. via introducing variables that characterize inflexible physique motions and pressure amounts, the modeling functions of person parts and the answer algorithms might be evaluated for accuracy by way of visible inspection. the second one e-book, The necessities of Finite aspect Modeling and Adaptive Refinement, validated the validity of the derivations inside the first e-book and prolonged the simplification of point formula and greater the mistake measures. This booklet, as its name shows, provides a simple creation to the finite aspect technique, errors research, and adaptive refinement. As such, it offers an easy-to-read assessment that enables the contents of alternative finite point books and finite point classes to be obvious in standpoint because the a variety of tactics are encountered. moreover, it offers advancements that enhance the techniques inside the normal finite point textbook. accordingly, whilst this e-book is used by myself or at the side of different displays, the reader is in a position to seriously assessing the functions of the finite point method. Read more...
summary: this is often the 3rd e-book in a sequence designed to make the finite aspect strategy and adaptive refinement extra obtainable. the 1st e-book, A Unified method of the Finite aspect process and mistake research systems, laid the theoretical history for simplifying and increasing the finite point and finite distinction equipment via introducing using a bodily interpretable notation. This notation simplifies and extends computational mechanics through reversing the standard mathematical strategy of abstracting the notation utilized in the improvement. by means of introducing variables that symbolize inflexible physique motions and pressure amounts, the modeling functions of person components and the answer algorithms might be evaluated for accuracy through visible inspection. the second one ebook, The necessities of Finite aspect Modeling and Adaptive Refinement, confirmed the validity of the derivations inside the first e-book and prolonged the simplification of aspect formula and superior the mistake measures. This publication, as its name shows, provides an easy advent to the finite aspect technique, mistakes research, and adaptive refinement. As such, it presents an easy-to-read evaluate that enables the contents of different finite aspect books and finite aspect classes to be noticeable in point of view because the numerous systems are encountered. additionally, it presents advancements that increase the systems inside the usual finite point textbook. therefore, whilst this ebook is used on my own or together with different shows, the reader is in a position to severely assessing the services of the finite point approach
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Additional info for A concise overview of the finite element method
3. 4. A work function expressed in terms of equivalent nodal loads and the nodal displacements is formed. 5). 6). 7). 4 THE FORMULATION OF THE FINITE ELEMENT STRUCTURAL MODEL This section develops the procedure for creating the mathematical representation of a truss or a finite element model. As we will see, the direct 10 • A CONCISE OVERVIEW OF THE FINITE ELEMENT METHOD formulation of the structural model is straightforward but the process is not computationally efficient. The matrices involved are extremely large and sparse.
The first example introduces the strain representations used to form the element. The second example develops a coordinate transformation that introduces the nodal displacements into the analysis. 4 FINITE ELEMENT DISPLACEMENT INTERPOLATION POLYNOMIALS Before proceeding to a discussion of the notation, we will demonstrate a procedure for identifying the algebraic terms needed for the displacement interpolation polynomial of a specific finite element. These polynomials are basic to individual finite elements in two ways.
In Dow (1999), it is shown that any four-sided element contains errors that are analogous to those discussed for the four-node element. The eight- and nine-node elements can represent linear strain distributions, but they contain errors in the higher-order strain representations that are similar to those identified for the four-node element. 8 EVALUATION OF A SIX-NODE FINITE ELEMENT The strain modeling characteristics of the six-node element will now be evaluated. 4. 1, the displacement interpolation polynomial for a six-node element consists of complete quadratic representations.
A concise overview of the finite element method by John Otto Dow