By John Otto Dow
This can be the 3rd publication in a chain designed to make the finite aspect process and adaptive refinement extra available. the 1st e-book, A Unified method of the Finite aspect technique and blunder research strategies, laid the theoretical history for simplifying and increasing the finite point and finite distinction equipment by way of introducing using a bodily interpretable notation. This notation simplifies and extends computational mechanics through reversing the standard mathematical technique of abstracting the notation utilized in the advance. by way of introducing variables that symbolize inflexible physique motions and pressure amounts, the modeling services of person components and the answer algorithms may be evaluated for accuracy by way of visible inspection. the second one e-book, The necessities of Finite point Modeling and Adaptive Refinement, established the validity of the derivations inside the first publication and prolonged the simplification of point formula and superior the mistake measures. This publication, as its identify shows, provides a simple creation to the finite aspect approach, mistakes research, and adaptive refinement. As such, it offers an easy-to-read evaluate that enables the contents of different finite aspect books and finite point classes to be visible in point of view because the numerous systems are encountered. in addition, it offers advancements that increase the techniques inside the usual finite point textbook. for that reason, whilst this ebook is used by myself or along side different displays, the reader is able to seriously assessing the services of the finite point method. Read more...
summary: this can be the 3rd publication in a chain designed to make the finite aspect technique and adaptive refinement extra available. the 1st booklet, A Unified method of the Finite aspect approach and mistake research methods, laid the theoretical heritage for simplifying and increasing the finite point and finite distinction equipment by means of introducing using a bodily interpretable notation. This notation simplifies and extends computational mechanics via reversing the standard mathematical strategy 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 should be evaluated for accuracy through visible inspection. the second one booklet, The necessities of Finite point Modeling and Adaptive Refinement, tested the validity of the derivations inside the first e-book and prolonged the simplification of point formula and greater the mistake measures. This ebook, as its identify exhibits, offers an easy advent to the finite aspect process, blunders research, and adaptive refinement. As such, it presents an easy-to-read evaluation that enables the contents of alternative finite point books and finite point classes to be obvious in standpoint because the a number of techniques are encountered. moreover, it presents advancements that enhance the methods inside the commonplace finite point textbook. therefore, while this e-book is used on my own or at the side of different shows, the reader is in a position to severely assessing the services of the finite point approach
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Extra info for A concise overview of the finite element method
This is significant because the coefficients are now expressed in terms of variables that produce the displacements and deformations in the continuum. 2 have been replaced by coefficients that have specific physical meaning in solid mechanics. The zeroth order coefficients are constants that represent the rigid body displacements (urb)0 and (vrb)0. The four first-order coefficients of the x and y terms (εx)0, (εy)0, and, (γxy)0 represent constant strains and the rigid body rotation (rrb)0 (see note 1 at the end of the chapter).
Similarly, the two symmetric off-diagonal terms k12 34 are located in row 14 of column 9 and row 9 of column 14, respectively. 10, which was formed by multiplying out the strain energy expression. Note that the off-diagonal elements are located symmetrically in the global stiffness matrix. The process of locating an element stiffness matrix in the global stiffness matrix will be demonstrated with another example. The objective of this example is to show how elements that are connected to each other in the structure are related in the global stiffness matrix.
This notation can be viewed as a straightforward modification of the existing interpolation polynomials used in the finite element method. In this modification, the coefficients are expressed in terms of strain quantities. Since strains are primary quantities that are sought in continuum mechanics, the resulting equations are directly related to continuum mechanics concepts. The use of this physically interpretable notation allows the equations to be interpreted visually. This capability is demonstrated in the next chapter.