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A concise overview of the finite element method - download pdf or read online

By John Otto Dow

ISBN-10: 1606505084

ISBN-13: 9781606505083

ISBN-10: 1606505092

ISBN-13: 9781606505090

This is often the 3rd booklet in a chain designed to make the finite aspect technique and adaptive refinement extra obtainable. the 1st ebook, A Unified method of the Finite point process and blunder research methods, laid the theoretical heritage for simplifying and increasing the finite aspect and finite distinction tools via introducing using a bodily interpretable notation. This notation simplifies and Read more...

summary: this can be the 3rd publication in a chain designed to make the finite point approach and adaptive refinement extra obtainable. the 1st booklet, A Unified method of the Finite point process and blunder research approaches, laid the theoretical heritage for simplifying and lengthening the finite aspect and finite distinction tools by way of introducing using a bodily interpretable notation. This notation simplifies and extends computational mechanics through reversing the standard mathematical process of abstracting the notation utilized in the advance. via introducing variables that signify inflexible physique motions and pressure amounts, the modeling functions of person components and the answer algorithms should be evaluated for accuracy by means of visible inspection. the second one publication, The necessities of Finite point Modeling and Adaptive Refinement, validated the validity of the derivations inside the first booklet and prolonged the simplification of point formula and stronger the mistake measures. This e-book, as its identify shows, offers a simple advent to the finite point procedure, mistakes research, and adaptive refinement. As such, it offers an easy-to-read evaluation that permits the contents of different finite aspect books and finite point classes to be noticeable in viewpoint because the numerous strategies are encountered. additionally, it presents advancements that increase the methods inside the commonplace finite aspect textbook. for that reason, whilst this ebook is used by myself or along with different displays, the reader is able to significantly assessing the functions of the finite point process

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Extra resources for A concise overview of the finite element method

Example text

In this case, the coefficients are those expected for a complete linear Taylor series expansion. The presence of the correct constant and linear terms in both of the normal strain components means that the Poisson effect is represented correctly. The shear strain representation is a complete linear polynomial. In the six-node element, these are the correct shear strain terms. The linear terms are not normal strain terms as was the case for the four-node element. We can conclude that a six-node element can accurately represent is a linear strain distribution.

As a result, the meaning of any equation formed from these quantities can be interpreted visually by comparing it to the concepts of continuum mechanics. This transparency provides insights into the finite element method and its capabilities. The insights provided by this transparency are important in two ways. First, all aspects of the finite element method are simplified and extended. These improvements occur because the theory of continuum mechanics and the solution techniques are directly connected by the notation.

The linear terms are not normal strain terms as was the case for the four-node element. We can conclude that a six-node element can accurately represent is a linear strain distribution. As might be expected, the six-node element is known as the linear strain triangle. If the actual strain distribution is more complex, the six-node element representation can only approximate the actual strain distribution. The differences between the finite element representation and the exact solution are called discretization errors.

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A concise overview of the finite element method by John Otto Dow


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