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Alexander Tsvelikh

Computational Geometry of Surfaces and Its Application to the Finite Element Analysis of Shells

by Olga Axenenko and Alexander Tsvelikh (Author)

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The book is devoted to two subjects representing some of the most challenging areas of computational methods of differential geometry and mechanics of shells; it also includes a CD-ROM with complete source codes (over 20,000 lines) in C/C++, ready to be compiled and used. (1) A new method is presented, allowing construction of the lines of principal curvature on arbitrarily complex curved surfaces. The authors explain in detail the developed algorithms and their implementation. (2) The book describes application of the developed algorithms to the Finite Element Analysis of thin shells, allowing to obtain high-quality numerical results, especially for the displacements and for the components of the stress tensor. All source codes are well commented. The book also includes several examples with known analytical solutions. The developed codes deliver solutions demonstrating excellent correspondence between the analytical and numerical results. This book is also available in paperback (listed separately).

ISBN-10

0646594044
ISBN-13

978-0646594040
Publisher

Computational Mechanics Australia Pty.Ltd.
Publication date

April 10, 2013
Language

English
Print length

307 pages
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Product details

Publisher ‏ : ‎ Computational Mechanics Australia Pty.Ltd. (April 10, 2013)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 307 pages
ISBN-10 ‏ : ‎ 0646594044
ISBN-13 ‏ : ‎ 978-0646594040
Item Weight ‏ : ‎ 3.08 pounds

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5.0 3 ratings

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I found this book very useful to solve engineering problems related to internal pressure in ...

Reviewed in the United States 🇺🇸 on October 17, 2014

Verified Purchase

I found this book very useful to solve engineering problems related to internal pressure in tanks, complex structure of shells of revolution and shallow thin shells. I like its didactic explanation of the finite element algorithms and their implementation in the source codes, as well as, its presentation of plots and graphics that are explained clearly connecting the analytical results with the evaluation of results from the engineering viewpoint, especially for the evaluation of displacements and stresses. As professor of engineering in Japan, I consider this book very didactic to be used as a textbook for undergraduate and graduate students, and as attractive reference material for engineering consultant companies and people interested in finite element analysis of shells.

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Leonid Korelstein

It's a good theoretical book for those

Reviewed in the United States 🇺🇸 on February 10, 2015

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It's a good theoretical book for those, who study meshing algorithms for shells. There is a good additional information for Quad-Surface program, developed by author's collective.

I especially want to mark chapters, which are allocated for FEM. They are very helpful for understanding method's application for engineering needs, as FEA of thin shells. There is short description of the FEM steps and principles, in relation of quadrilateral finite elements. Chapter 5 contains very visual explanation of the algorithm for constructing the lines of principal curvature at any point on the FE surface. Numerical examples at the end and source codes make the book a complete resource on meshing algorithms for shells.

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Rui Alves

making it a good reference for a broad range of people

Reviewed in the United States 🇺🇸 on December 16, 2014

Written by long-time experts in finite element methods and mesh generation, this book is an important contribution in the field of thin shell finite elements.

The book successfully addresses two main subjects:
- The development of a new method for the construction of the lines of principal curvature on arbitrarily complex curved surfaces,
- The formulation and implementation of a new 9-noded shell finite element that delivers high-quality numerical results, particularly for displacements and stresses.
Both the theoretical basis and the developed algorithms are thoroughly explained and fully implemented in the provided source codes.

As a professional working in the implementation of finite element analysis, I was most impressed by the extensive coverage of particular cases in the algorithms, putting in evidence that the authors devoted much effort to implement and test their formulations to obtain solid and reliable results. This aspect sets this work apart from most textbooks where you get the general idea but are left with many exceptions to solve on your own.

Furthermore, this book provides an introduction to differential geometry, as well as the mathematical fundamentals of the theory of thin shells, making it a good reference for a broad range of people, from students to engineering professional working with shell finite elements.

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