Spline-Interpolation Solution of One Elasticity Theory Problem


by

Elena A. Shirokova

DOI: 10.2174/97816080520971110101
eISBN: 978-1-60805-209-7, 2011
ISBN: 978-1-60805-620-0

  
  


Indexed in: Scopus

The book presents methods of approximate solution of the basic problem of elasticity for special types of solids. Engineers can apply ...[view complete introduction]
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Table of Contents

Foreword , Pp. i

Damir F. Abzalilov
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Preface , Pp. ii-iii (2)

Elena A. Shirokova and Pyotr. N. Ivanshin
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List of Contributors , Pp. iv

Elena A. Shirokova and Pyotr. N. Ivanshin
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Introduction , Pp. v-ix (5)

Elena A. Shirokova and Pyotr. N. Ivanshin
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Polynomial solution of the system of the equilibrium equations , Pp. 1-12 (12)

Elena A. Shirokova
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Interpolation solution of the second basic problem of elasticity for the circular cylinder , Pp. 13-45 (33)

Elena A. Shirokova and Pyotr N. Ivanshin
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Interpolation solution of the problems of elasticity for the pressurized tube , Pp. 46-77 (32)

Elena A. Shirokova and Pyotr N. Ivanshin
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Interpolation solution of the problem of elasticity for the non-circular cylinder , Pp. 78-93 (16)

Elena A. Shirokova and Pyotr N. Ivanshin
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Spline-interpolation solutions for the circular cylinder and for the tube , Pp. 94-122 (29)

Elena A. Shirokova and Pyotr N. Ivanshin
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Spline-interpolation solution for a solid of revolution , Pp. 123-150 (28)

Elena A. Shirokova and Pyotr N. Ivanshin
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Spline-interpolation solution for asymmetric cones or conoids , Pp. 151-171 (21)

Elena A. Shirokova and Pyotr N. Ivanshin
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Approximation estimates and properties of the interpolation and spline-interpolation solutions , Pp. 172-181 (10)

Elena A. Shirokova and Pyotr N. Ivanshin
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Dynamic problems , Pp. 182-210 (29)

Elena A. Shirokova and Pyotr N. Ivanshin
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Appendices , Pp. 211-252 (42)

Elena A. Shirokova and Pyotr N. Ivanshin
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References , Pp. 253-254 (2)

Elena A. Shirokova and Pyotr N. Ivanshin
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Index , Pp. 255

Elena A. Shirokova and Pyotr N. Ivanshin
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Foreword

The main purpose of this work is to demonstrate the new methods of solution of some 3D elasticity theory problems. These methods are based on complex analysis application. I have considered different types of approximate and precise solutions of different mechanical problems throughout almost all of my scientific career. So I am always interested in getting acquainted with some new method of solution. It seems interesting to consider passing from thorough methods applied in the case of 2D problems to the case of 3D ones. So the book seems to be of certain value. I feel obliged to note that it is necessary to find not only some method of problem solution but to make it possible to get actual numerical results. Since the book contains examples for almost all the considered questions, it becomes a nice piece of literature useful for almost immediate applications.

Dr. Sc. Damir F. Abzalilov


Preface

This book appeared as the result of the development of the Kolosov-Muskhelishvili plane elasticity theory solution methods. E.A.Shirokova applied the generalisation of this methods to the construction of the interpolation solution of the 3D problems of elasticity for cylinders and tubes in 2004.

The spline-interpolation solution was introduced as the development of the interpolation solution for solids different from cylinders. This solution is based on the interpolation solution but is more efficient computationally.

The second co-author has began his investigations in this field recently. His achievement is construction of continuous and smooth spline-interpolation solutions for some types of cylindrical and non-cylindrical solids and approximation estimates.

Also the authors would like to express their thanks to A.N. Schermann for the construction of one important example and for proof-reading of the text.

The order of reading is the following:



Elena A. Shirokova
Pyotr N. Ivanshin
Kazan Federal University
Russia

List of Contributors

Editor(s):
Elena A. Shirokova
Kazan Federal University
Russia




Contributor(s):
Elena A. Shirokova
Mechanics and Mathematics department
Kazan Federal University



Pyotr N. Ivanshin
Physics department
Kazan Federal University





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