#### 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