Editor: Elena A. Shirokova

Spline-Interpolation Solution of One Elasticity Theory Problem

eBook: US $39 Special Offer (PDF + Printed Copy): US $138
Printed Copy: US $119
Library License: US $156
ISBN: 978-1-60805-620-0 (Print)
ISBN: 978-1-60805-209-7 (Online)
Year of Publication: 2011
DOI: 10.2174/97816080520971110101


The book presents methods of approximate solution of the basic problem of elasticity for special types of solids. Engineers can apply the approximate methods (Finite Element Method, Boundary Element Method) to solve the problems but the application of these methods may not be correct for solids with the certain singularities or asymmetrical boundary conditions. The book is recommended for researchers and professionals working on elasticity modeling. It explains methods of solving elasticity problems for special solids. Approximate methods (Finite Element Method, Boundary Element Method) have been used to solve these problems. The interpolation and the spline-interpolation solutions of the 3D problem of the theory of elasticity have been constructed in this work. The spline-interpolation solution can be considered as a variant of the finite element method.


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