Integrodifferential Relations in Linear Elasticity / / Vasily V. Saurin, Georgy V. Kostin.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematical Physics eBook-Package
• VerfasserIn: Kostin, Georgy V.,; Saurin, Vasily V.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2012]; ©2012
• Year of Publication: 2012
• Language: English
• Series: De Gruyter Studies in Mathematical Physics , 10
• Physical Description: 1 online resource (280 p.)

Deformations of elastic bodies are encountered in many areas in science, engineering and technology. In the last decades, various numerical approaches using the finite element technique have been developed, but many are not adequate to address the full complexity.This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements. Other than comparable books, this work also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.

Table of Contents

Frontmatter -- Preface -- Contents -- Chapter 1. Introduction -- Chapter 2. Basic concepts of the linear theory of elasticity -- Chapter 3. Conventional variational principles -- Chapter 4. The method of integrodifferential relations -- Chapter 5. Variational properties of the integrodifferential statements -- Chapter 6. Advance finite element technique -- Chapter 7. Semi-discretization and variational technique -- Chapter 8. An asymptotic approach -- Chapter 9. A projection approach -- Chapter 10. 3D static beam modeling -- Chapter 11. 3D beam vibrations -- Appendix A. Vectors and tensors -- Appendix B. Sobolev spaces -- Bibliography -- Index