Integrodifferential Relations in Linear Elasticity

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.

Autorentext

Georgy V. Kostin and Vasily V. Saurin, Ishlinsky Institute for Problems in Mechanics, Russia.

Inhalt

1. Introduction
2. Basic concepts of the linear theory of elasticity
3. Conventional varational principles
4. The method of integrodifferential relations
5. Variational properties of the integrodifferential statements
6. Advance finite element technique
7. Semi-discretization and variational technique
8. An asymptotic approach
9. A projection approach
10. 3D static beam modeling
11. 3D beam vibrations
12. Projection FEM approach for thin walled structures
13. Appendix