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.

Zusammenfassung

"The aim of this very important book is the study of problems in solid mechanics whose variational forms are equalities, expressing the principle of virtual power in its equality form. This book is unique in that it presents a profound mathematical analysis of general elasticity of deformed bodies, including the resulting interior stresses and displacements." Mathematical Reviews

"This well-written and good-organized monograph can be recommended to highly-qualified experts in the field." Zentralblatt für Mathematik

Inhalt

Introduction2. Basic concepts of the linear theory of elasticity3. Conventional varational principles4. The method of integrodifferential relations5. Variational properties of the integrodifferential statements6. Advance finite element technique7. Semi-discretization and variational technique8. An asymptotic approach9. A projection approach10. 3D static beam modeling11. 3D beam vibrations12. Projection FEM approach for thin walled structures13. Appendix