Ebook: Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies
Author: Prof. Dr. A. N. Guz (auth.)
- Tags: Continuum Mechanics and Mechanics of Materials, Structural Mechanics, Computational Intelligence, Mechanics
- Series: Foundations of Engineering Mechanics
- Year: 1999
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
At the present time stability theory of deformable systems has been developed into a manifold field within solid mechanics with methods, techniques and approaches of its own. We can hardly name a branch of industry or civil engineering where the results of the stability theory have not found their application. This extensive development together with engineering applications are reflected in a flurry of papers appearing in periodicals as well as in a plenty of monographs, textbooks and reference books. In so doing, overwhelming majority of researchers, con cerned with the problems of practical interest, have dealt with the loss of stability in the thin-walled structural elements. Trying to simplify solution of the problems, they have used two- and one-dimensional theories based on various auxiliary hypotheses. This activity contributed a lot to the preferential development of the stability theory of thin-walled structures and organisation of this theory into a branch of solid mechanics with its own up-to-date methods and trends, but left three-dimensional linearised theory of deformable bodies stability (TL TDBS), methods of solving and solutions of the three-dimensional stability problems themselves almost without attention. It must be emphasised that by three dimensional theories and problems in this book are meant those theories and problems which do not draw two-dimensional plate and shell and one-dimensional rod theories.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Essentials of tensor analysis....Pages 3-22
Description of state of strain....Pages 23-42
Description of state of stress....Pages 43-62
Elastic solids....Pages 63-91
Plastic solids....Pages 93-127
Solids with rheological properties....Pages 129-153
Front Matter....Pages 155-155
States of stress and strain....Pages 157-186
Elastic solids....Pages 187-216
Non-elastic solids....Pages 217-255
Front Matter....Pages 257-257
Stability criteria for deformable bodies....Pages 259-274
General statement of stability problem for deformable bodies....Pages 275-294
Sufficient conditions of applicability of the static method....Pages 295-308
Variational principles....Pages 309-328
General solutions for uniform precritical states....Pages 329-379
Approximate approach in three-dimensional theory of stability....Pages 381-386
Front Matter....Pages 387-387
All-round compression of isotropic simply connected body. Application of the integral stability criteria....Pages 389-411
Internal (structural) instability. Properties of the basic system of simultaneous equations....Pages 413-434
Near-the-surface instability. Problems for semi-restricted regions....Pages 435-470
Compression of a strip (plane strain problem)....Pages 471-499
Compression of high-elastic non-circular cylindrical body. Implementation of variational principles....Pages 501-515
Back Matter....Pages 517-557
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Essentials of tensor analysis....Pages 3-22
Description of state of strain....Pages 23-42
Description of state of stress....Pages 43-62
Elastic solids....Pages 63-91
Plastic solids....Pages 93-127
Solids with rheological properties....Pages 129-153
Front Matter....Pages 155-155
States of stress and strain....Pages 157-186
Elastic solids....Pages 187-216
Non-elastic solids....Pages 217-255
Front Matter....Pages 257-257
Stability criteria for deformable bodies....Pages 259-274
General statement of stability problem for deformable bodies....Pages 275-294
Sufficient conditions of applicability of the static method....Pages 295-308
Variational principles....Pages 309-328
General solutions for uniform precritical states....Pages 329-379
Approximate approach in three-dimensional theory of stability....Pages 381-386
Front Matter....Pages 387-387
All-round compression of isotropic simply connected body. Application of the integral stability criteria....Pages 389-411
Internal (structural) instability. Properties of the basic system of simultaneous equations....Pages 413-434
Near-the-surface instability. Problems for semi-restricted regions....Pages 435-470
Compression of a strip (plane strain problem)....Pages 471-499
Compression of high-elastic non-circular cylindrical body. Implementation of variational principles....Pages 501-515
Back Matter....Pages 517-557
....