Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies (Foundations of Engineering Mechanics)

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. 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 Three-dimensional theory of deformable bodies stability, as it is treated in this book, comprises general issues, methods of solving, and solutions of problems in the context of the three-dimensional linearised equations, i.e. without reducing the problem to lower dimensions. Stability criteria corresponding to those of the well developed theory of thin-walled structures are used. Therefore, one of the most important tasks of the three-dimensional theory is the investigation of states which cannot be treated by a theory of thin-walled structures. The other one is the estimation of accuracy of stability theories of lower dimensions