Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies

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.

Stability is the very essential demand on every structure. This comprehensive monograph elucidates the fundamentals of the three-dimensional theory. Various models of material behavior are treated: elastic, elasto-plastic, viscoelastic and viscoelasto-plastic. Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt

1. Fundamentals of nonlinear solid mechanics.- 1 Essentials of tensor analysis.- 2 Description of state of strain.- 3 Description of state of stress.- 4 Elastic solids.- 5 Plastic solids.- 6 Solids with rheological properties.- 2. Fundamentals of linearised solid mechanics.- 7 States of stress and strain.- 8 Elastic solids.- 9 Non-elastic solids.- 3. General issues of three-dimensional linearised theory of deformable bodies stability (TLTDBS).- 10 Stability criteria for deformable bodies.- 11 General statement of stability problem for deformable bodies.- 12 Sufficient conditions of applicability of the static method.- 13 Variational principles.- 14 General solutions for uniform precritical states.- 15 Approximate approach in three-dimensional theory of stability.- 4. Analysis of the simplest problems.- 16 All-round compression of isotropic simply connected body. Application of the integral stability criteria.- 17 Internal (structural) instability. Properties of the basic system of simultaneous equations.- 18 Near-the-surface instability. Problems for semi-restricted regions.- 19 Compression of a strip (plane strain problem).- 20 Compression of high-elastic non-circular cylindrical body. Implementation of variational principles.- Supplement. Exact solutions of mixed plane problems of linearised solid mechanics.- References.- References supplement.- Biography.