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.

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.