Fundamentals of the three-dimensional theory of stability of deformable bodies / A. N. Guz

Includes bibliographical references and index.

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.

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.