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

1. Front Matter

   Pages I-XVI

   PDF

2. Fundamentals of nonlinear solid mechanics

   1. Front Matter

      Pages 1-1

      PDF

   2. Essentials of tensor analysis

      • A. N. Guz

      Pages 3-22

   3. Description of state of strain

      • A. N. Guz

      Pages 23-42

   4. Description of state of stress

      • A. N. Guz

      Pages 43-62

   5. Elastic solids

      • A. N. Guz

      Pages 63-91

   6. Plastic solids

      • A. N. Guz

      Pages 93-127

   7. Solids with rheological properties

      • A. N. Guz

      Pages 129-153

3. Fundamentals of linearised solid mechanics

   1. Front Matter

      Pages 155-155

      PDF

   2. States of stress and strain

      • A. N. Guz

      Pages 157-186

   3. Elastic solids

      • A. N. Guz

      Pages 187-216

   4. Non-elastic solids

      • A. N. Guz

      Pages 217-255

4. General issues of three-dimensional linearised theory of deformable bodies stability (TLTDBS)

   1. Front Matter

      Pages 257-257

      PDF

   2. Stability criteria for deformable bodies

      • A. N. Guz

      Pages 259-274

   3. General statement of stability problem for deformable bodies

      • A. N. Guz

      Pages 275-294

   4. Sufficient conditions of applicability of the static method

      • A. N. Guz

      Pages 295-308

   5. Variational principles

      • A. N. Guz

      Pages 309-328

   6. General solutions for uniform precritical states

      • A. N. Guz

      Pages 329-379

   7. Approximate approach in three-dimensional theory of stability

      • A. N. Guz

      Pages 381-386

5. Analysis of the simplest problems

   1. Front Matter

      Pages 387-387

      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.

• mechanics
• solid
• stability
• structures

• Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine

  A. N. Guz

Policies and ethics