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Contents 461
8.2. Three-dimensional equilibrium equations in isostatic co-ordinate net
8.3. The derivative equations
8.4. Three-dimensional incremental equilibrium equations in isostatic co-ordinate net
8.5. The compatibility equations for principal strains ”increments”
8.6. The Cauchy formulas in isostatic co-ordinates
8.7. Plane strain formulation in isostatic co-ordinates
8.8. Axially-symmetric formulation in isostatic co-ordinates
Appendix to Chapters 1–8: The Legendre and Ampere Transformations
1. The Legendre transformation
2. The Ampere transformation
References to Chapters 1–8
Chapter 9. Plane Stress State of a Perfectly Plastic Solid
9.1. Introductory remarks
9.2. Basic equations formulation for the von Mises yielding criterion
9.3. A self-similar solution of plane stress equations
9.4. Stress distribution near a mode I crack tip under plane stress conditions
9.5. The exact formulas for near crack tip stress field
9.6. A proof of a complementary relation for the intervening geometric angles
References to Chapter 9
Chapter 10. Classification and t-hyperbolic Property of the Equations for an
Axially-Symmetric State
10.1. Introductory remarks and formulation of the problem
10.2. Basic equations in 2/3-isostatic co-ordinate net
10.3. Basic equations formulation for an axially-symmetric state
10.4. Essential non-linearity. Classification and characteristics
10.5. t-hyperbolic property of the axially-symmetric equations
References to Chapter 10
Chapter 11. Maximally Simple Normal Forms of Three-Dimensional Equations
11.1. Formulation of the problem
11.2. Obtaining the maximally simple normal forms of three-dimensional
equations
11.3. Determination of characteristic surfaces by t-hyperbolic property
References to Chapter 11
Chapter 12. Self-Similar Solutions of the Axially-Symmetric Equations
12.1. Introductory remarks
12.2. Three-dimensional equations corresponding to an edge of the Tresca prism
12.3. Separation of variables in the three-dimensional equations
12.4. Self-similar solutions in the case of axial symmetry
12.5. Principal stresses distributions
References to Chapter 12
Chapter 13. Symmetry Groups of Partial Differential Equations of an Axially
Symmetric State
13.1. Problem formulation and requisite equations
Ю.Н. Радаев
