THE TABLE OF CONTENTS

INTRODUCTION........................................................................................................... 5

CHAPTER 1. NON-UNIFORM DESIGNS WITH IZMENJAJUSHCHIMISJAPO TO THEIR THICKNESS prochnostnymi HARAKTRISTIKAMI.MATEMATICHESKIE CALCULATION MODELS (REVIEW SOSTOJANIJAVOPROSA)...........................

1.1. The analysis and prospects of application of non-uniform designs............... 19

1.2. Ways of creation of heterogeneity............................................................. 20

1.3. Influence of strengthening technologies on prochnostnye and deformation

Characteristics of structural materials.................................................... 23

1.4. The review of mathematical models of calculation of non-uniform designs....... 42

Conclusions on chapter 1...................................................................................... 52

CHAPTER 2. THE EQUATIONS DEFINING IS INTENSE-DEFORMED THIN-WALL prostranstvennyhkonstruktsy WITH CHANGING ON TOLSHCHINEPROCHNOSTNYMI BY CHARACTERISTICS........................ 54

2.1. Inkrementalnye the equations of a bending down non-uniform physically nonlinear

Flat envelopment of a variable thickness............................................................ 54

2.2. Inkrementalnoe the equation of a bending down non-uniform physically nonlinear

Plates of a variable thickness.......................................................................... 67

2.3. Inkrementalnoe the equation of a bending down non-uniform physically nonlinear

Girders of a variable thickness................................................................................. 74

2.4. Boundary conditions....................................................................................... 81

2.4.1. Boundary conditions for flat envelopments.............................................. 81

2.4.2. Boundary conditions for plates............................................................ 82

2.4.3. Boundary conditions for girders................................................................... 83

2.5. Construction of function of heterogeneity......................................................... 84

2.6. A decision method linearizovannyh the equations.............................................. 88

Conclusions on the second chapter...................................................................................... 94

CHAPTER 3. NUMERICAL REALIZATION OF MATHEMATICAL MODEL IANALIZ OF RESULTS OF CALCULATION NON-UNIFORM FIZICHESKINELINEJNYH THE THIN-WALL SPATIAL

DESIGNS................................................................................................ 96

3.1. The decision of a problem of a bending down of physically nonlinear girder at two-sided and

Single-sided heterogeneity on a thickness...................................................... 96

3.2. The decision of a problem of a bending down of physically nonlinear plate at two-sided and

Single-sided heterogeneity on a thickness.................................................... 107

3.3. The decision of a problem of a bending down of physically nonlinear flat envelopment at

Two-sided heterogeneity on a thickness...................................................... 116

Conclusions on the third chapter.................................................................................... 126

CHAPTER 4. NUMERICAL REALIZATION OF MATHEMATICAL MODEL IANALIZ OF RESULTS OF CALCULATION PHYSICALLY nelinejnyhtonkostennyh SPATIAL DESIGNS

VARIABLE THICKNESS......................................................................... 128

4.1. The decision of a problem of a bending down of physically nonlinear girder of a variable thickness 128

4.2. The decision of a problem of a bending down of physically nonlinear plate of a variable

Thickness.............................................................................................................. 134

4.3. The decision of a problem of a bending down of physically nonlinear flat envelopment of a variable

Thickness.............................................................................................................. 141

Conclusions on the fourth chapter................................................................................ 147

THE CONCLUSION................................................................................................ 149

THE LITERATURE LIST............................................................................... 151

APPENDIX AOsnovnye of a parity in the form of a method of final differences

For flat envelopments, plates and girders........................................................ 163

APPENDIX BSpravki and adoption deeds of materials of the dissertational

Researches....................................................................................................... 182

APPENDIX VSvidetelstva about the state registration of programs for

THE COMPUTER.................................................................................................................... 185