Mixed Method in Elasticity in the Analysis of Layered Beams

TABLE OF CONTENTS

ABSTRACT . . ACKNOWLEDGEMENT

LIST OF TABLES

LIST OF FIGURES

LIST OF SYMBOLS

CHAPTER ONE: INTRODUCTION . * . . . . 

1.1 Approach To Elasticity Problems-General .. 

1.2 Reduction Of A Two-Dimensional Problem To A One-Dimensional One . . . . 

1.3 Vlasov's Mixed Method , . . 

1.4 Aim And Scope . @ . . 

1.5 Review Of Literature .a . . 

CHAPTER TWO: FORMULATIONS OF THE GOVERNING EQUATIONS .. 0. . . 

2.1 Plane Stress Formulation . . a . 

2.2 Plane Strain Case . . . . . . 

2.3 Application To Horno~enaus Beams In

General . . . . . rn . 

2.4 Application To Layered Beams In General

2.4.1 Two-Layered Beam rn . . 

2.4.2 Three-Layered Beam . . . .

CHAPTER THREE: APPLICATIONS OF THE GOVERNING RELATIONS TO UNIFORULY-LOADED, SIMPLY SUPPORTED HOMOGENOUS AND LAYERED BEAMS .. . . e

3.1 Homogenous Beam . . . o . . .. 

3.1.1 The Solutions . . . . . . I . 

3.1.2 Numerical Results *a . . . 

3.1.3 Discussions . . . . . . . .

Two-Layered Beam . . 

The Solutluns . . 

Yunerical Results

Discuflsims *.

Three-tayared €laam . ,

The Solutions a

Numesical Results

Discussions . .

CHAPTER FOUR: CONCLUSIONS

REFERENCES . . ..

APPENDIX . b