AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

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ACKNOWLEDGEMENTS I would like to express my gratitude to all those who gave me the possibility to complete this thesis. I am deeply indebted to my supervising professor, Dr. Seiichi Nomura for his guidance, patience and motivation. I sincerely thank him for his help not only in completing my thesis but also for his invaluable suggestions and encouragement. I sincerely thank committee members Dr. Wen Chan and Dr. Dereje Agonafer for serving on my committee. They have been a continuous source of inspiration throughout my study at The University of Texas at Arlington. I would like to end by saying that this thesis came to a successful end due to the support and blessings from my family. Last but not the least I thank Sameer Chandragiri and all my other friends for their help and encouragement. ii November 18th, 2005
Supervising Professor: Dr. Seiichi Nomura ABSTRACT AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION PROBLEMS Publication No. ______ Dharshini Rao Kavati, MS The University of Texas at Arlington, 2005 This thesis addresses a problem of finding the elastic fields in a two- dimensional body containing an inhomogeneous inclusion using the Airy stress function. The Airy stress function is determined so that the prescribed boundary condition at a far field and the continuity condition of the traction force and the displacement field at the interface are satisfied exactly. All the derivations and solving simultaneous equations are carried out using symbolic software. iii
Page 1: AIRY STRESS FUNCTION FOR TWO DIMENS
Page 5 and 6: 3.2 Infinite Plate with a Hole Subj
Page 7 and 8: CHAPTER 1 INTRODUCTION 1.1 Overview
Page 9 and 10: our best knowledge. This thesis add
Page 11 and 12: • A finite plate with a hole subj
Page 13 and 14: epresentation It is observed that t
Page 15 and 16: 2 2 2 2 ⎛ ⎞ ⎛ ⎞ 4 ∂ 1 ∂
Page 17 and 18: where λ is called the Lame’s con
Page 19 and 20: σ + σ = σ + σ r θ x y 2iθ σ
Page 21 and 22: γ ( z) = − ψ ( z) = n ∑ k = 1
Page 23 and 24: CHAPTER 3 ADVANCED APPLICATIONS OF
Page 25 and 26: σ σ x y ( ± l, y) = S, ( x, ± c
Page 27 and 28: Sz b b χ ( z) = (log z) b . z z
Page 29 and 30: from which the stress components ca
Page 31 and 32: in σ = 2c + 2c r cosθ − d cos2
Page 33 and 34: 1 2a 4 4 4 2 ( a S + a S cos2θ + 2
Page 35 and 36: a b c 1 1 0 2 a d 2 a2 κ 1a2 − 2
Page 37 and 38: u out θ 4 2 2 4 S( a ( − µ + µ
Page 39 and 40: τ τ in xy out xy = 0, 6 10 6 2 6
Page 41 and 42: -50 -100 -150 0 τ 100 150 200 alon
Page 43 and 44: CHAPTER 4 CONCLUSIONS AND SUGGESTIO
Page 45 and 46: APPENDIX A MATHEMATICA CODE 39
Page 47 and 48: χ = Integrate[ϕ,z] χ1 = Integrat
Page 49 and 50: σθθ1 =FullSimplify@HD@φ1, 8r,2
Page 51 and 52: THE SIMULTANEOUS EQUATIONS THAT HAV
Page 53 and 54:
aS aSκ1 aa1 − − 8 µ1 8 µ1 2
Page 55 and 56:
PLATE τrθ1Final = ExpandAτrθ1In
Page 57 and 58:
VERIFICATION OF THE EQUILIBRIUM EQU
Page 59:
BIOGRAPHICAL INFORMATION Dharshini,
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