AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

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PLATE rHSH−1+κLH1+κ1Lµ+4rH2µ+H−1+κLµ1LHH−2+κLCos@θDa2−Cos@3θDb2LL 8µH2µ+H−1+κLµ1L ur1Final = FullSimplifyA ur1Ini ê.f1 →− a2 S 2 + a2 HS+Sκ1Lµ 2H2µ−µ1 +κµ1L ê.f3 → − a4 Sµ−a 4 Sµ1 2Hκ1 µ+µ1L ê. 1 8r3 i µ1k Si k m1 →− a2 HSµ−Sµ1L 2Hκ1 µ+µ1L ê.f2 →0 ê.m2 →0E r 2 Hr 2 H−1+κ1LH2µ+H−1+κLµ1L−2a 2 HH−1+κ1Lµ+µ1−κµ1LL 2µ+H−1+κLµ1 2Ha 4 Hµ−µ1L+a 2 r 2 H1+κ1LH−µ+µ1L+r 4 Hκ1µ+µ1LLCos@2θD κ1µ+µ1 ANGULAR DISPLACEMENTS <strong>FOR</strong> THE INNER DISC AND THE OUTER uθFinal =FullSimplifyAuθIniê.b0→κa0ê.b1→− Sµ+Sκ1µ 2Hκ1µ+µ1L ê.a2→0ê.b2→0E − rSH1+ κ1LSin@2θD 4Hκ1µ+ µ1L uθ1Final = FullSimplifyAuθ1Iniê.f3→− a4 Sµ−a 4 Sµ1 2Hκ1µ+µ1L ê.m1→− a2 HSµ−Sµ1L 2Hκ1µ+µ1L ê.f2→0ê.m2→0E − S Ha4 H−µ + µ1L+a 2 r 2 H−1 +κ1L H−µ +µ1L +r 4 Hκ1 µ +µ1LLSin@2θD 4r 3 µ1Hκ1µ+ µ1L 50 y { +
VERIFICATION OF THE EQUILIBRIUM EQUATIONS Simplify@D@σrrFinal,rD +D@τrθFinal,θD∗1êr + HσrrFinal−σθθFinalLêrD 0 Simplify@D@σrr1Final,rD +D@τrθ1Final,θD∗1êr +Hσrr1Final − σθθ1FinalLêrD 0 Simplify@D@τrθFinal, rD + D@σθθFinal, θD∗1êr + H2∗τrθFinalêrLD 0 Simplify@D@τrθ1Final, rD + D@σθθ1Final, θD∗1êr +2 ∗τrθ1FinalêrD 0 51
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AIRY STRESS FUNCTION FOR TWO DIMENS
Page 3 and 4:
Supervising Professor: Dr. Seiichi
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: PLATE τrθ1Final = ExpandAτrθ1In
Page 59: BIOGRAPHICAL INFORMATION Dharshini,
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AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

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