AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

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inclusion Mathematica code for finding the stresses and displacements for a circular γ = ‚ ϕ = ‚ 2 an∗z n=0 n 2 bn∗z n=0 n a 0 +za 1+z 2 a 2 b 0 +zb 1+z 2 b 2 γ1 = HS ∗zê4L + ‚ Sz 4 + m1 z + m2 z 2 ϕ1 = HG ∗ zê2L + ‚ Gz 2 + f1 z d = D@γ,zD d1 = D@γ1,zD a 1 +2za 2 S 4 m1 2m2 − − z2 z3 f2 f3 + + z2 z3 2 mn∗z n=1 −n 3 fn∗z n=1 −n 40
χ = Integrate[ϕ,z] χ1 = Integrate[ϕ1,z] zb0 + z2b1 2 + z3b2 3 Gz 2 4 +Log@zDf1− f2 z − f3 2z 2 z =ComplexExpand@r∗ Exp@I∗ θDD rCos@θD + rSin@θD e = ComplexExpand[Conjugate[z]] rCos@θD − rSin@θD h =FullSimplify@ComplexExpand@He∗γL+ χDD êêTrigReduce h1 = FullSimplify@ComplexExpand@χ1 + Hγ1 ∗eLDD êêTrigReduce 1 6 − θ r H6a0 +6 θ ra1 +6 2 θ r 2 a2 +6 2 θ b0 +3 3 θ rb1 +2 4 θ r 2 b2L 1 4Abs@rD 4 H 4Im@θD r 2 H− 4Hθ−Re@θDL Conjugate@rD 2 HH−1+ 2θ Lr 2 S+4HIm@θD−Log@ Re@θD rDLf 1L− 2 −2θ f 3+4 −2Re@θD Conjugate@rDH− θ f 2+rm 1L+4 −3θ rm 2LL φ = FullSimplify[ComplexExpand[Re[h]]] φ1= FullSimplify[ComplexExpand[Re[h1]]] 1 6 rH6ra1+6Cos@θDHa0+r 2 a2+b0L+3rCos@2θDb1+2r 2 Cos@3θDb2L r 4 SSin@θD 2 −Cos@2θDf3+rHrLog@r 2 Df1−2Cos@θDf2+2rCos@2θDm1+2Cos@3θDm2L 2r 2 41
Page 1 and 2: 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: APPENDIX A MATHEMATICA CODE 39
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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