AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

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VonMises 1200 1100 1000 900 800 150 200 250 300 alongxaxis Figure 3-10 Variation of the Von Mises stress along the x-axis. VonMises 3000 2750 2500 2250 2000 1750 1500 150 200 250 300 alongyaxis Figure 3-11 Variation of the Von Mises stress along the y-axis. 36
CHAPTER 4 CONCLUSIONS AND SUGGESTIONS <strong>FOR</strong> FUTURE WORK This thesis demonstrated how to solve an elasticity problem using the Airy stress function. It showed how the method can be applied to find the stresses and displacements at any point on a two-dimensional plate subjected to different boundary conditions. This eventually led to how the Airy stress function can be applied to a two- phase plate with a circular inclusion in finding the stresses and displacements at any point. The problem studied in Chapter 3 further demonstrated how the Airy stress function is applied to an infinite plate with a circular inclusion. On studying the graphical representation of the result, it can be seen that all stresses within the inclusion are constant and the shear stress is zero when subjected to a far-field stress. The maximum tensile stress occurs at the boundary of the disc intersecting the y-axis and is decreased along the boundary of the disc as it nears the x-axis. The maximum compressive stress occurs at the boundary intersecting with the x-axis and decreases as it nears the y-axis along the interfacing boundary. thesis: The following extension is suggested to further exploit the content of the present a. The boundary conditions can be generalized to include all the stress components at far fields. 37
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: -50 -100 -150 0 τ 100 150 200 alon
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,

AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

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