AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

More documents

Recommendations

Info

The displacements at infinity would indicate unbounded behavior as even a bounded strain over an infinite length will produce infinite displacements. Therefore the case of the above region is obtained by dropping the summation terms in (2.3.4). 16
CHAPTER 3 ADVANCED APPLICATIONS OF THE AIRY STRESS FUNCTION 3.1 Finite Plate with a Hole Subjected to Tensile Loading Applying the same approach as the finite multiply connected domains in Chapter 2 for the plate shown below, the respective potential functions would be the same as discussed in (2.3.2). Figure 3-1 Finite Plate with a Hole Subjected to Tensile Loading. Assume a finite plate of length 2l and width 2c with a central hole of radius a subjected to uniform tension S along the x-axis. This is the case of a finite multiply connected region, whose complex potential functions can be expressed as (2.3.2). Sinceψ ( z) = χ ′ ( z) , integrating the second complex function in (2.3.2) yields n ⎛ κFk ⎞ * χ ( z) = ∫ ⎜ ∑ log( z − zk ) + ψ ( z) ⎟dz, ⎝ 2π ( 1 + κ ) ⎠ k = 1 17 (3.1.1) where k = 1 since there is only one internal boundary and zk is 0 since the center of the circle is taken as the origin (0,0) and γ * (z) and ψ * (z) are arbitrary analytic functions. 2 l Y a X 2c S
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: γ ( z) = − ψ ( z) = n ∑ k = 1
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,

AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?