AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

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REFERENCES [1] Sadd, Martin H. (2005). Elasticity: Theory, Applications and Numerics (pp. 123-259). Burlington, MA.: Elsevier Academic Press. [2] Wolfram, Stephen (1988). Mathematica: A System for Doing Mathematics by Computer. Redwood City, CA.: Addison-Wesley. [3] Martin, Emily (1996). Mathematica 3.0: Standard Add-On Packages. Champaign, IL.: Woolfram Media [4] Hearn, E. J. (1985). Mechanics of Materials (2 nd Ed.). Elmsford, N.Y.: Pergamon Press. [5] L.M. Milne-Thomson (1960). Theoretical Hydrodynamics (4 th Ed.). N.Y.: The Macmillan Company (pp. 128-134). [6] Sokolnikoff, I.S. (1956). Mathematical Theory of Elasticity (2 nd Ed.). N.Y.: McGraw-Hill. [7] Ian McLeod & Hao Yu. Timing Comparisons of Mathematica, MATLAB, R, S- Plus, C & Fortran, published in March 2002 located at http://www.stats.uwo.ca/faculty/aim/epubs/MatrixInverseTiming/default.htm [8] Wolfram Research. Mathematica: The Smart Approach to Engineering Education, published in 2001 located at http://www.wolfram.com/solutions/engineering/enged.pdf 52
BIOGRAPHICAL IN<strong>FOR</strong>MATION Dharshini, finished her Bachelor’s in Mechanical Engineering from Vijaynagar Engineering college, Bellary, Karnataka, India. She worked on a project in Hindustan Aeronautics Limited for three months and realized her interest in design and analyses. In January 2004 she left her homeland to pursue her dream. She graduated as a Master of Science in Mechanical Engineering in December 2005 from the University of Texas at Arlington, with a great deal of confidence and knowledge and the satisfaction of being a step closer to her goal. 53
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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 and 56: PLATE τrθ1Final = ExpandAτrθ1In
Page 57: VERIFICATION OF THE EQUILIBRIUM EQU
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