Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Two-dimensional inhomogeneities of minimum stress concentration


Authors: Ren-Jieh Shih and Lewis T. Wheeler
Journal: Quart. Appl. Math. 44 (1986), 567-581
MSC: Primary 73C40; Secondary 73K40
DOI: https://doi.org/10.1090/qam/860906
MathSciNet review: 860906
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  • [1] L. Wheeler, The problem of minimizing stress concentration at a rigid inclusion, Trans. ASME J. Appl. Mech. 52 (1985), no. 1, 83–86. MR 786802, https://doi.org/10.1115/1.3169031
  • [2] Bahir H. Eldiwany and Lewis T. Wheeler, On rigid inclusions of minimum stress concentration, J. Mech. Phys. Solids 34 (1986), no. 1, 19–28. MR 825936, https://doi.org/10.1016/0022-5096(86)90003-7
  • [3] L. T. Wheeler, On the pole of constant stress surfaces in the problem of minimizing elastic stress concentration, Internat. J. Solids and Structures 12, 779-789 (1976)
  • [4] L. T. Wheeler, On optimum profiles for the minimization of elastic stress concentration, ZAMM, T235-T236 (1978)
  • [5] Lewis T. Wheeler and Isaak A. Kunin, On voids of minimum stress concentration, Internat. J. Solids and Structures 18 (1982), no. 1, 85–89. MR 636875
  • [6] N. V. Banichuk, Optimality conditions in the problem of seeking the hole shapes in elastic bodies; Russian transl., J. Appl. Math. Mech. 41 (1977), no. 5, 920–925. MR 519746
  • [7] B. H. Eldiwany and L. T. Wheeler, Groove-bottom contours of minimum stress concentration for antiplane deformation, J. Appl. Mech. 52, No. 2, 379-384 (1985)
  • [8] Lewis T. Wheeler, Tayfun E. Tezduyar, and Bahir H. Eldiwany, Profiles of minimum stress concentration for antiplane deformation of an elastic solid, J. Elasticity 15 (1985), no. 3, 271–282. MR 804499, https://doi.org/10.1007/BF00041425
  • [9] A. J. Durrelli, and W. M. Murray, Stress distribution around an elliptic discontinuity in any two-dimensional, uniform, and axial system of combined stress, Exp. Stress Anal. Proc. 1, No. 1, 19-31 (1943)
  • [10] H. Neuber, Der zugbeanspruchte Flachstab mit Optimalem Querschnittubeigang, Forsch. Ingenieurwesen 35, No. 1, 29-30 (1969)
  • [11] H. Neuber, Zur Optimierung der Spannungskonzentration, in Continuum Mechanics and Related Problems of Analysis, Nauka, Moscow, 375-380 (1972)
  • [12] G. P. Cherepanov, Inverse problem of the plane theory of elasticity, PMM, 38, No. 6, 963-979 (1974)
  • [13] G. S. Bjorkman, Jr. and R. Richards, Jr., Harmonic holes--an inverse problem in elasticity, J. Appl. Mech. 43, No. 3, 414-418 (1976)
  • [14] G. S. Bjorkman, Jr. and R. Richards, Jr., Optimum shapes for unlined tunnels and cavities, Engineering Geol. 12, 171-179 (1978)
  • [15] G. S. Bjorkman, Jr. and R. Richards, Jr., Harmonic holes for nonconstant fields, J. Appl. Mech. 46, No. 3, 573-576 (1979)
  • [16] G. S. Bjorkman, Jr. and R. Richards, Jr., Harmonic Shapes and Optimum Design, Journal of the Engineering Mechanics Division, ASCE, Vol. 106, pp. 1125-1134, 1980
  • [17] G. S. Bjorkman, Jr. and R. Richards, Jr., Neutral Holes; Theory and Design, Journal of the Engineering Mechanics Division, ASCE, Vol. 108, pp. 945-960, 1982
  • [18] Bahir H. Eldiwany and Lewis T. Wheeler, A three-dimensional inverse problem for inhomogeneities in elastic solids, J. Elasticity 16 (1986), no. 2, 201–211. MR 849672, https://doi.org/10.1007/BF00043586
  • [19] Arthur P. Boresi, and Omar M. Sidebottom, Advanced mechanics of Materials, Fourth Ed., John Wiley and Sons, New York, 1985
  • [20] Oliver Dimon Kellogg, Foundations of potential theory, Reprint from the first edition of 1929. Die Grundlehren der Mathematischen Wissenschaften, Band 31, Springer-Verlag, Berlin-New York, 1967. MR 0222317
  • [21] William Duncan MacMillan, The theory of the potential, MacMillan’s Theoretical Mechanics, Dover Publications, Inc., New York, 1958. MR 0100172

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DOI: https://doi.org/10.1090/qam/860906
Article copyright: © Copyright 1986 American Mathematical Society


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