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Contact problem for regular hexagon weakened with full-strength hole

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Abstract

A problem of the plane elasticity theory is addressed for a doubly connected body with an external boundary of the regular hexagon shape and with a 6-fold symmetric hole at the center. It is assumed that all the six sides of the hexagon are subjected to uniform normal displacements via smooth rigid stamps, while the uniformly distributed normal stress is applied to the internal hole boundary. Using the methods of complex analysis, the analytical image of Kolosov-Muskhelishvili’s complex potentials and the shape of the hole contour are determined from the condition that the circumferential normal stress is constant along the hole contour. Numerical results are given and shown in relevant graphs.

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References

  1. Banichuk, N. V. Optimality conditions in the problem of seeking the hole shapes in elastic bodies. J. Appl. Math. Mech., 41(5), 920–925 (1977)

    Article  MathSciNet  Google Scholar 

  2. Banichuk, N. V. Optimization of Forms of Elastic Bodies, Nauka, Moscow (1980)

    MATH  Google Scholar 

  3. Cherepanov, G. P. Inverse problems of the plane theory of elasticity. Prikl. Mat. Meh., 38(6), 963–979 (1974)

    MathSciNet  Google Scholar 

  4. Neuber, H. The optimization of stresses concentracion. Continuum Mechanics and Related Problems of Analysis, Nauka, Moscow, 375–380 (1972)

    Google Scholar 

  5. Vigdergauz, S. B. On a case of the inverse problem of the two-dimensional theory of elasticity. J. Appl. Math. Mech., 41(5), 902–908 (1977)

    Article  MathSciNet  Google Scholar 

  6. Bantsuri, R. D. Some inverse problems of plane elasticity and of bending of thin plates. Continuum Mechanics and Related Problems of Analysis (Tbilisi, 1991), Metsniereba, Tbilisi, 100–107 (1993)

  7. Bantsuri, R. D. and Isakhanov, R. S. Some inverse problems in elasticity theory. Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR, 87, 3–20 (1987)

    MathSciNet  MATH  Google Scholar 

  8. Bantsuri, R. On one mixed problem of the plane theory of elasticity with a partially unknown boundary. Proc. A. Razmadze Math. Inst., 140, 9–16 (2006)

    MathSciNet  MATH  Google Scholar 

  9. Bantsuri, R. Solution of the mixed problem of plate bending for a multi-connected domain with partially unknown boundary in the presence of cyclic symmetry. Proc. A. Razmadze Math. Inst., 145, 9–22 (2007)

    MathSciNet  MATH  Google Scholar 

  10. Bantsuri, R. and Mzhavanadze, S. The mixed problem of the theory of elasticity for a rectangle weakened by unknown equiv-strong holes. Proc. A. Razmadze Math. Inst., 145, 23–33 (2007)

    MathSciNet  MATH  Google Scholar 

  11. Odishelidze, N. T. and Criado-Aldeanueva, F. On a mixed problem in the plane theory of elasticity for a domain with a partially unknown boundary. Prikl. Mekh. Tekh. Fiz., 42(3), 110–118 (2006)

    MathSciNet  MATH  Google Scholar 

  12. Odishelidze, N. and Criado-Aldeanueva, F. Some axially symmetric problems of the theory of plane elasticity with partially unknown boundaries. Acta Mech., 199(1–4), 227–240 (2008)

    Article  MATH  Google Scholar 

  13. Odishelidze, N. T. Solution of the mixed problem of the plane theory of elasticity for a multiply connected domain with partially unknown boundary in the presence of axial symmetry. Proc. A. Razmadze Math. Inst., 146, 97–112 (2008)

    MathSciNet  MATH  Google Scholar 

  14. Odishelidze, N. and Criado-Aldeanueva, F. A mixed problem of plate bending for a doubly connected domains with partially unknown boundary in the presence of cycle symmetry. Sci. China Phys. Mech. Astron., 53(10), 1884–1894 (2010)

    Article  Google Scholar 

  15. Muskhelishvili, N. I. Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff International Publishing, Leiden (1977)

    Google Scholar 

  16. Keldysh, M. V. and Sedov, L. D. The effective solution of some boundary problems for harmonic functions. Dokl. Akad. Nauk SSSR, 16(1), 7–10 (1937)

    MATH  Google Scholar 

  17. Muskhelishvili, N. I. Singular Integral Equations, Dover Publications, New York (1992)

    Google Scholar 

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Odishelidze, N., Criado-Aldeanueva, F. & Sanchez, J.M. Contact problem for regular hexagon weakened with full-strength hole. Appl. Math. Mech.-Engl. Ed. 34, 239–248 (2013). https://doi.org/10.1007/s10483-013-1666-9

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  • DOI: https://doi.org/10.1007/s10483-013-1666-9

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