214
Views
10
CrossRef citations to date
0
Altmetric
Articles

Shape optimization of two equal holes in an infinite elastic plate

, &
Pages 133-145 | Received 23 Oct 2018, Accepted 14 May 2019, Published online: 23 May 2019

References

  • Argod, V., S. K. Nayak, A. K. Singh, and A. D. Belegundu. 2010. Shape optimization of solid isotropic plates to mitigate the effects of air blast loading. Mechanics Based Design of Structures & Machines 38(3):362–71. doi: 10.1080/15397731003745428.
  • Banichuk, N. V. 1977. Optimality conditions in the problem of seeking the hole shapes in elastic bodies. Journal of Applied Mathematics & Mechanics 41(5):920–5. doi: 10.1016/0021-8928(77)90179-4.
  • Banichuk, N. V. 1983. Problems and methods of optimal structural design. Vol. 26 of mathematical concepts & methods in science & engineering. New York: Plenum Press.
  • Bjorkman, G. S., and R. Richards. 1976. Harmonic holes-an inverse problem in elasticity. Journal of Applied Mechanics 43(3):414–8. doi: 10.1115/1.3423882.
  • Bjorkman, G. S., and R. Richards. 1979. Harmonic holes for nonconstant fields. Journal of Applied Mechanics 46(3):573–6. doi: 10.1115/1.3424608.
  • Cherepanov, G. P. 1974. Inverse problems of the plane theory of elasticity. Journal of Applied Mathematics & Mechanics 38(6):915–31. doi: 10.1016/0021-8928(75)90085-4.
  • Dai, M., P. Schiavone, and C.-F. Gao. 2016. Harmonic holes with surface tension in an elastic plane under uniform remote loading. Mathematics & Mechanics of Solids 22(9):1806–12. doi: 10.1177/1081286516647205.
  • Dhir, S. K. 1981. Optimization in a class of hole shapes in plate structures. Journal of Applied Mechanics 48(4):905–8. doi: 10.1115/1.3157754.
  • Ding, Y.-L. 1986. Shape optimization of structures: a literature survey. Computers & Structures 24:985–1004. doi: 10.1016/0045-7949(86)90307-X.
  • Korn, G. A., and T. M. Korn. 1986. Mathematical handbook for scientists and engineers. New York: McGraw-Hill.
  • Le, C., T. Bruns, and D. Tortorelli. 2011. A gradient-based, parameter-free approach to shape optimization. Computer Methods in Applied Mechanics & Engineering 200(9-12):985–96. doi: 10.1016/j.cma.2010.10.004.
  • Muskhelishvili, N. I. 1953. Some basic problems of mathematical theory of elasticity. Groningen: Noordhoff.
  • Naik, N. K., R. R. Kumar, and K. Rajaiah. 1986. Optimum hole shapes in beams under pure bending. Journal of Engineering Mechanics 112(4):407–11. doi: 10.1061/(ASCE)0733-9399(1986)112:4(407).
  • Pedersen, P. 2000. On optimal shapes in materials and structures. Structural and Multidisciplinary Optimization 19(3):169–82. doi: 10.1007/s001580050100.
  • Richards, R., and G. S. Bjorkman. 1978. Optimum shapes for unlined tunnels and cavities. Engineering Geology 12:171–9. doi: 10.1016/0013-7952(78)90010-8.
  • Storn, R., and K. Price. 1997. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4):341–59. doi: 10.1023/A:1008202821328.
  • Vaidya, A., S. H. Yu, J. St. Ville, D. T. Nguyen, and S. D. Rajan. 2006. Multiphysics CAD-based design optimization. Mechanics Based Design of Structures & Machines 34(2):157–80. doi: 10.1080/15397730600745807.
  • Vigdergauz, S. 2006. The stress-minimizing hole in an elastic plate under remote shear. Journal of Mechanics of Materials and Structures 1(2):387–406. doi: 10.2140/jomms.2006.1.387.
  • Vigdergauz, S. 2007. Shape optimization of a rigid inclusion in a shear-loaded elastic plane. Journal of Mechanics of Materials and Structures 2(2):275–91. doi: 10.2140/jomms.2007.2.275.
  • Vigdergauz, S. 2008. Shape optimization in an elastic plate under remote shear: from single to interacting holes. Journal of Mechanics of Materials and Structures 3(7):1341–63. doi: 10.2140/jomms.2008.3.1341.
  • Vigdergauz, S. 2010. Energy-minimizing openings around a fixed hole in an elastic plate. Journal of Mechanics of Materials and Structures 5(4):661–77. doi: 10.2140/jomms.2010.5.661.
  • Vigdergauz, S. 2011. Stress smoothing holes in planar elastic domains. Journal of Mechanics of Materials and Structures 5(6):987–1006. doi: 10.2140/jomms.2010.5.987.
  • Vigdergauz, S. 2015. Equi-stress boundaries in two- and three-dimensional elastostatics: The single-layer potential approach. Mathematics & Mechanics of Solids 22(4):837–51. doi: 10.1177/1081286515615001.
  • Vigdergauz, S. 2017. Simply and doubly periodic arrangements of the equi-stress holes in a perforated elastic plane: The single-layer potential approach. Mathematics & Mechanics of Solids 23(5):805–19. doi: 10.1177/1081286517691807.
  • Vigdergauz, S. B., and A. V. Cherkayev. 1986. A hole in a plate, optimal for its biaxial extension-compression. Journal of Applied Mathematics & Mechanics 50(3):401–4. doi: 10.1016/0021-8928(86)90141-3.
  • Wang, G.-F., P. Schiavone, and C.-Q. Ru. 2005. Harmonic shapes in finite elasticity under nonuniform loading. Journal of Applied Mechanics 72(5):691–4. doi: 10.1115/1.1979514.
  • Wang, G.-F., P. Schiavone, and C.-Q. Ru. 2007. Harmonic shapes in finite elasticity. Mathematics & Mechanics of Solids 12(5):502–12. doi: 10.1177/1081286506066344.
  • Wang, S.-J., A.-Z. Lu, X.-L. Zhang, and N. Zhang. 2018. Shape optimization of the hole in an orthotropic plate. Mechanics Based Design of Structures & Machines 46(1):23–37. doi: 10.1080/15397734.2016.1261036.
  • Week, M., and P. Stelnke. 1983. An efficient technique in shape optimization. Journal of Structural Mechanics 11(4):433–49. doi: 10.1080/03601218308907451.
  • Wessel, C., A. Cisilino, and B. Sensale. 2004. Structural shape optimisation using boundary elements and the biological growth method. Structural & Multidisciplinary Optimization 28 (2-3):221–7. doi: 10.1007/s00158-004-0403-2.
  • Wu, Z.-X. 2005. An efficient approach for shape optimization of components. International Journal of Mechanical Sciences 47(10):1595–610. doi: 10.1016/j.ijmecsci.2005.06.012.
  • Yang, R.-J. 1990. Component shape optimization using BEM. Computers & Structures 37(4):561–8. doi: 10.1016/0045-7949(90)90045-4.
  • Zeng, X.-T., A.-Z. Lu, and N. Zhang. 2018. Analytical stress solution for an infinite plate containing two oval holes. European Journal of Mechanics - A/Solids 67:291–304. doi: 10.1016/j.euromechsol.2017.09.011.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.