Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 867079, 33 pages
http://dx.doi.org/10.1155/2013/867079
Research Article

Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

1DICAM-Department, School of Engineering, University of Bologna, viale del Risorgimento 2, 40136 Bologna, Italy
2DIN-Department, School of Engineering, University of Bologna, viale del Risorgimento 2, 40136 Bologna, Italy

Received 14 February 2013; Accepted 2 April 2013

Academic Editor: Abdelouahed Tounsi

Copyright © 2013 Francesco Tornabene and Alessandro Ceruti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York, NY, USA, 1959.
  2. W. Flügge, Stresses in Shells, Springer, Berlin, Germany, 1960. View at Zentralblatt MATH · View at MathSciNet
  3. A. L. Gol’denveizer, Theory of Elastic Thin Shells, Pergamon Press, Oxford, UK, 1961. View at MathSciNet
  4. V. V. Novozhilov, Thin Shell Theory, P. Noordhoff, Groningen, The Netherlands, 1964. View at Zentralblatt MATH · View at MathSciNet
  5. V. Z. Vlasov, “General Theory of Shells and Its Application in Engineering, NASA-TT-F-99,” 1964.
  6. S. A. Ambartusumyan, “Theory of Anisotropic Shells, NASA-TT-F-118,” 1964.
  7. H. Kraus, Thin Elastic Shells, John Wiley & Sons, New York, NY, USA, 1967.
  8. A. W. Leissa, “Vibration of Plates, NASA-SP-160,” 1969.
  9. A. W. Leissa, “Vibration of Shells, NASA-SP-288,” 1973.
  10. S. Markuš, The Mechanics of Vibrations of Cylindrical Shells, Elsevier, New York, NY, USA, 1988.
  11. E. Ventsel and T. Krauthammer, Thin Plates and Shells, Marcel Dekker, New York, NY, USA, 2001.
  12. W. Soedel, Vibrations of Shells and Plates, Marcel Dekker, New York, NY, USA, 2004.
  13. E. Reissner, “The effect of transverse shear deformation on the bending of elastic plates,” Journal of Applied Mechanics, vol. 12, pp. 66–77, 1945. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. D. Mindlin, “Influence of rotatory inertia and shear on flexural vibration of isotropic, elastic plates,” Journal of Applied Mechanics, vol. 18, pp. 31–38, 1951. View at Google Scholar
  15. P. L. Gould, Finite Element Analysis of Shells of Revolution, Pitman Publishing, London, UK, 1984.
  16. P. L. Gould, Analysis of Plates and Shells, Prentice-Hall, New York, NY, USA, 1999.
  17. A. W. Leissa and J.-D. Chang, “Elastic deformation of thick, laminated composite shells,” Composite Structures, vol. 35, no. 2, pp. 153–170, 1996. View at Publisher · View at Google Scholar · View at Scopus
  18. M. S. Qatu, “Accurate equations for laminated composite deep thick shells,” International Journal of Solids and Structures, vol. 36, no. 19, pp. 2917–2941, 1999. View at Google Scholar · View at Scopus
  19. M. S. Qatu, Vibration of Laminated Shells and Plates, Elsevier, New York, NY, USA, 2004.
  20. M. H. Toorani and A. A. Lakis, “General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects,” Journal of Sound and Vibration, vol. 237, no. 4, pp. 561–615, 2000. View at Publisher · View at Google Scholar · View at Scopus
  21. M. H. Toorani and A. A. Lakis, “Free vibrations of non-uniform composite cylindrical shells,” Nuclear Engineering and Design, vol. 236, no. 17, pp. 1748–1758, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. J. N. Reddy, Mechanics of Laminated Composites Plates and Shells, CRC Press, New York, NY, USA, 2003.
  23. F. Tornabene, Meccanica delle Strutture a Guscio in Materiale Composito. Il Metodo Generalizzato di Quadratura Differenziale, Esculapio, Bologna, Italy, 2012.
  24. E. Carrera, S. Brischetto, and P. Nali, Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis, John Wiley & Sons, New York, NY, USA, 2011.
  25. E. Carrera, “Historical review of Zig-Zag theories for multilayered plates and shells,” Applied Mechanics Reviews, vol. 56, no. 3, pp. 287–308, 2003. View at Publisher · View at Google Scholar · View at Scopus
  26. C. Shu, Differential Quadrature and Its Application in Engineering, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  27. C. W. Bert and M. Malik, “Differential quadrature method in computational mechanics: a review,” Applied Mechanics Reviews, vol. 49, no. 1, pp. 1–27, 1996. View at Google Scholar · View at Scopus
  28. K. M. Liew, J. B. Han, and Z. M. Xiao, “Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility,” International Journal of Solids and Structures, vol. 33, no. 18, pp. 2647–2658, 1996. View at Publisher · View at Google Scholar · View at Scopus
  29. C. Shu and H. Du, “Free vibration analysis of laminated composite cylindrical shells by DQM,” Composites B, vol. 28, no. 3, pp. 267–273, 1997. View at Google Scholar · View at Scopus
  30. K. M. Liew and T. M. Teo, “Modeling via differential quadrature method: three-dimensional solutions for rectangular plates,” Computer Methods in Applied Mechanics and Engineering, vol. 159, no. 3-4, pp. 369–381, 1998. View at Google Scholar · View at Scopus
  31. F.-L. Liu and K. M. Liew, “Differential quadrature element method: a new approach for free vibration analysis of polar Mindlin plates having discontinuities,” Computer Methods in Applied Mechanics and Engineering, vol. 179, no. 3-4, pp. 407–423, 1999. View at Google Scholar · View at Scopus
  32. S. Moradi and F. Taheri, “Delamination buckling analysis of general laminated composite beams by differential quadrature method,” Composites B, vol. 30, no. 5, pp. 503–511, 1999. View at Publisher · View at Google Scholar · View at Scopus
  33. T. Y. Ng, L. Hua, K. Y. Lam, and C. T. Loy, “Parametric instability of conical shells by the generalized differential quadrature method,” International Journal for Numerical Methods in Engineering, vol. 44, no. 6, pp. 819–837, 1999. View at Google Scholar · View at Scopus
  34. T. C. Fung, “Solving initial value problems by differential quadrature method-part 1: first-order equations,” International Journal for Numerical Methods in Engineering, vol. 50, no. 6, pp. 1411–1427, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. T. C. Fung, “Solving initial value problems by differential quadrature method. II. Second- and higher-order equations,” International Journal for Numerical Methods in Engineering, vol. 50, no. 6, pp. 1429–1454, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  36. K. M. Liew, T. Y. Ng, and J. Z. Zhang, “Differential quadrature-layerwise modeling technique for three-dimensional analysis of cross-ply laminated plates of various edge-supports,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 35, pp. 3811–3832, 2002. View at Publisher · View at Google Scholar · View at Scopus
  37. T. Y. Wu, Y. Y. Wang, and G. R. Liu, “Free vibration analysis of circular plates using generalized differential quadrature rule,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 46, pp. 5365–5380, 2002. View at Publisher · View at Google Scholar · View at Scopus
  38. G. Karami and P. Malekzadeh, “Static and stability analyses of arbitrary straight-sided quadrilateral thin plates by DQM,” International Journal of Solids and Structures, vol. 39, no. 19, pp. 4927–4947, 2002. View at Publisher · View at Google Scholar · View at Scopus
  39. J. Yang and H.-S. Shen, “Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions,” Composites B, vol. 34, no. 2, pp. 103–115, 2003. View at Publisher · View at Google Scholar · View at Scopus
  40. K. M. Liew, J. Z. Zhang, C. Li, and S. A. Meguid, “Three-dimensional analysis of the coupled thermo-piezoelectro-mechanical behaviour of multilayered plates using the differential quadrature technique,” International Journal of Solids and Structures, vol. 42, no. 14, pp. 4239–4257, 2005. View at Publisher · View at Google Scholar · View at Scopus
  41. E. Viola and F. Tornabene, “Vibration analysis of damaged circular arches with varying cross-section,” SID Structural Integrity and Durability, vol. 1, no. 2, pp. 155–169, 2005. View at Google Scholar · View at Scopus
  42. E. Viola and F. Tornabene, “Vibration analysis of conical shell structures using GDQ method,” Far East Journal of Applied Mathematics, vol. 25, pp. 23–39, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  43. F. Tornabene, Modellazione e soluzione di strutture a Guscio in materiale anisotropo [Ph.D. thesis], University of Bologna-DISTART Department, Bologna, Italy, 2007.
  44. F. Tornabene and E. Viola, “Vibration analysis of spherical structural elements using the GDQ method,” Computers and Mathematics with Applications, vol. 53, no. 10, pp. 1538–1560, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  45. E. Viola, M. Dilena, and F. Tornabene, “Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches,” Journal of Sound and Vibration, vol. 299, no. 1-2, pp. 143–163, 2007. View at Publisher · View at Google Scholar · View at Scopus
  46. A. Marzani, F. Tornabene, and E. Viola, “Nonconservative stability problems via generalized differential quadrature method,” Journal of Sound and Vibration, vol. 315, no. 1-2, pp. 176–196, 2008. View at Publisher · View at Google Scholar · View at Scopus
  47. F. Tornabene and E. Viola, “2-D solution for free vibrations of parabolic shells using generalized differential quadrature method,” European Journal of Mechanics, A/Solids, vol. 27, no. 6, pp. 1001–1025, 2008. View at Publisher · View at Google Scholar · View at Scopus
  48. A. Alibeigloo and R. Madoliat, “Static analysis of cross-ply laminated plates with integrated surface piezoelectric layers using differential quadrature,” Composite Structures, vol. 88, no. 3, pp. 342–353, 2009. View at Publisher · View at Google Scholar · View at Scopus
  49. F. Tornabene, “Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution,” Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 37–40, pp. 2911–2935, 2009. View at Publisher · View at Google Scholar · View at Scopus
  50. F. Tornabene and E. Viola, “Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution,” European Journal of Mechanics, vol. 28, no. 5, pp. 991–1013, 2009. View at Publisher · View at Google Scholar · View at Scopus
  51. F. Tornabene and E. Viola, “Free vibration analysis of functionally graded panels and shells of revolution,” Meccanica, vol. 44, no. 3, pp. 255–281, 2009. View at Publisher · View at Google Scholar · View at Scopus
  52. F. Tornabene, E. Viola, and D. J. Inman, “2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical and annular shell structures,” Journal of Sound and Vibration, vol. 328, no. 3, pp. 259–290, 2009. View at Publisher · View at Google Scholar
  53. E. Viola and F. Tornabene, “Free vibrations of three parameter functionally graded parabolic panels of revolution,” Mechanics Research Communications, vol. 36, no. 5, pp. 587–594, 2009. View at Publisher · View at Google Scholar · View at Scopus
  54. Y. Li and Z. Shi, “Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature,” Composite Structures, vol. 87, no. 3, pp. 257–264, 2009. View at Publisher · View at Google Scholar · View at Scopus
  55. A. Alibeigloo and V. Nouri, “Static analysis of functionally graded cylindrical shell with piezoelectric layers using differential quadrature method,” Composite Structures, vol. 92, no. 8, pp. 1775–1785, 2010. View at Publisher · View at Google Scholar · View at Scopus
  56. A. Andakhshideh, S. Maleki, and M. M. Aghdam, “Non-linear bending analysis of laminated sector plates using Generalized Differential Quadrature,” Composite Structures, vol. 92, no. 9, pp. 2258–2264, 2010. View at Publisher · View at Google Scholar · View at Scopus
  57. M. Farid, P. Zahedinejad, and P. Malekzadeh, “Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method,” Materials and Design, vol. 31, no. 1, pp. 2–13, 2010. View at Publisher · View at Google Scholar · View at Scopus
  58. Sh. Hosseini-Hashemi, H. Akhavan, H. R. D. Taher, N. Daemi, and A. Alibeigloo, “Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundation,” Materials and Design, vol. 31, no. 4, pp. 1871–1880, 2010. View at Publisher · View at Google Scholar · View at Scopus
  59. Sh. Hosseini-Hashemi, M. Fadaee, and M. Es'Haghi, “A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates,” International Journal of Mechanical Sciences, vol. 52, no. 8, pp. 1025–1035, 2010. View at Publisher · View at Google Scholar · View at Scopus
  60. P. Malekzadeh and A. Alibeygi Beni, “Free vibration of functionally graded arbitrary straight-sided quadrilateral plates in thermal environment,” Composite Structures, vol. 92, no. 11, pp. 2758–2767, 2010. View at Publisher · View at Google Scholar · View at Scopus
  61. O. Sepahi, M. R. Forouzan, and P. Malekzadeh, “Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM,” Composite Structures, vol. 92, no. 10, pp. 2369–2378, 2010. View at Publisher · View at Google Scholar · View at Scopus
  62. B. Sobhani Aragh and M. H. Yas, “Three-dimensional free vibration of functionally graded fiber orientation and volume fraction cylindrical panels,” Materials and Design, vol. 31, no. 9, pp. 4543–4552, 2010. View at Publisher · View at Google Scholar · View at Scopus
  63. F. Tornabene, A. Marzani, E. Viola, and I. Elishakoff, “Critical flow speeds of pipes conveying fluid by the generalized differential quadrature method,” Advances in Theoretical and Applied Mechanics, vol. 3, no. 3, pp. 121–138, 2010. View at Google Scholar
  64. M. H. Yas and B. Sobhani Aragh, “Three-dimensional analysis for thermoelastic response of functionally graded fiber reinforced cylindrical panel,” Composite Structures, vol. 92, no. 10, pp. 2391–2399, 2010. View at Publisher · View at Google Scholar · View at Scopus
  65. O. Sepahi, M. R. Forouzan, and P. Malekzadeh, “Thermal buckling and postbuckling analysis of functionally graded annular plates with temperature-dependent material properties,” Materials and Design, vol. 32, no. 7, pp. 4030–4041, 2011. View at Publisher · View at Google Scholar · View at Scopus
  66. A. H. Sofiyev and N. Kuruoglu, “Natural frequency of laminated orthotropic shells with different boundary conditions and resting on the Pasternak type elastic foundation,” Composites B, vol. 42, no. 6, pp. 1562–1570, 2011. View at Publisher · View at Google Scholar · View at Scopus
  67. F. Tornabene, “Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method,” Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 9–12, pp. 931–952, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  68. F. Tornabene, “2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution,” Composite Structures, vol. 93, no. 7, pp. 1854–1876, 2011. View at Publisher · View at Google Scholar · View at Scopus
  69. F. Tornabene, “Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler-Pasternak elastic foundations,” Composite Structures, vol. 94, no. 1, pp. 186–206, 2011. View at Publisher · View at Google Scholar
  70. F. Tornabene, A. Liverani, and G. Caligiana, “FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations,” International Journal of Mechanical Sciences, vol. 53, no. 6, pp. 446–470, 2011. View at Publisher · View at Google Scholar · View at Scopus
  71. F. Tornabene, A. Liverani, and G. Caligiana, “Laminated composite rectangular and annular plates: a GDQ solution for static analysis with a posteriori shear and normal stress recovery,” Composites B, vol. 43, no. 4, pp. 1847–1872, 2012. View at Publisher · View at Google Scholar
  72. F. Tornabene, A. Liverani, and G. Caligiana, “Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using generalized differentialquadrature method,” International Journal of Mechanical Sciences, vol. 61, pp. 71–87, 2012. View at Publisher · View at Google Scholar
  73. F. Tornabene, A. Liverani, and G. Caligiana, “FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations,” International Journal of Mechanical Sciences, vol. 53, no. 6, pp. 446–470, 2011. View at Publisher · View at Google Scholar · View at Scopus
  74. E. Viola, F. Tornabene, and N. Fantuzzi, “General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels,” Composite Structures, vol. 95, pp. 639–666, 2013. View at Publisher · View at Google Scholar
  75. F. Tornabene and E. Viola, “Static analysis of functionally graded doubly-curved shells and panels of revolution,” Meccanica, vol. 48, no. 4, pp. 901–930, 2013. View at Publisher · View at Google Scholar
  76. F. Tornabene and A. Ceruti, “Free-form laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations: a 2-D GDQ solution for static and free vibration analysis,” World Journal of Mechanics, vol. 3, pp. 1–25, 2013. View at Publisher · View at Google Scholar
  77. E. Viola, F. Tornabene, and N. Fantuzzi, “Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories,” Composite Structures, vol. 101, pp. 59–93, 2013. View at Publisher · View at Google Scholar
  78. B. Chen and L. Tong, “Sensitivity analysis of heat conduction for functionally graded materials,” Materials and Design, vol. 25, no. 8, pp. 663–672, 2004. View at Publisher · View at Google Scholar · View at Scopus
  79. H.-S. Shen, Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, New York, NY, USA, 2009.
  80. P. Malekzadeh, S. A. Shahpari, and H. R. Ziaee, “Three-dimensional free vibration of thick functionally graded annular plates in thermal environment,” Journal of Sound and Vibration, vol. 329, no. 4, pp. 425–442, 2010. View at Publisher · View at Google Scholar · View at Scopus
  81. X. Zhao and K. M. Liew, “Free vibration analysis of functionally graded conical shell panels by a meshless method,” Composite Structures, vol. 93, no. 2, pp. 649–664, 2011. View at Publisher · View at Google Scholar · View at Scopus
  82. P. Malekzadeh, M. R. G. Haghighi, and M. M. Atashi, “Free vibration analysis of elastically supported functionally raded annular plates subjected to thermal environment,” Meccanica, vol. 46, no. 5, pp. 893–913, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  83. A. H. Akbarzadeh, M. Abbasi, S. K. Hosseini zad, and M. R. Eslami, “Dynamic analysis of functionally graded plates using the hybrid Fourier-Laplace transform under thermo-mechanical loading,” Meccanica, vol. 46, no. 6, pp. 1373–1392, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  84. S. K. Jalali, M. H. Naei, and A. Poorsolhjouy, “Thermal stability analysis of circular functionally graded sandwich plates of variable thickness using pseudo-spectral method,” Materials and Design, vol. 31, no. 10, pp. 4755–4763, 2010. View at Publisher · View at Google Scholar · View at Scopus
  85. E. Jomehzadeh, A. R. Saidi, and S. R. Atashipour, “An analytical approach for stress analysis of functionally graded annular sector plates,” Materials and Design, vol. 30, no. 9, pp. 3679–3685, 2009. View at Publisher · View at Google Scholar · View at Scopus
  86. Y. Fu, P. Zhang, and F. Yang, “Interlaminar stress distribution of composite laminated plates with functionally graded fiber volume fraction,” Materials and Design, vol. 31, no. 6, pp. 2904–2915, 2010. View at Publisher · View at Google Scholar · View at Scopus
  87. N. Wattanasakulpong, B. G. Prusty, D. W. Kelly, and M. Hoffman, “Free vibration analysis of layered functionally graded beams with experimental validation,” Materials & Design, vol. 36, pp. 182–190, 2012. View at Google Scholar
  88. W. Montealegre Rubio, G. H. Paulino, and E. C. Nelli Silva, “Analysis, manufacture and characterization of Ni/Cu functionally graded structures,” Materials & Design, vol. 41, pp. 255–265, 2012. View at Google Scholar
  89. A. Shaghaghi Moghaddam, M. Alfano, and R. Ghajar, “Determining the mixed mode stress intensity factors of surface cracks in functionally graded hollow cylinders,” Materials & Design, vol. 43, pp. 475–484, 2013. View at Google Scholar
  90. R. Moradi-Dastjerdi, M. Foroutan, and A. Pourasghar, “Dynamic analysis of functionally graded material cylinders under an impact load by a mesh-free method,” Acta Mechanica, vol. 219, no. 3-4, pp. 281–290, 2011. View at Publisher · View at Google Scholar · View at Scopus
  91. M. Heshmati and M. H. Yas, “Vibrations of non-uniform functionally graded MWCNTs-polystyrene nanocomposite beams under action of moving load,” Materials & Design, vol. 46, pp. 206–218, 2013. View at Google Scholar
  92. M. Yas, S. Kamarian, J. E. Jam, and A. Pourasghar, “Weight minimization of functionally graded structures using ICA and ANN,” International Journal of Advanced Scientific and Technical Research, vol. 2, pp. 679–696, 2012. View at Google Scholar
  93. J. E. Jam, S. Kamarian, and A. Pourasghar, “Application of ICA and ANN for optimization of functionally graded conical shells,” International Journal of Engineering Trends in Engineering and Development, vol. 2, pp. 171–189, 2012. View at Google Scholar
  94. F. Glover and M. Laguna, Tabu Search, Kluwer Academic, Boston, Mass, USA, 1997. View at Zentralblatt MATH · View at MathSciNet
  95. S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, no. 4598, pp. 671–680, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  96. H. H. Hoos and T. Stutzle, Stochastic Local Search: Foundations and Applications, Elsevier, Amsterdam, The Netherlands, 2005.
  97. A. Colorni, M. Dorigo, and V. Manniezzo, “An investigation of some properties of an ant algorithm,” in Parallel Problem Solving from Nature 2, R. Manner and B. Manderick, Eds., pp. 509–520, North-Holland, Amsterdam, The Netherlands, 1992. View at Google Scholar
  98. M. Dorigo and G. Di Caro, “Ant colony optimization: a new meta-heuristic,” in Proceedings of the 1999 Congress on Evolutionary Computation (CEC '99), vol. 2, pp. 1477–1484, 1999.
  99. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Boston, Mass, USA, 1989.
  100. J. Koza, Genetic Programming: on the Programming of Computers by Means of Natural Selection, MIT Press, Cambridge, UK, 1992.
  101. R. Beasly, D. Bull, and R. Martin, “An overview on genetic algorithms: part I, fundamentals,” University Computing, vol. 15, pp. 58–69, 1993. View at Google Scholar
  102. A. Ceruti, G. Caligiana, and F. Persiani, “Comparative evaluation of different optimization methodologies for the design of UAVs having shape obtained by hot wire cutting techniques,” International Journal on Interactive Design and Manufacturing, 2012. View at Publisher · View at Google Scholar
  103. H. V. Hultmann Ayala and L. Dos Santos Coelho, “Tuning of PID controller based on a multi-objective genetic algorithm applied to a robotic manipulator,” Expert Systems With Applications, vol. 39, no. 10, pp. 8968–8974, 2012. View at Publisher · View at Google Scholar
  104. K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Processing Magazine, vol. 13, no. 6, pp. 22–37, 1996. View at Google Scholar · View at Scopus
  105. M. M. Karim, K. Suzuki, and H. Kai, “Optimal design of hydrofoil and marine propeller using micro-genetic algorithm,” Journal of Naval Architecture and Marine Engineering, vol. 1, pp. 47–61, 2004. View at Google Scholar
  106. A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: a tutorial,” Reliability Engineering and System Safety, vol. 91, no. 9, pp. 992–1007, 2006. View at Publisher · View at Google Scholar · View at Scopus
  107. J. H. Holland, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, Mich, USA, 1975. View at MathSciNet
  108. D. Kaur and M. M. Murugappan, “Performance enhancement in solving traveling salesman problem using hybrid genetic algorithm,” in Proceedings of the Annual Conference of the North American Fuzzy Information Processing Society (NAFIPS '08), May 2008. View at Publisher · View at Google Scholar · View at Scopus
  109. E. Verdú, M. J. Verdú, L. M. Regueras, J. P. De Castro, and R. García, “A genetic fuzzy expert system for automatic question classification in a competitive learning environment,” Expert Systems With Applications, vol. 39, no. 8, pp. 7471–7478, 2012. View at Publisher · View at Google Scholar
  110. R. Storn and K. Price, “Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  111. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the 1995 IEEE International Conference on Neural Networks. Part 1 (of 6), pp. 1942–1948, December 1995. View at Scopus
  112. R. Poli, “An analysis of publications on particle swarm optimization applications,” Technical Report CSM-469, Department of Computer Science, University of Essex, Essex, UK, 2007. View at Google Scholar
  113. Y. Shi and R. C. Eberhart, “Parameter selection in particle swarm optimization,” in Proceedings of the 7th International Conference on Evolutionary Programming VII (EP '98), pp. 591–600, 1998.
  114. L. Zhang, E. Dong, and Y. Xing, “Steering trapezoid mechanism design based on Monte Carlo method,” in Proceedings of the International Conference on Electronic & Mechanical Engineering and Information Technology, 2011.
  115. B. Birge, “PSOt: a particle swarm optimization toolbox for use with MATLAB,” in Proceedings of the IEEE Swarm Intelligence Symposium (SIS '03), pp. 182–186, Indianapolis, Ind, USA, 2003.
  116. X. Hu, L. Wang, and Y. Zhong, “An improved particle swarm optimization algorithm for site index curve model,” in Proceedings 2011 International Conference on Business Management and Electronic Information (BMEI '11), vol. 3, pp. 838–842, 2011.
  117. J. Yoo and P. Hajela, “Immune network simulations in multicriterion design,” Structural and Multidisciplinary Optimization, vol. 18, no. 2-3, pp. 85–94, 1999. View at Google Scholar · View at Scopus
  118. C. A. Coello Coello and N. C. Cortés, “Use of emulations of the immune system to handle constraints in evolutionary algorithms,” in Proceedings of the Intelligent Engineering Systems Through Artificial Neural Networks (ANNIE '01), C. H. Dagli, A. L. Buczak, J. Ghosh et al., Eds., vol. 11, pp. 141–146, ASME Press, 2001.
  119. Y. T. Hsiao, C. L. Chuang, J. A. Jiang, and C. C. Chien, “A novel optimization algorithm: space gravitational optimization,” in Proceedings of the International Conference on Systems, Man and Cybernetics, pp. 2323–2328, Waikoloa, Hawaii, USA, October 2005. View at Scopus
  120. B. Abdi, H. Mozafari, A. Ayob, and R. Kohandel, “Imperialist competitive algorithm and its application in optimization of laminated composite structures,” European Journal of Scientific Research, vol. 55, no. 2, pp. 174–187, 2011. View at Google Scholar · View at Scopus
  121. H. Shah-Hosseini, “The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm,” International Journal of Bio-Inspired Computation, vol. 1, pp. 71–79, 2008. View at Google Scholar
  122. H. Duan, S. Liu, and X. Lei, “Air robot path planning based on intelligent water drops optimization,” in Proceedings of the 2008 International Joint Conference on Neural Networks (IJCNN '08), pp. 1397–1401, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  123. K. Mosegaard and M. Sambridge, “Monte Carlo analysis of inverse problems,” Inverse Problems, vol. 18, no. 3, pp. R29–R54, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  124. G. S. Fishman, Monte Carlo: Concepts, Algorithms, and Applications, Springer, New York, NY, USA, 1995. View at MathSciNet
  125. S. Ghahramani, Fundamentals of Probability Theory, Prentice Hall, Upper Saddle River, NJ, USA, 2000.
  126. E. M. T. Hendrix and N. J. Olieman, “The smoothed Monte Carlo method in robustness optimization,” Optimization Methods and Software, vol. 23, no. 5, pp. 717–729, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  127. K. Madani and J. R. Lund, “A Monte-Carlo game theoretic approach for Multi-Criteria decision making under uncertainty,” Advances in Water Resources, vol. 34, no. 5, pp. 607–616, 2011. View at Publisher · View at Google Scholar · View at Scopus