Steel and Composite Structures

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Multi-objective optimization of anisogride composite lattice plate for free vibration, mass, buckling load, and post-buckling

  • F. Rashidi (Department of Mechanical Engineering, Tarbiat Modares University) ;
  • A. Farrokhabadi (Department of Mechanical Engineering, Tarbiat Modares University) ;
  • M. Karamooz Mahdiabadi (Department of Mechanical Engineering, Tarbiat Modares University)
  • Received : 2023.10.28
  • Accepted : 2024.06.20
  • Published : 2024.07.10
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Abstract

This article focuses on the static and dynamic analysis and optimization of an anisogrid lattice plate subjected to axial compressive load with simply supported boundary conditions. The lattice plate includes diagonal and transverse ribs and is modeled as an orthotropic plate with effective stiffness properties. The study employs the first-order shear deformation theory and the Ritz method with a Legendre approximation function. In the realm of optimization, the Non-dominated Sorting Genetic Algorithm-II is utilized as an evolutionary multi-objective algorithm to optimize. The research findings are validated through finite element analysis. Notably, this study addresses the less-explored areas of optimizing the geometric parameters of the plate by maximizing the buckling load and natural frequency while minimizing mass. Furthermore, this study attempts to fill the gap related to the analysis of the post-buckling behavior of lattice plates, which has been conspicuously overlooked in previous research. This has been accomplished by conducting nonlinear analyses and scrutinizing post-buckling diagrams of this type of lattice structure. The efficacy of the continuous methods for analyzing the natural frequency, buckling, and post-buckling of these lattice plates demonstrates that while a degree of accuracy is compromised, it provides a significant amount of computational efficiency.

Keywords

References

  1. Akl, W., Ruzzene, M. and Baz, A. (2002), "Optimal design of underwater stiffened shells", Struct. Multidiscipl. Optimiz., 23, 297-310
  2. Ambur, D.R. and Jaunky, N. (2001), "Optimal design of grid-stiffened panels and shells with variable curvature", Compos. Struct., 52(2), 173-180. https://doi.org/10.1016/S0263-8223(00)00165-3.
  3. Aydogdu, M. (2005), "Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method", Int. J. Mech. Sci., 47(11), 1740-1755. https://doi.org/10.1016/j.ijmecsci.2005.06.010.
  4. Bagheri, M., Jafari, A. and Sadeghifar, M. (2011), "Multi-objective optimization of ring stiffened cylindrical shells using a genetic algorithm", J. Sound Vib., 330(3), 374-384. https://doi.org/10.1016/j.jsv.2010.08.019.
  5. Belardi, V.G., Fanelli, P. and Vivio, F. (2018), "Structural analysis and optimization of anisogrid composite lattice cylindrical shells", Compos. Part B: Eng., 139, 203-215. https://doi.org/10.1016/j.compositesb.2017.11.058.
  6. Buragohain, M. and Velmurugan, R. (2009), "Buckling analysis of composite hexagonal lattice cylindrical shell using smeared stiffener model", Defence Sci. J., 59(3), 230
  7. Buragohain, M. and Velmurugan, R. (2011), "Study of filament wound grid-stiffened composite cylindrical structures", Compos. Struct., 93(2), 1031-1038. https://doi.org/10.1016/j.compstruct.2010.06.003.
  8. Cancer Patient Receives 3D Printed Ribs in World-First Surgery (2015), https://blog.csiro.au/cancer-patient-receives-3d-printed-ribs-in-world-first-surgery/
  9. Chapra, S.C. and Canale, R.P. (2010), Numerical Methods for Engineers, The Mcgraw-Hill Companies
  10. Cheung, Y. and Zhou, D. (2000), "Vibrations of moderately thick rectangular plates in terms of a set of static Timoshenko beam functions", Comput. Struct., 78(6), 757-768. https://doi.org/10.1016/S0045-7949(00)00058-4.
  11. Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T. (2002), "A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transact. Evolution. Comput., 6(2), 182-197. https://doi.org/10.1109/4235.996017.
  12. Dong, G., Tang, Y., Li, D. and Zhao, Y.F. (2020), "Design and optimization of solid lattice hybrid structures fabricated by additive manufacturing", Additive Manufact., 33, 101116. https://doi.org/10.1016/j.addma.2020.101116.
  13. Eftekhari, S. and Jafari, A. (2013), "A simple and accurate Ritz formulation for free vibration of thick rectangular and skew plates with general boundary conditions", Acta Mechanica. 224(1), 193-209. https://doi.org/10.1007/s00707-012-0737-6.
  14. Ehsani, A. and Dalir, H. (2019), " Multi-objective optimization of composite angle grid plates for maximum buckling load and minimum weight using genetic algorithms and neural networks", Compos. Struct., 229, 111450. https://doi.org/10.1016/j.compstruct.2019.111450.
  15. Ehsani, A. and Dalir, H. (2021), " Multi-objective design optimization of variable ribs composite grid plates", Struct. Multidiscipl. Optimiz., 63(1), 407-418. https://doi.org/10.1007/s00158-020-02672-7.
  16. Ehsani, A. and Rezaeepazhand, J. (2016), "Stacking sequence optimization of laminated composite grid plates for maximum buckling load using genetic algorithm", Int. J. Mech. Sci., 119, 97-106. https://doi.org/10.1016/j.ijmecsci.2016.09.028.
  17. Eschknauer, H. (1995), "Vasiliev, VV: Mechanics of Composite Structures. Washington etc., Taylor & Francis Ltd. 1993. XI, 506 pp.,£ 35.00. IS N 1-56032-034-6", Zeitschrift Angewandte Mathematik und Mechanik. 75(3), 206-206. https://doi.org/10.1002/zamm.19950750305.
  18. Fan, H., Jin, F. and Fang, D. (2009), "Uniaxial local buckling strength of periodic lattice composites", Mater. Des., 30(10), 4136-4145. https://doi.org/10.1016/j.matdes.2009.04.034.
  19. Farkas, J. and Jarmai, K. (2000), "Optimum design of welded stiffened plates loaded by hydrostatic normal pressure", Struct. Multidiscipl. Optimiz., 20, 311-316. https://doi.org/10.1007/s001580050161.
  20. Fright, M.S. (1973), Isogrid Design Handbook, NASA
  21. Ghadi, N., Mattikalli, A. and Ghadi, A. (2017), "Design and Fe analysis of composite grid structure for skin stiffening applications", Int. Res. J. Eng. Technol., 4(08),
  22. Ghannadpour, S. and Barekati, M. (2016), "Initial imperfection effects on postbuckling response of laminated plates under end-shortening strain using Chebyshev techniques", Thin-Wall. Struct., 106, 484-494
  23. Ghannadpour, S. and Rashidi, F. (2022), " Efficient and accurate semi-analytical simulation of nonlinear behavior of imperfect variable stiffness plates containing rectangular holes", ThinWall. Struct., 171, 108830. https://doi.org/10.1016/j.tws.2021.108830.
  24. Ghannadpour, S.A.M. and Rashidi, F. (2021), "A semi-analytical study on effects of geometric imperfection and curved fiber paths on nonlinear response of compression-loaded laminates", Steel Compos. Struct., 40(4), 621-632. https://doi.org/10.12989/scs.2021.40.4.621.
  25. Inc., T.M. (2023), gamultiobj, The athWorks Inc. https://www.mathworks.com/help/gads/gamultiobj.html.
  26. Jaunky, N., Knight Jr, N.F. and Ambur, D.R. (1996), "Formulation of an improved smeared stiffener theory for buckling analysis of grid-stiffened composite panels", Compos. Part B: Eng., 27(5), 519-526. https://doi.org/10.1016/1359-8368(96)00032-7.
  27. Jing, Z. (2023), "Variable stiffness discrete Ritz method for free vibration analysis of plates in arbitrary geometries", J. Sound Vib., 553, 117662. https://doi.org/10.1016/j.jsv.2023.117662.
  28. Jing, Z. and Duan, L. (2023), "Discrete Ritz method for buckling analysis of arbitrarily shaped plates with arbitrary cutouts", Thin-Wall. Struct., 193, 111294. https://doi.org/10.1016/j.tws.2023.111294.
  29. Kalyanmoy, D. (2001), Multi-Objective Optimization Using Evolutionary Algorithms, John Wiley & sons, Inc
  30. Kidane, S., Li, G., Helms, J., Pang, S.-S. and Woldesenbet, E. (2003), "Buckling load analysis of grid stiffened composite cylinders", Compos. Part B: Eng., 34(1), 1-9. https://doi.org/10.1016/S1359-8368(02)00074-4.
  31. Kim, P. and Park, J. (2023), "An approximate method for Buckling analysis and optimization of composite lattice conical panels considering geometric parameters", Int. J. Aeronautic. Space Sci., 1-13. https://doi.org/10.1007/s42405-023-00589-1.
  32. Kim, Y. and Park, J. (2021), "An approximate method for the progressive failure analysis of a composite lattice rectangular plate", Mech. Adv. Mater. Struct., 28(19), 1992-2008. https://doi.org/10.1080/15376494.2020.1716413.
  33. Kim, Y., Kim, P.,Kim, H. and Park, J. (2017), "An approximate method for the buckling analysis of a composite lattice rectangular plate", Int. J. Aeronautic. Space Sci., 18(3), 450-466. http://dx.doi.org/10.5139/IJASS.2017.18.3.450.
  34. Kim, Y., Kim, P., Kim, H. and Park, J. (2018), "Optimal design of a composite lattice rectangular plate for solar panels of a high-agility satellite", Int. J. Aeronautic. Space Sci., 19, 762-775. https://doi.org/10.1007/s42405-018-0050-2.
  35. Knighton, D.J. (1972), "Delta launch vehicle isogrid structure NASTRAN analysis", NASTRAN: Users' Experiences.
  36. Lee, Y., Zhao, X. and Reddy, J. (2010), "Postbuckling analysis of functionally graded plates subject to compressive and thermal loads", Comput. Meth. Appl. Mech. Eng., 199(25-28), 1645-1653. https://doi.org/10.1016/j.cma.2010.01.008.
  37. Liew, K., Wang, J., Tan, M. and Rajendran, S. (2006), "Postbuckling analysis of laminated composite plates using the mesh-free kp-Ritz method", Comput. Meth. Appl. Mech. Eng., 195(7-8), 551-570. https://doi.org/10.1016/j.cma.2005.02.004.
  38. Lopatin, A., Morozov, E. and Shatov, A. (2016), "Buckling of uniaxially compressed composite anisogrid lattice plate with clamped edges", Compos. Struct., 157, 187-196. https://doi.org/10.1016/j.compstruct.2016.08.034.
  39. Lopatin, A., Morozov, E. and Shatov, A. (2017), "Buckling of the composite anisogrid lattice plate with clamped edges under shear load", Compos. Struct., 159, 72-80. https://doi.org/10.1016/j.compstruct.2016.09.025.
  40. Lopatin, A., Morozov, E. and Shatov, A. (2017), "Buckling of uniaxially compressed composite anisogrid lattice cylindrical panel with clamped edges", Compos. Struct., 160, 765-772. https://doi.org/10.1016/j.compstruct.2016.10.055.
  41. Lopatin, A., Morozov, E. and Shatov, A. (2018), "Fundamental frequency of a composite anisogrid lattice cylindrical panel with clamped edges", Compos. Struct., 201, 200-207. https://doi.org/10.1016/j.compstruct.2018.06.006.
  42. Lopatin, A., Morozov, E. and Shatov, A. (2019), "Buckling and vibration of composite lattice elliptical cylindrical shells", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications. 233(7), 1255-1266. https://doi.org/10.1177/1464420717736549
  43. Milazzo, A. and Oliveri, V. (2021), "Investigation of buckling characteristics of cracked variable stiffness composite plates by an eXtended Ritz approach", Thin-Wall. Struct., 163, 107750. https://doi.org/10.1016/j.tws.2021.107750.
  44. Mindlin, R. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", https://doi.org/10.1115/1.4010217.
  45. Morozov, E. and Lopatin, A. (2009). "Innovative design of the composite lattice frame of a spacecraft solar array", Proceedings of the 17th international conference on composite materials (ICCM-17), Edinburgh, Scotland.
  46. Murthy, V. and Santhanakrishnanan, S. (2020), "Isogrid lattice structure for armouring applications", Procedia Manufacturing. 48, e1-e11. https://doi.org/10.1016/j.promfg.2020.05.099.
  47. Ossola, E., Borgonia, J.P., Hendry, M., Sunada, E., Brusa, E. and Sesana, R. (2021), "Design of isogrid shells for venus surface probes", J. Spacecraft Rockets. 58(3), 643-652. https://doi.org/10.2514/1.A34823.
  48. Paschero, M. and Hyer, M.W. (2009), "Axial buckling of an orthotropic circular cylinder: Application to orthogrid concept", Int. J. Solids Struct., 46(10), 2151-2171. https://doi.org/10.1016/j.ijsolstr.2008.08.033.
  49. Pavlov, L., te Kloeze, I., Smeets, B. and Simonian, S. (2016), "Development of mass and cost efficient grid-stiffened and lattice structures for space applications", Proceedings of the 14th European Conference on Spacecraft Structures, Materials and Environmental Testing (ECSSMET), Toulouse, France.
  50. Pavlov, L., te Kloeze, I., Smeets, B.J. and Simonian, S. (2016). "Development of mass and cost efficient grid-stiffened and lattice structures for space applications", Proceedings of the 14th European Conference on Spacecraft Structures, Materials and Environmental Testing (ECSSMET), Toulouse, France.
  51. Rashidi, F., Ghannadpour, S. and Farrokhabadi, A. (2024), "Exploring the nonlinear response of cracked variable stiffness composite plates using plate decomposition method", Compos. Struct., 118095. https://doi.org/10.1016/j.compstruct.2024.118095.
  52. Reddy, A. (1981). "Damage tolerance of continuous filament composite isogrid structures: a preliminary assessment", Japan-US Conference Proceddings.
  53. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press
  54. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", https://doi.org/10.1115/1.4009435.
  55. Saadatpour, M.M., Azhari, M. and Bradford, M. (2002), "Analysis of general quadrilateral orthotropic thick plates with arbitrary boundary conditions by the Rayleigh-Ritz method", Int. J. Numer. Methods Eng., 54(7), 1087-1102. https://doi.org/10.1002/nme.485.
  56. Sensmeier, M.D. (1996), Optimum Crashworthiness Design of Grid-Stiffened Composite Fuselage Structures, Virginia Polytechnic Institute and State University
  57. Slinchenko, D. and Verijenko, V. (2001), "Structural analysis of composite lattice shells of revolution on the basis of smearing stiffness", Compos. Struct., 54(2-3), 341-348. https://doi.org/10.1016/S0263-8223(01)00108-8.
  58. Totaro, G. (2012), "Local buckling modelling of isogrid and anisogrid lattice cylindrical shells with triangular cells", Compos. Struct., 94(2), 446-452. https://doi.org/10.1016/j.compstruct.2011.08.002.
  59. Totaro, G. (2013), "Local buckling modelling of isogrid and anisogrid lattice cylindrical shells with hexagonal cells", Compos. Struct., 95, 403-410. https://doi.org/10.1016/j.compstruct.2012.07.011.
  60. Totaro, G. (2015), "Optimal design concepts for flat isogrid and anisogrid lattice panels longitudinally compressed", Compos. Struct., 129, 101-110. https://doi.org/10.1016/j.compstruct.2015.03.067.
  61. Totaro, G. and Gurdal, Z. (2009), "Optimal design of composite lattice shell structures for aerospace applications", Aerosp. Sci. Technol., 13(4-5), 157-164. https://doi.org/10.1016/j.ast.2008.09.001.
  62. Vasiliev, V. and Razin, A. (2006), "Anisogrid composite lattice structures for spacecraft and aircraft applications", Compos. Struct., 76(1-2), 182-189. https://doi.org/10.1016/j.compstruct.2006.06.025.
  63. Vasiliev, V., Barynin, V. and Rasin, A. (2001), "Anisogrid lattice structures-survey of development and application", Compos. Struct., 54(2-3), 361-370. https://doi.org/10.1016/S0263-8223(01)00111-8.
  64. Vasiliev, V.V. (2017), Mechanics of Composite Structures, CRC Press
  65. Vasiliev, V.V. and Morozov, E.V. (2013), Advanced Mechanics of Composite Materials and Structural Elements, Newnes
  66. Vasiliev, V.V., Barynin, V.A. and Razin, A.F. (2012), "Anisogrid composite lattice structures-Development and aerospace applications", Compos. Struct., 94(3), 1117-1127. https://doi.org/10.1016/j.compstruct.2011.10.023.
  67. Wang, S. (1997), "A unified Timoshenko beam B-spline Rayleigh-Ritz method for vibration and buckling analysis of thick and thin beams and plates", Int. J. Numer. Meth. Eng., 40(3), 473-491. https://doi.org/10.1002/(SICI)1097-0207(19970215)40:3<473::AID-N 75>3.0.CO;2-U.
  68. Zheng, Q., Ju, S. and Jiang, D. (2014), "Anisotropic mechanical properties of diamond lattice composites structures", Compos. Struct., 109, 23-30. https://doi.org/10.1016/j.compstruct.2013.10.053.
  69. Zhou, D., Cheung, Y., Au, F. and Lo, S. (2002), "Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method", Int. J. Solids Struct., 39(26), 6339-6353. https://doi.org/10.1016/S0020-7683(02)00460-2.