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Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials pp 205–237Cite as

Optimization of Functionally Graded Materials Considering Dynamical Analysis

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 49))

Abstract

Functionally graded materials (FGMs) are a new class of bio-inspired composite materials made from different material phases, in which their volume fraction changes gradually towards a particular direction. Accordingly, continuous changes in the composition, microstructure and porosity of the graded materials results in material properties gradients; for this reason, the material properties move smoothly and continuously from one surface to another, eliminating the interface problem. Hence, with appropriate design, FGMs can develop better properties than their homogeneous counterpart due to their better designability. One potential employment of FGMs is as damper or energy absorber in dynamic applications, in which optimization techniques such as the topology optimization method (TOM) can contribute to a better performance in relation to a non-optimized design. In this chapter, functionally graded structures are designed with and without the TOM in order to explore the advantages of the FGM concept in low-velocity impact condition, which is a special case in the world of dynamic analysis, and has interest for designing machinery parts and components.

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Notes

  1. 1.

    Since we use 2D domains, the holes seem circular; however, the model is asymmetric and thus the holes are toroidal. We hereafter refer to them simply as holes.

  2. 2.

    The area under the curve indicates strictly power per unit volume, which is directly related to the elastic deformation energy per unit volume.

References

  1. Zukas, J.A.: High Velocity Impact Dynamics. Wiley, New York (1990)

    Google Scholar 

  2. Goicolea, J.M.: Estructuras sometidas a impacto. In: Car, E., López, F., y Oller, S. (eds.) Estructuras sometidas a acciones dinámicas, pp. 535–567. Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE), Barcelona (2000)

    Google Scholar 

  3. Rosenberg, Z., Dekel, E.: Terminal Ballistics. Springer, Berlin (2012)

    Book  Google Scholar 

  4. Anderson, C.E.: A review of computational ceramic armor modeling. In: Prokurat, L., Wereszczak, A., Lara-Curzio, E. (eds.) Advances in Ceramic Armor II: Ceramic Engineering and Science Proceedings, vol. 27, no. 7, pp. 1–18. Wiley, Hoboken, NJ, USA (2008)

    Google Scholar 

  5. McCauley, J.W., D’Andrea, G., Cho, K., Burkins, M.S., Dowding, R.J., Gooch, W.A.: Status Report on SPS TiB2/TiB/Ti Functionally Graded Materials (FGMs) for Armor, U.S. Army Research Laboratory (2006)

    Google Scholar 

  6. Koizumi, M.: FGM activities in Japan. Compos. B Eng. 28(1–2), 1–4 (1997)

    Article  Google Scholar 

  7. Markworth, A.J., Ramesh, K.S., Parks, W.P.: Modelling studies applied to functionally graded materials. J. Mater. Sci. 30(9), 2183–2193 (1995)

    Article  Google Scholar 

  8. Huang, J., Fadel, G.M., Blouin, V.Y., Grujicic, M.: Bi-objective optimization design of functionally gradient materials. Mater. Des. 23(7), 657–666 (2002)

    Article  Google Scholar 

  9. Birman, V., Byrd, L.W.: Modeling and analysis of functionally graded materials and structures. Appl. Mech. Rev. 60(5), 195 (2007)

    Article  Google Scholar 

  10. Obata, Y., Noda, N.: Optimum material design for functionally gradient material plate. Arch. Appl. Mech. 66(8), 581–589 (1996)

    Article  MATH  Google Scholar 

  11. Cardoso, E.L., Fonseca, J.S.O.: Complexity control in the topology optimization of continuum structures. J. Braz. Soc. Mech. Sci. Eng. 25(3), 293–301 (2003)

    Article  Google Scholar 

  12. Bendsøe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer, Berlin (2003)

    Google Scholar 

  13. Eschenauer, H.A.: Topology optimization of continuum structures: a review. Appl. Mech. Rev. 54(4), 331–389 (2001)

    Article  Google Scholar 

  14. Michell, A.G.M.: LVIII. The limits of economy of material in frame-structures. Philos. Mag. Ser. 6 8(47), 589–597 (1904)

    Google Scholar 

  15. Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sigmund, O.: Topology optimization: a tool for the tailoring of structures and materials. Philos. Trans. Roy. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 358(1765), 211–227 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Sigmund, O.: A 99 line topology optimization code written in Matlab. Struct. Multi. Optim. 21(2), 120–127 (2001)

    Article  Google Scholar 

  18. Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Optim. 1(4), 193–202 (1989)

    Article  Google Scholar 

  19. Bendsøe, M.P., Sigmund, O.: Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69(9), 635–654 (1999)

    MATH  Google Scholar 

  20. Rozvany, G.I.N.: A critical review of established methods of structural topology optimization. Struct. Multi. Optim. 37(3), 217–237 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Dadalau, A., Hafla, A., Verl, A.: A new adaptive penalization scheme for topology optimization. Prod. Eng. Res. Devel. 3(4–5), 427–434 (2009)

    Article  Google Scholar 

  22. Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Multi. Optim. 16(1), 68–75 (1998)

    Article  Google Scholar 

  23. Hassani, B., Hinton, E.: A review of homogenization and topology optimization III—topology optimization using optimality criteria. Comput. Struct. 69(6), 739–756 (1998)

    Article  MATH  Google Scholar 

  24. Tovar, A., Patel, N.M., Niebur, G.L., Sen, M., Renaud, J.E.: Topology optimization using a hybrid cellular automaton method with local control rules. J. Mech. Des. 128(6), 1205–1216 (2006)

    Article  Google Scholar 

  25. Lamberti, L., Pappalettere, C.: Move limits definition in structural optimization with sequential linear programming. Part I: optimization algorithm. Comput. Struct. 81(4), 197–213 (2003)

    Article  MathSciNet  Google Scholar 

  26. Zhang, X., Zhang, H.: Optimal design of functionally graded foam material under impact loading. Int. J. Mech. Sci. 68, 199–211 (2013)

    Google Scholar 

  27. Paulino, G.H., Silva, E.C.N.: Design of functionally graded structures using topology optimization. Mater. Sci. Forum 492, 435–440 (2005)

    Article  Google Scholar 

  28. Kim, J.-H., Paulino, G.H.: Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. J. Appl. Mech. 69(4), 502–514 (2002)

    Article  MATH  Google Scholar 

  29. Matsui, K., Terada, K.: Continuous approximation of material distribution for topology optimization. Int. J. Numer. Meth. Eng. 59(14), 1925–1944 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  30. Vatanabe, S.L., Rubio, W.M., Silva, E.C.N.: Modeling of functionally graded materials. In: Comprehensive Materials Processing, pp. 261–282. Elsevier (2014)

    Google Scholar 

  31. Cook, R.D., Plesha, M.E., Malkus, D.S., Witt, R.J.: Concepts and Applications of Finite Element Analysis, 4th edn. Wiley, New York (2002)

    Google Scholar 

  32. Patel, N.M., Tovar, A., Kang, B.-S., Renaud, J.E.: Crashworthiness design using topology optimization. J. Mech. Des. 131(6), 061013 (2009)

    Article  Google Scholar 

  33. Xie, Y.M., Steven, G.P.: Evolutionary Structural Optimization. Springer, London (1997)

    Book  MATH  Google Scholar 

  34. Tovar, A., Patel, N.M., Kaushik, A.K., Renaud, J.E.: Optimality conditions of the hybrid cellular automata for structural optimization. AIAA J. 45(3), 673–683 (2007)

    Article  Google Scholar 

  35. Evans, A.G., Hutchinson, J.W., Fleck, N.A., Ashby, M.F., Wadley, H.N.G.: The topological design of multifunctional cellular metals. Prog. Mater Sci. 46(3–4), 309–327 (2001)

    Article  Google Scholar 

  36. Choi, W.S., Park, G.J.: Transformation of dynamic loads into equivalent static loads based on modal analysis. Int. J. Numer. Meth. Eng. 46(1), 29–43 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  37. Kang, B.S., Choi, W.S., Park, G.J.: Structural optimization under equivalent static loads transformed from dynamic loads based on displacement. Comput. Struct. 79(2), 145–154 (2001)

    Article  Google Scholar 

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Acknowledgments

The first author acknowledges financial support from COLCIENCIAS by the scholarship “Becas de Colciencias, Doctorado en Colombia, 567—2012”. The third author acknowledges the financial support of CNPq (National Council for Research and Development), under grants 304121/2013-4.

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Authors and Affiliations

  1. Faculty of Mines, Department of Mechanical Engineering, Universidad Nacional de Colombia, 050034, Medellín, Colombia

    F. J. Ramírez-Gil, J. E. Murillo-Cardoso & W. Montealegre-Rubio

  2. Department of Mechatronics and Mechanical Systems Engineering, Escola Politécnica of the University of São Paulo, Butantã, São Paulo, 05508-900, Brazil

    E. C. N. Silva

Authors
  1. F. J. Ramírez-Gil
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  2. J. E. Murillo-Cardoso
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  3. E. C. N. Silva
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  4. W. Montealegre-Rubio
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Correspondence to W. Montealegre-Rubio .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Santa Catarina State Uni. - UDESC, Joinville, Santa Catarina, Brazil

    Pablo Andrés Muñoz-Rojas

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Ramírez-Gil, F.J., Murillo-Cardoso, J.E., Silva, E.C.N., Montealegre-Rubio, W. (2016). Optimization of Functionally Graded Materials Considering Dynamical Analysis. In: Muñoz-Rojas, P. (eds) Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials. Advanced Structured Materials, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-04265-7_8

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  • DOI: https://doi.org/10.1007/978-3-319-04265-7_8

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