DOI QR코드

DOI QR Code

Material distribution optimization of 2D heterogeneous cylinder under thermo-mechanical loading

  • Asgari, Masoud (Faculty of Mechanical Engineering, K. N. Toosi University of Technology)
  • 투고 : 2014.03.15
  • 심사 : 2014.11.18
  • 발행 : 2015.02.25

초록

In this paper optimization of volume fraction distribution in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to steady state thermal and mechanical loadings is considered. The finite element method with graded material properties within each element (graded finite elements) is used to model the structure. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective function selected as having the normalized effective stress equal to one at all points that leads to a uniform stress distribution in the structure. Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicates that by using the uniform distribution of normalized effective stress as objective function, considerably more efficient usage of materials can be achieved compared with the power law volume fraction distribution. Also considering uniform distribution of safety factor as design criteria instead of minimizing peak effective stress affects remarkably the optimum volume fractions.

키워드

참고문헌

  1. Abudi, J. and Pindera, M.J. (1996), "Thermoelastic theory for the response of materials functionally graded in two directions", Int. J. Solid. Struct., 33(7), 931-966. https://doi.org/10.1016/0020-7683(95)00084-4
  2. Arora, J. (2004), Introduction to Optimum Design, 2nd Edition, Academic Press.
  3. Asgari, M. and Akhlaghi, M. (2009), "Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length", Heat Mass Trans., 45, 1383-1392. https://doi.org/10.1007/s00231-009-0515-8
  4. Asgari, M. and Akhlaghi, M. (2010), "Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length", Arch. Appl. Mech., 80, 353-376. https://doi.org/10.1007/s00419-009-0321-2
  5. Asgari, M. and Akhlaghi, M. (2011), "Thermo-mechanical analysis of 2D-FGM thick hollow cylinder using graded finite elements", Adv. Struct. Eng., 14, 1059-1073. https://doi.org/10.1260/1369-4332.14.6.1059
  6. Boresi, B., Peter, A. and Ken, P. (1999), Elasticity in Engineering Mechanics, 2nd Edition,Wiley, New York.
  7. Boussaa, D. (2009), "Optimization of temperature-dependent functionally graded material bodies", Comput. Meth. Appl. Mech. Eng., 198, 2827-2838. https://doi.org/10.1016/j.cma.2009.02.013
  8. Brodlie, K., Mashwama, P. and Butt, S. (1995), "Visualization of surface data to preserve positivity and other simple constraints", Comput. Graph., 19, 585-594. https://doi.org/10.1016/0097-8493(95)00036-C
  9. Chen, B. and Tong, L. (2005), "Thermomechanically coupled sensitivity analysis and design optimization of functionally graded materials", Comput. Meth. Appl. Mech. Eng., 194, 1891-1911. https://doi.org/10.1016/j.cma.2004.07.005
  10. Cho, J.R. and Choi, J.H. (2004), "A yield-criteria tailoring of the volume fraction in metal-ceramic functionally graded material", Eur. J. Mech. A/Solid, 23, 271-281. https://doi.org/10.1016/j.euromechsol.2003.11.004
  11. Cho, J.R. and Ha, D.Y. (2009), "Optimal tailoring of 2D volume-fraction distributions for heat-resisting functionally graded materials using FDM", Comput. Meth. Appl., 191, 3195-3211
  12. Cho, J.R. and Ha, D.Y. (2001), "Thermo-elastoplastic characteristics of heat-resisting functionally graded composite structures", Struct. Eng. Mech., 11(1), 49-70. https://doi.org/10.12989/sem.2001.11.1.049
  13. Cho, J.R. and Ha, D.Y. (2002), "Volume fraction optimization for minimizing thermal stress in Ni-$Al_2O_3$ functionally graded materials", Mater. Sci. Eng., 334, 147-155. https://doi.org/10.1016/S0921-5093(01)01791-9
  14. Cho, J.R. and Shin, S.W. (2004), "Material composition optimization for heat-resisting FGMs by artificial neural network", Compos. Part A, 35, 585-594. https://doi.org/10.1016/j.compositesa.2003.12.003
  15. Goupee, A.J. and Vel, S.S. (2007), "Multi-objective optimization of functionally graded materials with temperature-dependent material properties", Mater. Des., 28, 1861-1879. https://doi.org/10.1016/j.matdes.2006.04.013
  16. Goupee, A.J. and Vel, S.S. (2006), "Two-dimensional optimization of material composition of functionally graded materials using meshless analyses and a genetic algorithm", Comput. Meth. Appl. Mech. Eng., 195, 5926-5948. https://doi.org/10.1016/j.cma.2005.09.017
  17. Jinhua, H, George, M.F., Vincent, Y.B. and Grujicic, M. (2002), "Bi-objective optimization design of functionally gradient materials", Mater. Des., 23, 657-666. https://doi.org/10.1016/S0261-3069(02)00048-1
  18. Kim, J.H. and Paulino, G.H. (2002), "Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials", J. Appl. Mech., 69(4), 502-514. https://doi.org/10.1115/1.1467094
  19. Koizumi, M. (2003), "The concept of FGM, ceramic transaction, functionally graded materials", 34, 3-10.
  20. Kou, X.Y., Parks, G.T. and Tana, S.T. (2012), "Optimal design of functionally graded materials using a procedural model and particle swarm optimization", Comput. Aid. Des., 44, 300-310. https://doi.org/10.1016/j.cad.2011.10.007
  21. Lancaster, P. and Alkauskas, K.S. (1986), Curve and Surface Fitting: An Introduction, Academic Press, London.
  22. Lee, D., Shin, S., Park, H. and Park, S. (2014), "Topological material distribution evaluation for steel plate reinforcement by using CCARAT optimizer", Struct. Eng. Mech., 51(5), 793-808 https://doi.org/10.12989/sem.2014.51.5.793
  23. MATLAB and Statistics Toolbox Release (2012b), The MathWorks, Inc., Natick, Massachusetts, United States.
  24. Na, K. and Kim, J.H. (2010), "Volume fraction optimization for step-formed functionally graded plates considering stress and critical temperature", Compos. Struct., 92, 1283-1290. https://doi.org/10.1016/j.compstruct.2009.11.004
  25. Na, K. and Kim, J.H. (2009), "Volume fraction optimization of functionally graded composite panels for stress reduction and critical temperature", Finite Elem. Anal. Des., 45, 845-851. https://doi.org/10.1016/j.finel.2009.06.023
  26. Nemat-Alla, M. (2003), "Reduction of thermal stresses by developing two dimensional functionally graded materials", Int. J. Solid. Struct., 40(26), 7339-56. https://doi.org/10.1016/j.ijsolstr.2003.08.017
  27. Nie, G.J., Zhong, Z. and Batra, R.C. (2011), "Material tailoring for functionally graded hollow cylinders and spheres", Compos. Sci. Tech., 71, 666-673. https://doi.org/10.1016/j.compscitech.2011.01.009
  28. Rao Singiresu, S. (2009), Engineering Optimization Theory and Practice, Willy.
  29. Santare, M.H. and Lambros, J. (2000), "Use of a graded finite element to model the behavior of nonhomogeneous materials", J. Appl. Mech., 67(4), 819-822. https://doi.org/10.1115/1.1328089
  30. Sivanandam, S.N. and Deepa, S.N. (2008), Introduction to Genetic Algorithms, Springer, Berlin Heidelberg New York.
  31. Takezawa, A., Yoon, G.H., Jeong, S.H. and Kitamura, M. (2014), "Structural topology optimization with strength and heat conduction constraints", Comput. Meth. Appl. Mech. Eng., 276, 341-361. https://doi.org/10.1016/j.cma.2014.04.003
  32. Takezawa, A and Kitamura, M. (2012), "Geometrical design of thermoelectric generators based on topology optimization", Int. J. Numer. Meth. Eng., 90, 1363-1392. https://doi.org/10.1002/nme.3375
  33. Turteltaub, S. (2002), "Functionally graded materials for prescribed field evolution", Comput. Meth. Appl. Mech. Eng., 191, 2283-2296. https://doi.org/10.1016/S0045-7825(01)00408-X
  34. Turteltaub, S. (2002), "Optimal control and optimization of functionally graded materials for thermomechanical processes", Int. J. Solid. Struct., 39, 3175-3197. https://doi.org/10.1016/S0020-7683(02)00243-3
  35. Vel, S.S. and Pelletier, J.L. (2007), "Multi-objective optimization of functionally graded thick shells for thermal loading", Compos. Struct., 81, 386-400. https://doi.org/10.1016/j.compstruct.2006.08.027

피인용 문헌

  1. Free vibration analysis of composite cylindrical shells with non-uniform thickness walls vol.20, pp.5, 2016, https://doi.org/10.12989/scs.2016.20.5.1087
  2. Material optimization of functionally graded heterogeneous cylinder for wave propagation vol.50, pp.25, 2016, https://doi.org/10.1177/0021998315622051
  3. Thermo mechanical analysis of a ceramic coated piston used in a diesel engine vol.21, pp.2, 2016, https://doi.org/10.12989/scs.2016.21.2.429
  4. Mechanical stress reduction in a pressurized 2D-FGM thick hollow cylinder with finite length vol.153, 2017, https://doi.org/10.1016/j.ijpvp.2017.05.007
  5. Nonlinear size-dependent vibration behavior of graphene nanoplate considering surfaces effects using a multiple-scale technique pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1494870
  6. Effect of magnetic-thermal field on nonlinear wave propagation of circular nanoplates vol.33, pp.17, 2015, https://doi.org/10.1080/09205071.2019.1677271
  7. Architected functionally graded porous lattice structures for optimized elastic-plastic behavior vol.234, pp.8, 2015, https://doi.org/10.1177/1464420720923004
  8. Mechanical performance of additively manufactured uniform and graded porous structures based on topology-optimized unit cells vol.235, pp.9, 2021, https://doi.org/10.1177/0954406220947119