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Thermoelastic topology optimization for structures with temperature-dependent material properties

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Abstract

A thermoelastic topology optimization is proposed for structures with temperature-dependent material properties. Different from the common assumption of constant material properties in traditional thermoelastic topology optimization, the temperature-dependent material properties related to mechanical and thermal fields are taken into account. The non-uniform temperature distribution of the structure is a design dependent field that may vary during the optimization, and the nonlinear heat transfer analysis is considered according to the large temperature gradient. Based on these, a thermoelastic topology optimization model considering temperature-dependent material properties is formulated. The sensitivities with respect to the design variables are derived and the Method of Moving Asymptotes (MMA) algorithm is used to update the topological design variables. A cooperation platform based on MATLAB and ABAQUS is developed for the proposed thermoelastic topology optimization method to deal with problems with arbitrary domains for the design of complex engineering structures. Several typical numerical examples are given to illustrate the effectiveness of the proposed method and show the important influence of the temperature-dependent material properties.

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References

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

    Article  Google Scholar 

  2. Xie Y M, Steven G P. A simple evolutionary procedure for structural optimization. Comput Struct, 1993, 49: 885–896

    Article  Google Scholar 

  3. Huang X, Xie Y M. Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des, 2007, 43: 1039–1049

    Article  Google Scholar 

  4. Wang M Y, Wang X M, Guo D M. A level set method for structural topology optimization. Comput Methods Appl Mech Eng, 2003, 192: 227–246

    Article  MathSciNet  MATH  Google Scholar 

  5. Guo X, Zhang W, Zhang J, et al. Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons. Comput Methods Appl Mech Eng, 2016, 310: 711–748

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhu J H, Zhang W H, Xia L. Topology optimization in aircraft and aerospace structures design. Arch Computat Methods Eng, 2016, 23: 595–622

    Article  MathSciNet  MATH  Google Scholar 

  7. Aage N, Andreassen E, Lazarov B S, et al. Giga-voxel computational morphogenesis for structural design. Nature, 2017, 550: 84–86

    Article  Google Scholar 

  8. Zhang W H, Zhang Z D, Zhu J H, et al. Structural topology optimization: Extensibility and attainability. Sci China Tech Sci, 2014, 57: 1310–1321

    Article  Google Scholar 

  9. Sigmund O, Maute K. Topology optimization approaches. Struct Multidisc Optim, 2013, 48: 1031–1055

    Article  MathSciNet  Google Scholar 

  10. Dbouk T. A review about the engineering design of optimal heat transfer systems using topology optimization. Appl Therm Eng, 2017, 112: 841–854

    Article  Google Scholar 

  11. Rodrigues H, Fernandes P. A material based model for topology optimization of thermoelastic structures. Int J Numer Meth Eng, 1995, 38: 1951–1965

    Article  MathSciNet  MATH  Google Scholar 

  12. Gao T, Zhang W. Topology optimization involving thermo-elastic stress loads. Struct Multidisc Optim, 2010, 42: 725–738

    Article  MathSciNet  MATH  Google Scholar 

  13. Yang X, Li Y. Topology optimization to minimize the dynamic compliance of a bi-material plate in a thermal environment. Struct Multidisc Optim, 2013, 47: 399–408

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang L, Zhang H W, Wu J, et al. A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials. Acta Mech Sin, 2016, 32: 481–490

    Article  MathSciNet  MATH  Google Scholar 

  15. Li H, Li H, Xiao M, et al. Robust topology optimization of thermo-elastic metamaterials considering hybrid uncertainties of material property. Compos Struct, 2020, 248: 112477

    Article  Google Scholar 

  16. Zhang W, Yang J, Xu Y, et al. Topology optimization of thermoelastic structures: Mean compliance minimization or elastic strain energy minimization. Struct Multidisc Optim, 2014, 49: 417–429

    Article  MathSciNet  Google Scholar 

  17. Xu Z, Zhang W, Gao T, et al. A B-spline multi-parameterization method for multi-material topology optimization of thermoelastic structures. Struct Multidisc Optim, 2020, 61: 923–942

    Article  MathSciNet  Google Scholar 

  18. Zhu J, Li Y, Wang F, et al. Shape preserving design of thermo-elastic structures considering geometrical nonlinearity. Struct Multidisc Optim, 2020, 61: 1787–1804

    Article  MathSciNet  Google Scholar 

  19. Song L, Gao T, Tang L, et al. An all-movable rudder designed by thermo-elastic topology optimization and manufactured by additive manufacturing. Comput Struct, 2021, 243: 106405

    Article  Google Scholar 

  20. Xia Q, Wang M Y. Topology optimization of thermoelastic structures using level set method. Comput Mech, 2008, 42: 837–857

    Article  MATH  Google Scholar 

  21. Vermaak N, Michailidis G, Parry G, et al. Material interface effects on the topology optimizationof multi-phase structures using a level set method. Struct Multidisc Optim, 2014, 50: 623–644

    Article  Google Scholar 

  22. Chung H, Amir O, Kim H A. Level-set topology optimization considering nonlinear thermoelasticity. Comput Methods Appl Mech Eng, 2020, 361: 112735

    Article  MathSciNet  MATH  Google Scholar 

  23. Li L. Multiscale topology optimization of thermoelastic structures using the level set method. In: Proceedings of the AIAA Scitech Forum. Orlando, 2020. 2245

  24. Li L, Du Z, Kim H A. Design of architected materials for thermo-elastic macrostructures using level set method. JOM, 2020, 72: 1734–1744

    Article  Google Scholar 

  25. Pedersen P, Pedersen N L. Strength optimized designs of thermo-elastic structures. Struct Multidisc Optim, 2010, 42: 681–691

    Article  Google Scholar 

  26. Deaton J D, Grandhi R V. Stress-based design of thermal structures via topology optimization. Struct Multidisc Optim, 2016, 53: 253–270

    Article  MathSciNet  Google Scholar 

  27. Chin T W. Multimaterial thermoelastic stress-constrained topology optimization of structures with adaptive mesh refinement. In: Proceedings of the Multidisciplinary Analysis and Optimization. Atlanta, 2018. 4054

  28. Alacoque L, Watkins R T, Tamijani A Y. Stress-based and robust topology optimization for thermoelastic multi-material periodic microstructures. Comput Methods Appl Mech Eng, 2021, 379: 113749

    Article  MathSciNet  MATH  Google Scholar 

  29. Du Y, Luo Z, Tian Q, et al. Topology optimization for thermo-mechanical compliant actuators using mesh-free methods. Eng Optimization, 2009, 41: 753–772

    Article  MathSciNet  Google Scholar 

  30. Deng J, Yan J, Cheng G. Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material. Struct Multidisc Optim, 2013, 47: 583–597

    Article  MathSciNet  MATH  Google Scholar 

  31. Correia V M F, Madeira J F A, Araújo A L, et al. Multiobjective optimization of functionally graded material plates with thermo-mechanical loading. Compos Struct, 2019, 207: 845–857

    Article  Google Scholar 

  32. Ogawa S, Yamada T. Topology optimization for transient response problems involving thermoelastic materials. Finite Elem Anal Des, 2022, 201: 103695

    Article  MathSciNet  Google Scholar 

  33. Deng S, Suresh K. Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensitivity based level-set. Struct Multidisc Optim, 2017, 56: 1413–1427

    Article  MathSciNet  Google Scholar 

  34. Hooijkamp E C, van Keulen F. Topology optimization for linear thermo-mechanical transient problems: Modal reduction and adjoint sensitivities. Int J Numer Meth Eng, 2018, 113: 1230–1257

    Article  MathSciNet  Google Scholar 

  35. Meng Q, Xu B, Wang C, et al. Stress constrained thermo-elastic topology optimization based on stabilizing control schemes. J Thermal Stresses, 2020, 43: 1040–1068

    Article  Google Scholar 

  36. Fang L, Wang X, Zhou H. Topology optimization of thermoelastic structures using MMV method. Appl Math Model, 2022, 103: 604–618

    Article  MathSciNet  MATH  Google Scholar 

  37. Shi G, Guan C, Quan D, et al. An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing. Chin J Aeronaut, 2020, 33: 1252–1259

    Article  Google Scholar 

  38. Meng Z, Guo L, Yıldız A R, et al. Mixed reliability-oriented topology optimization for thermo-mechanical structures with multi-source uncertainties. Eng Comput, 2022, 38: 5489–5505

    Article  Google Scholar 

  39. Zheng J, Ding S, Jiang C, et al. Concurrent topology optimization for thermoelastic structures with random and interval hybrid uncertainties. Numer Meth Eng, 2022, 123: 1078–1097

    Article  MathSciNet  MATH  Google Scholar 

  40. Matsumori T, Kawamoto A, Kondoh T. Topology optimization for thermal stress reduction in power semiconductor module. Struct Multidisc Optim, 2019, 60: 2615–2620

    Article  Google Scholar 

  41. Yang Q, Gao B, Xu Z, et al. Topology optimisations for integrated thermal protection systems considering thermo-mechanical constraints. Appl Therm Eng, 2019, 150: 995–1001

    Article  Google Scholar 

  42. Kruijf N, Zhou S, Li Q, et al. Topological design of structures and composite materials with multiobjectives. Int J Solids Struct, 2007, 44: 7092–7109

    Article  MATH  Google Scholar 

  43. Krysko A V, Awrejcewicz J, Pavlov S P, et al. Topological optimization of thermoelastic composites with maximized stiffness and heat transfer. Compos Part B-Eng, 2019, 158: 319–327

    Article  Google Scholar 

  44. Zhang J, Liu T, Wang S, et al. Thermomechanical coupling multi-objective topology optimization of anisotropic structures based on the element-free Galerkin method. Eng Optimization, 2022, 54: 428–449

    Article  MathSciNet  MATH  Google Scholar 

  45. Zhu X, Zhao C, Wang X, et al. Temperature-constrained topology optimization of thermo-mechanical coupled problems. Eng Optimization, 2019, 51: 1687–1709

    Article  MathSciNet  MATH  Google Scholar 

  46. Kambampati S, Gray J S, Alicia Kim H. Level set topology optimization of structures under stress and temperature constraints. Comput Struct, 2020, 235: 106265

    Article  Google Scholar 

  47. Meng Q, Xu B, Huang C, et al. Topology optimization of thermo-elastic structures considering stiffness, strength, and temperature constraints over a wide range of temperatures. Numer Meth Eng, 2022, 123: 1627–1653

    Article  MathSciNet  MATH  Google Scholar 

  48. Tang L, Gao T, Song L, et al. Topology optimization of nonlinear heat conduction problems involving large temperature gradient. Comput Methods Appl Mech Eng, 2019, 357: 112600

    Article  MathSciNet  MATH  Google Scholar 

  49. Álvarez Hostos J C, Fachinotti V D, Peralta I. Computational design of thermo-mechanical metadevices using topology optimization. Appl Math Model, 2021, 90: 758–776

    Article  MathSciNet  MATH  Google Scholar 

  50. Wang B, Wang G, Shi Y, et al. Stress-constrained thermo-elastic topology optimization of axisymmetric disks considering temperature-dependent material properties. Mech Adv Mater Struct, 2021, 29: 7459–7475

    Article  Google Scholar 

  51. Chen Y, Ye L, Zhang Y X, et al. A multi-material topology optimization with temperature-dependent thermoelastic properties. Eng Optimization, 2021, 54: 2140–2155

    Article  Google Scholar 

  52. Boyer H E, Gall T L. Metals handbook. Version American Society for Metals, 1985

  53. Wang F, Lazarov B S, Sigmund O. On projection methods, convergence and robust formulations in topology optimization. Struct Multidisc Optim, 2011, 43: 767–784

    Article  MATH  Google Scholar 

  54. Xu S, Cai Y, Cheng G. Volume preserving nonlinear density filter based on heaviside functions. Struct Multidisc Optim, 2010, 41: 495–505

    Article  MathSciNet  MATH  Google Scholar 

  55. Li L, Khandelwal K. Volume preserving projection filters and continuation methods in topology optimization. Eng Struct, 2015, 85: 144–161

    Article  Google Scholar 

  56. Svanberg K. The method of moving asymptotes—A new method for structural optimization. Int J Numer Meth Eng, 1987, 24: 359–373

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Chao Jiang.

Additional information

This work was supported by the National Key R&D Program of China (Grant No. 2022YFB3403800) and the National Natural Science Foundation of China (Grant Nos. 52005172, 52207049, and 52235005).

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Zheng, J., Rong, X. & Jiang, C. Thermoelastic topology optimization for structures with temperature-dependent material properties. Sci. China Technol. Sci. 66, 3488–3503 (2023). https://doi.org/10.1007/s11431-023-2458-6

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  • DOI: https://doi.org/10.1007/s11431-023-2458-6

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