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Topology optimization of thermoelastic structures under transient thermal loads limited to stress constraints

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Abstract

For the optimization design of the thermoelastic structures in transient heat transfer, the commonly used design methods in previous studies which transforms the transient heat transfer into a steady-state heat transfer could result in significant inaccuracy in the analysis and design of the thermoelastic structure. This study presents a topology optimization method for thermoelastic structures under transient thermal loads considering thermal stress constraints to realize the accurate optimization and effective stress control of transient thermoelastic structures. Condensed integrals in the time and space domains are used to approximately represent the maximum temperature and thermal stress. Two optimization models are proposed. One is to minimize the weighted sum of the dimensionless strain energy and the maximum temperature with a material volume constraint, and the other is to minimize the strain energy with constraints on the maximum stress and material volume. The temperature field and elastic responses are obtained by solving the transient thermal conductive equations and thermoelastic equations. The adjoint method is used to derive the sensitivity expressions. Three numerical examples are provided to illustrate the effectiveness and necessity of the proposed method. The results showed that to realize the accurate design of transient thermoelastic structures, it is necessary for the adopted design method to accurately reflect the influence of the transient effects on the structural response, while the method proposed in this paper can achieve this.

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References

  • Alacoque L, Watkins RT, Tamijani AY (2021) Stress-based and robust topology optimization for thermoelastic multi-material periodic microstructures. Comput Methods Appl Mech Eng 379(17):113749

    MATH  Google Scholar 

  • Bendsoe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202

    Google Scholar 

  • Cao X, Wang Y (2016) Optimization of load–carrying and heat–insulating multi–layered thin–walled structures based on bionics using genetic algorithm. Struct Multidisc Optim 53(4):813–824

    Google Scholar 

  • Chen Y, Tao Y, Xu B, Ai S, Fang D (2018) Assessment of thermal-mechanical performance with structural efficiency concept on design of lattice-core thermal protection system. Appl Therm Eng 143:200–208

    Google Scholar 

  • Deaton JD, Grandhi RV (2013a) Stiffening of restrained thermal structures via topology optimization. Struct Multidisc Optim 48(4):731–745

    Google Scholar 

  • Deaton JD, Grandhi RV (2013b) Topology optimization of thermal structures with stress constraints. Schizophr Res 136(2):259–263

    Google Scholar 

  • Deng S, Suresh K (2016) Topology optimization under thermo-elastic buckling. Struct Multidisc Optim 55(5):1–14

    Google Scholar 

  • Deng S, Suresh K (2017) Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensitivity based level-set. Struct Multidisc Optim 56(1):1413–1427

    Google Scholar 

  • Deng S, Suresh K, Joo J (2014) Stress-constrained thermo-elastic topology optimization: a topological sensitivity approach. Asme International Design Engineering Technical Conferences & Computers & Information in Engineering Conference.

  • Desmorat B (2013) Structural rigidity optimization with an initial design dependent stress field. application to thermo-elastic stress loads. Eur J Mech A 37:150–159

    MATH  Google Scholar 

  • Giraldo-Londoño ML, Dalloro L, Paulino GH (2020) Multi-material thermomechanical topology optimization with applications to additive manufacturing: design of main composite part and its support structure. Comput Methods Appl Mech Eng 363:112812

    MATH  Google Scholar 

  • Gogu C, Bapanapalli SK, Haftka RT, Sankar BV (2009) Comparison of materials for integrated thermal protection systems for spacecraft reentry. J Spacecr Rocket 46(3):501–513

    Google Scholar 

  • Hu SB, Chen LP, Zhang Y, Jiang M (2012) Design 3d thermo-mechanical structures with multidisciplinary topology optimization. Adv Mater Res 466–467:1212–1216

    Google Scholar 

  • Hyun J, Kim HA (2021) Level-set topology optimization for effective control of transient conductive heat response using eigenvalue. Int J Heat Mass Transfer 176:121374

    Google Scholar 

  • Kambampati S, Gray JS, Kim HA (2020) Level set topology optimization of structures under stress and temperature constraints. Comput Struct 235:106265

    Google Scholar 

  • Kruijf ND, Zhou S, Li Q, Mai YW (2007) Topological design of structures and composite materials with multiobjectives. Int J Solids Struct 44(22):7092–7109

    MATH  Google Scholar 

  • Leader M K, Kennedy G (2021) Thermoelastic topology optimization using steady-state and transient analysis for stress and thermal performance. AIAA Scitech 2021 Forum.

  • Li Q, Steven GP, Querin OM, Xie YM (2000) Structural topology design with multiple thermal criteria. Eng Comput 17(6):715–734

    MATH  Google Scholar 

  • Li Q, Steven GP, Xie YM (1999) Displacement minimization of thermoelastic structures by evolutionary thickness design. Comput Methods Appl Mech Eng 179(3–4):361–378

    MATH  Google Scholar 

  • Li Q, Steven GP, Xie YM (2001) Thermoelastic topology optimization for problems with varying temperature fields. J Therm Stresses 24(4):347–366

    Google Scholar 

  • Li D, Zhang X, Guan Y, Zhan J (2010) Topology optimization of thermo-mechanical continuum structure. IEEE.

  • Liu XJ, Wang C (2014) Zhou, Y H (2014) Topology optimization of thermoelastic structures using the guide-weight method. Sci China (technol Sci) 57(005):968–979

    Google Scholar 

  • Long K, Wang X, Gu X (2018) Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm. Eng Optim 50:1–17

    MATH  Google Scholar 

  • Luo Y, Sigmund O, Li Q, Liu S (2020) Additive manufacturing oriented topology optimization of structures with self-supported enclosed voids. Compur Methods Appl Mech Eng 372:113385

    MATH  Google Scholar 

  • LuoY LQ, Liu S (2019) Topology optimization of shell-infill structures using an erosion-based interface identification method. Comput Methods Appl Mech Eng 355:94–112

    MATH  Google Scholar 

  • Mao Z, Yan S (2018) Design and analysis of the thermal-stress coupled topology optimization of the battery rack in an auv. Ocean Eng 148:401–411

    Google Scholar 

  • Matsumori T, Kawamoto A, Kondoh T (2019) Topology optimization for thermal stress reduction in power semiconductor module. Struct Multidisc Optim 60(2):2615–2620

    Google Scholar 

  • Meng QQ, Xu B, Wang C, Zhao L (2020) Stress constrained thermo-elastic topology optimization based on stabilizing control schemes. J Therm Stresses 43(8):1040–1068

    Google Scholar 

  • Pauli P, Pedersen Niels L (2012) Interpolation/penalization applied for strength design of 3D thermoelastic structures. Struct Multidisc Optim 45(6):773–786

    MATH  Google Scholar 

  • Pedersen P, Pedersen NL (2010) Strength optimized designs of thermoelastic structures. Struct Multidisc Optim 42(5):681–691

    Google Scholar 

  • Pl A, Ls B, Zhan KA (2020) Multi-material structural topology optimization considering material interfacial stress constraints. Comput Methods Appl Mech Eng 363:1–27

    Google Scholar 

  • Rodrigues H, Fernandes P (1995) A material based model for topology optimization of thermoelastic structures. Int J Numer Meth Eng 38(12):1951–1965

    MATH  Google Scholar 

  • Shi G, Guan C, Quan D, Wu D, Tang L, Gao T (2020) An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing. Chin J Aeronaut 169(04):138–145

    Google Scholar 

  • da Silva GA, Beck AT, Cardoso EL (1998) Topology optimization of continuum structures with stress constraints. Int J Numer Meth Eng 43(8):1453–1478

    Google Scholar 

  • Song L, Gao T, Tang L, Du X, Zhang W (2020) An all-movable rudder designed by thermo-elastic topology optimization and manufactured by additive manufacturing. Comput Struct 243:106405

    Google Scholar 

  • Takalloozadeh M, Yoon GH (2016) Development of pareto topology optimization considering thermal loads. Comput Methods Appl Mech Eng 317(15):554–579

    MATH  Google Scholar 

  • Takezawa A, Yoon GH, Jeong SH, Kobashi M, Kitamura M (2014) Structural topology optimization with strength and heat conduction constraints. Comput Methods Appl Mech Eng 276:341–361

    MATH  Google Scholar 

  • Wei K, Cheng X, Mo F, Wen W, Fang D (2016) Design and analysis of integrated thermal protection system based on lightweight c/sic pyramidal lattice core sandwich panel. Mater Des 111(5):435–444

    Google Scholar 

  • Wu SH, Zhang YC, Liu S (2019) Topology optimization for minimizing the maximum temperature of transient heat conduction structure. Struct Multidisc Optim 60(1):69–82

    Google Scholar 

  • Wu SH, Zhang YC, Liu S (2021) Transient thermal dissipation efficiency based method for topology optimization of transient heat conduction structures. Int J Heat Mass Transf 05(170):121004

    Google Scholar 

  • Xia Q, Wang MY (2008) Topology optimization of thermoelastic structures using level set method. Comput Mech 42(6):837–857

    MATH  Google Scholar 

  • Xie G, Wang Q, Sunden B, Zhang W (2013) Thermomechanical optimization of lightweight thermal protection system under aerodynamic heating. Appl Therm Eng 59(1–2):425–434

    Google Scholar 

  • Xu Q, Li S, Meng Y (2021) Optimization and re-design of integrated thermal protection systems considering thermo-mechanical performance. Appl Sci 11(15):6916

    Google Scholar 

  • Yan J, Cheng GD, Liu L (2006) A uniform optimum material based model for concurrent optimization of thermoelastic structures and materials. Int J Simul Multidisc Des Optim 2:259–266

    Google Scholar 

  • Yan J, Yang S, Duan Z, Yang C (2015) Minimum compliance optimization of a thermoelastic lattice structure with size-coupled effects. J Thermal Stress 38(3):338–357

    Google Scholar 

  • Yang Q, Gao B, Xu Z, Xie W, Meng S (2019) Topology optimisations for integrated thermal protection systems considering thermo-mechanical constraints. Appl Therm Eng 150:995–1001

    Google Scholar 

  • Yang X, Li Y (2013) Topology optimization to minimize the dynamic compliance of a bi-material plate in a thermal environment. Struct Multidisc Optim 47(3):399–408

    MATH  Google Scholar 

  • Yang Q, Meng S, Xie W, Jin H, Xu C, Du S (2017) Effective mitigation of the thermal short and expansion mismatch effects of an integrated thermal protection system through topology optimization. Compos Part B 118(6):149–157

    Google Scholar 

  • Zhan Jin Q (2013) Topology optimization of thermo-mechanical structure using the hybrid celluar automata method. Appl Mech Mater 365–366:111–116

    Google Scholar 

  • Zhang W, Yang J, Xu Y, Gao T (2013) Topology optimization of thermoelastic structures: mean compliance minimization or elastic strain energy minimization. Struct Multidisc Optim 49(3):417–429

    Google Scholar 

  • Zhang S, Yin J, Liu Y, Sha Z, Ma F, Wang Y, Rolfe B (2018) Multiobjective structure topology optimization of wind turbine brake pads considering thermal-structural coupling and brake vibration. Math Probl Eng 10:1–10

    Google Scholar 

  • Zhao SY, Li JJ, Zhang CX, Zhang WJ, Lin X, He XD, Yao YT (2015) Thermo-structural optimization of integrated thermal protection panels with one-layer and two-layer corrugated cores based on simulated annealing algorithm. Struct Multidisc Optim 51(2):479–494

    Google Scholar 

  • Zhu J, Yu LI, Wang F, Zhang W (2020) Shape preserving design of thermo-elastic structures considering geometrical nonlinearity. Struct Multidisc Optim 61(7674):1787–1804

    Google Scholar 

  • Zhu XF, Zhao C, Wang X, Zhou Y, Hu P, Ma ZD (2019) Temperature-constrained topology optimization of thermo-mechanical coupled problems. Eng Optim 51(10):1687–1709

    MATH  Google Scholar 

  • Zhuang C, Xiong Z (2014) A global heat compliance measure based topology optimization for the transient heat conduction problem. Numer Heat Transfer, Part B 65(5):445–471

    Google Scholar 

  • Zhuang C, Xiong ZH (2015) Temperature-constrained topology optimization of transient heat conduction problems. Numer Heat Transfer, Part B 8(4):366–385

    Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the financial support to this work by the National Natural Science Foundation of China (Grant Nos. U1808215, 11972105), the 111 Project (B14013) and the Fundamental Research Funds for the Central Universities of China (DUT21GF101).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Shuai Li, Yongcun Zhang, Shutian Liu & Shuhao Wu

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  1. Shuai Li
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Correspondence to Shutian Liu.

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The results provided in this paper are generated by MATLAB codes developed by the authors. The codes can be available upon request by contacting the corresponding author via email.

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Li, S., Zhang, Y., Liu, S. et al. Topology optimization of thermoelastic structures under transient thermal loads limited to stress constraints. Struct Multidisc Optim 66, 9 (2023). https://doi.org/10.1007/s00158-022-03406-7

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