ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Topology optimization design of thermoelastic multi-configuration gradient lattice structures
Received date: 2024-03-11
Revised date: 2024-05-15
Accepted date: 2024-06-07
Online published: 2024-06-17
Supported by
National Natural Science Foundation of China(52375245)
This paper presents a topology optimization method for the design of thermoelastic multi-configuration gradient lattice structures. Specifically, the structure is assumed to consist of several spatially varying lattice substructures. For each substructure, two design variables are considered: a quasi-discrete variable, which determines its spatial topological layout; a continuous density variable, which determines its material usage. For the lattice substructures with predefined geometric topology, a series of samples of lattice substructures with fixed configuration and variable density are obtained by varying their feature sizes, and static condensation of the substructures is performed to reduce the number of degrees of freedom. On this basis, the corresponding data-driven interpolation model is built to explicitly correlate the density variable with the thermoelastic equivalent constitutive behavior of the lattice substructure. Furthermore, to realize the hybrid layout design of multi-configuration lattice substructures, a multi-material interpolation model for quasi-discrete lattice selection variables is constructed. The numerical example results show that the design method is able to utilize the gradient lattice structures to balance the mechanical deformation caused by temperature loading, which in turn effectively enhances the thermo-mechanical load carrying capacity of the structure. Moreover, since the gradient lattice structure is modeled based on the substructure method, the geometrical configuration and thermoelastic properties of the whole structure and the lattice structures are coupled. Compared with the design method based on the homogenization theory, the design scheme proposed in this paper does not require additional geometric post-processing, effectively avoiding the performance deviation between design and fabrication.
Qi WANG , Long WU , Zhen LIU , Jianxia LIU , Liang XIA . Topology optimization design of thermoelastic multi-configuration gradient lattice structures[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2024 , 45(23) : 230367 -230367 . DOI: 10.7527/S1000-6893.2024.30367
1 | BENDS?E M P, KIKUCHI N. Generating optimal topologies in structural design using a homogenization method[J]. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197-224. |
2 | BENDS?E M P. Optimal shape design as a material distribution problem[J]. Structural Optimization, 1989, 1(4): 193-202. |
3 | ZHOU M, ROZVANY G. The COC algorithm, Part II: Topological, geometrical and generalized shape optimization[J]. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1-3): 309-336. |
4 | BENDS?E M P, SIGMUND O. Material interpolation schemes in topology optimization[J]. Archive of Applied Mechanics, 1999, 69(9): 635-654. |
5 | RODRIGUES H, GUEDES J M, BENDS?E M P. Hierarchical optimization of material and structure[J]. Structural and Multidisciplinary Optimization, 2002, 24(1): 1-10. |
6 | ZHANG W H, SUN S P. Scale-related topology optimization of cellular materials and structures[J]. International Journal for Numerical Methods in Engineering, 2006, 68(9): 993-1011. |
7 | XIA L, BREITKOPF P. Recent advances on topology optimization of multiscale nonlinear structures[J]. Archives of Computational Methods in Engineering, 2017, 24(2): 227-249. |
8 | WU Z J, XIA L, WANG S T, et al. Topology optimization of hierarchical lattice structures with substructuring[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 345: 602-617. |
9 | LIU Z, XIA L, XIA Q, et al. Data-driven design approach to hierarchical hybrid structures with multiple lattice configurations[J]. Structural and Multidisciplinary Optimization, 2020, 61(6): 2227-2235. |
10 | THOMSEN J. Topology optimization of structures composed of one or two materials[J]. Structural Optimization, 1992, 5(1): 108-115. |
11 | SIGMUND O, TORQUATO S. Design of materials with extreme thermal expansion using a three-phase topology optimization method[J]. Journal of the Mechanics and Physics of Solids, 1997, 45(6): 1037-1067. |
12 | STEGMANN J, LUND E. Discrete material optimization of general composite shell structures[J]. International Journal for Numerical Methods in Engineering, 2005, 62(14): 2009-2027. |
13 | GAO T, ZHANG W H. A mass constraint formulation for structural topology optimization with multiphase materials[J]. International Journal for Numerical Methods in Engineering, 2011, 88(8): 774-796. |
14 | SANDERS E D, AGUILó M A, PAULINO G H. Multi-material continuum topology optimization with arbitrary volume and mass constraints[J]. Computer Methods in Applied Mechanics and Engineering, 2018, 340: 798-823. |
15 | RODRIGUES H, FERNANDES P. A material based model for topology optimization of thermoelastic structures[J]. International Journal for Numerical Methods in Engineering, 1995, 38(12): 1951-1965. |
16 | LI Q, STEVEN G P, XIE Y M. Displacement minimization of thermoelastic structures by evolutionary thickness design[J]. Computer Methods in Applied Mechanics and Engineering, 1999, 179(3-4): 361-378. |
17 | LI Q, STEVEN G P, XIE Y M. Thermoelastic topology optimization for problems with varying temperature fields[J]. Journal of Thermal Stresses, 2001, 24(4): 347-366. |
18 | XIA Q, WANG M Y. Topology optimization of thermoelastic structures using level set method[J]. Computational Mechanics, 2008, 42(6): 837-857. |
19 | 孙士平, 张卫红. 热弹性结构的拓扑优化设计[J]. 力学学报, 2009, 41(6): 878-887. |
SUN S P, ZHANG W H. Topology optimal design of thermo-elastic structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(6): 878-887 (in Chinese). | |
20 | STOLPE M, SVANBERG K. An alternative interpolation scheme for minimum compliance topology optimization[J]. Structural and Multidisciplinary Optimization, 2001, 22(2): 116-124. |
21 | GAO T, ZHANG W H. Topology optimization involving thermo-elastic stress loads[J]. Structural and Multidisciplinary Optimization, 2010, 42(5): 725-738. |
22 | PEDERSEN P, PEDERSEN N L. Strength optimized designs of thermoelastic structures[J]. Structural and Multidisciplinary Optimization, 2010, 42(5): 681-691. |
23 | ZHANG W H, YANG J G, XU Y J, et al. Topology optimization of thermoelastic structures: Mean compliance minimization or elastic strain energy minimization[J]. Structural and Multidisciplinary Optimization, 2014, 49(3): 417-429. |
24 | XU B, HUANG X, ZHOU S W, et al. Concurrent topological design of composite thermoelastic macrostructure and microstructure with multi-phase material for maximum stiffness[J]. Composite Structures, 2016, 150: 84-102. |
25 | 贾娇, 龙凯, 程伟. 稳态热传导下基于多相材料的一体化设计[J]. 航空学报, 2016, 37(4): 1218-1227. |
JIA J, LONG K, CHENG W. Concurrent topology optimization based on multiphase materials under steady thermal conduction[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(4): 1218-1227 (in Chinese). | |
26 | 李信卿, 赵清海, 张洪信, 等. 周期性功能梯度结构稳态热传导拓扑优化设计[J]. 中国机械工程, 2021, 32(19):2348-2356. |
LI X Q, ZHAO Q H, ZHANG H X, et al. Steady-state heat conduction topology optimization design for periodic functional gradient structures [J]. China Mechanical Engineering, 2021, 32(19):2348-2356 (in Chinese). | |
27 | 李信卿, 赵清海, 龙凯, 等. 考虑瞬态效应的周期性多材料传热结构拓扑优化[J]. 航空学报, 2022, 43(12): 425964. |
LI X Q, ZHAO Q H, LONG K, et al. Topology optimization of periodic multi-material heat conduction structures considering transient effects[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(12): 425964 (in Chinese). | |
28 | WANG F W, LAZAROV B S, SIGMUND O. On projection methods, convergence and robust formulations in topology optimization[J]. Structural and Multidisciplinary Optimization, 2011, 43(6): 767-784. |
29 | ANDREASSEN E, CLAUSEN A, SCHEVENELS M, et al. Efficient topology optimization in MATLAB using 88 lines of code[J]. Structural and Multidisciplinary Optimization, 2011, 43(1): 1-16. |
30 | SVANBERG K. The method of moving asymptotes—A new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373. |
/
〈 |
|
〉 |