In practical engineering problems, there exists a class of engineering structures sustaining distributed force. To satisfy the requirement of the stiffness design for this kind of structure, a new topological design formulation is proposed to restrict the deflection on the load-bearing surface. The KS aggregation function is applied to integrate a mass of the displacement constraints on load-bearing surface into one single constraint. The corresponding adjoin equation and sensitivity expressions are conducted. Following the construction of the independent continuous mapping method, the explicit expressions of the objective function and constraint function are obtained by first-order and second-order Taylor expansion. Consequently, the optimization problem is transformed into a series of standard quadratic programs, which can be solved efficiently and robustly using the sequential quadratic programming. The feasibility and effectiveness of the proposed method are then verified by 2D and 3D numerical examples. The optimized results clearly demonstrate that the proposed formulation and corresponding optimization algorithm can effectively control the maximum deflection of local region.
LONG Kai
,
CHEN Zhuo
,
GU Chunlu
,
WANG Xuan
. Structural topology optimization method with maximum displacement constraint on load-bearing surface[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020
, 41(7)
: 223577
-223577
.
DOI: 10.7527/S1000-6893.2019.23577
[1] MAUTE K, SIGMUND O. Topology optimization approaches[J]. Structural and Multidisciplinary Optimization, 2013, 48(6):1-25.
[2] DEATON J D, GRANDHI R V. A survey of structural and multidisciplinary continuum topology optimization:Post 2000[J]. Structural and Multidisciplinary Optimization, 2014, 49(1):1-38.
[3] ZHU J, ZHANG W, XIA L. Topology optimization in aircraft and aerospace structures[J]. Archives of Computational Methods in Engineering, 2016, 23(4):595-622.
[4] RONG J H, YI J H. A structural topological optimization method for multi-displacement constraints and any initial topology configuration[J]. Acta Mechanica Sinica, 2010, 26(5):735-744.
[5] 俞燎宏, 荣见华, 唐承铁, 等. 基于可行域调整的多相材料结构拓扑优化设计[J]. 航空学报, 2018, 39(9):222023. YU L H, RONG J H, TANG C T, et al. Multi-phase material structural topology optimization design based on feasible domain adjustment[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(9):222023(in Chinese).
[6] HUANG X, XIE Y M. Evolutionary topology optimization of continuum structures with an additional displacement constraint[J]. Structural and Multidisciplinary Optimization, 2010, 40(1-6):409-416.
[7] ZUO Z H, XIE Y M. Evolutionary topology optimization of continuum structures with a global displacement control[J]. Computer Aided Design, 2014, 56:58-67.
[8] QIAO H T, LIU S. Topology optimization by minimizing the geometric average displacement[J]. Engineering Optimization 2013, 45(1):1-18.
[9] LI D, KIM I Y. Multi-material topology optimization for practical lightweight design[J]. Structural and Multidisciplinary Optimization, 2018, 58(3):1081-1094.
[10] LONG K, WANG X, GU X. Local optimum in multi-material topology optimization and solution by reciprocal variables[J]. Structural and Multidisciplinary Optimization, 2018, 57(3):1283-1295.
[11] ZHU J, LI Y, ZHANG W, et al. Shape preserving design with structural topology optimization[J]. Structural and Multidisciplinary Optimization, 2016, 53:893-906.
[12] LI Y, ZHU J, ZHANG W, et al. Structural topology optimization for directional deformation behavior design with orthotropic artificial weak element method[J]. Structural and Multidisciplinary Optimization, 2018, 57(3):1251-1266.
[13] LI Y, ZHU J, WANG F, et al. Shape preserving design of geometrically nonlinear structures using topology optimization[J]. Structural and Multidisciplinary Optimization, 2019, 59(4):1033-1051.
[14] CASTRO M S, SILVA O M, LENZI A, et al. Shape preserving design of vibrating structures using topology optimization[J]. Structural and Multidisciplinary Optimization, 2018, 58(3):1109-1119.
[15] 隋允康. 建模变换优化-结构综合方法新进展[M]. 大连:大连理工大学出版社,1996. SUI Y K. Modelling, transformation and optimization-new developments of structural synthesis method[M]. Dalian:Dalian University of Technology Press, 1996(in Chinese).
[16] 隋允康,叶红玲. 连续体结构拓扑优化的ICM方法[M]. 北京:科学出版社,2013. SUI Y K, YE H L. Continuum topology optimization methods ICM[M]. Beijing:Science Press, 2013(in Chinese).
[17] SIGMUND O. A 99 line topology optimization code written in Matlab[J]. Structural and Multidisciplinary Optimization, 2001, 21(2):120-127.
[18] FLEURY C, BRAIBANT V. Structural optimization:A new dual method using mixed variables[J]. International Journal for Numerical Methods in Engineering, 1986, 23:409-428.
[19] SVANBERG K. The method of moving asymptotes-a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24:359-373.
[20] BRUYNEEL M, DUYSINX P, FLEURY C. A family of MMA approximations for structural optimization[J]. Structural and Multidisciplinary Optimization, 2002, 24(4):263-276.
[21] CHENG G D, GUO X. ε-relaxed approach in structural topology optimization[J]. Structural Optimization, 1997, 13(4):258-266.
[22] DUYSINX P, BENDSE M P. Topology optimization of continuum structures with local stress constraints[J]. International Journal for Numerical Methods in Engineering, 1998, 43(8):1453-1478.
[23] YANG D, LIU H, ZHANG W, et al. Stress-constrained topology optimization based on maximum stress measures[J]. Computers and Structures, 2018, 198:23-29.
[24] LONG K, WANG X, LIU H. Stress-constrained topol ogy optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming[J]. Structural and Multidisciplinary Optimization, 2019, 59(5):1747-1759.
[25] 龙凯,谷先广, 王选. 基于多相材料的连续体结构动态轻量化设计方法[J]. 航空学报, 2017, 38(10):221022. LONG K, GU X G, WANG X. Lightweight design method for continuum structure under vibration using multiphase materials[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(10):221022(in Chinese).
CJA