多组件结构系统布局拓扑优化中处理组件干涉约束的惩罚函数方法

doi:10.7527/S1000-6893.2016.0137

Abstract

Abstract:

There are an amount of overlap constraints in the integrated layout and topology optimization design of a multi-component system containing tens of components. The integrated layout and topology optimization design of multi-component systems containing varieties of components are discussed in this paper. The finite-circle method (FCM) based penalty function is applied to deal with the overlap constraints among different components. A combined penalty function consisting of compliance and overlap constraints functions is chosen as the new objective. The gradient based optimization algorithm is implemented to maximize the stiffness of the system involving hundreds of overlap constraints, a total of tens of different components. Clear configurations of structure and non-overlapping positions of components are obtained in the simultaneous integrated layout and topology optimization deign. The optimized designs have shown the validity and efficiency of the proposed penalty function in dealing with overlap constraints in the integrated layout and topology optimization design of multi-component systems.

Key words: topology optimization, multi-component system, combined penalty function, overlap constraint, finite-circle method

CLC Number:

V214.19

ZHU Jihong, GUO Wenjie, ZHANG Weihong, HE Fei. A penalty function based method for dealing with overlap constraints in integrated layout and topology optimization design of multi-component systems[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(12): 3721-3733.

References

[1] CHICKERMANE H, GEA H C. Design of multi-component structural systems for optimal layout topology and joint locations[J]. Engineering with Computers, 1997, 13(4):235-243.
[2] LI Q, STEVEN G P, XIE Y M. Evolutionary structural optimization for connection topology design of multi-component systems[J]. Engineering Computations, 2001, 18(3/4):460-479.
[3] MA Z D, KIKUCHI N, PIERRE C, et al. Multidomain topology optimization for structural and material designs[J]. Journal of Applied Mechanics, 2006, 73(4):565-573.
[4] ZHU J H, ZHANG W H, BECHERS P. Integrated layout design of multi-component system[J]. International Journal for Numerical Methods in Engineering, 2009, 78(6):631-651.
[5] ZHU J H, ZHANG W H. Coupled design of components layout and supporting structures using shape and topology optimization[C]//Proceedings of the Fourth China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems.[S.l.]:[s.n.], 2006.
[6] ZHU J H, ZHANG W H, BECKERS P, et al. Simultaneous design of components layout and supporting structures using coupled shape and topology optimization technique[J]. Structural and Multidisciplinary Optimization, 2008, 36(1):29-41.
[7] ZHU J H, ZHANG W H. Integrated layout design of sup-ports and structures[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(9):557-569.
[8] 张卫红, 郭文杰, 朱继宏. 部件级多组件结构系统的整体式拓扑布局优化[J]. 航空学报, 2015, 36(8):2662-2669. ZHANG W H, GUO W J, ZHU J H. Integrated layout and topology optimization design of multi-component systems with assembly units[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(8):2662-2669(in Chinese).
[9] MEAGHER D. Geometric modeling using octree encod-ing[J]. Computer Graphics and Image Processing, 1982, 19(2):129-147.
[10] SAMET H, WEBBER R E. Hierarchical data structures and algorithms for computer graphics. I. Fundamentals[J]. IEEE Computer Graphics and Applications, 1988, 8(3):48-68.
[11] MOORE A. The circle tree-A hierarchical structure for efficient storage, access and multi-scale representation of spatial data[C]//14th Annual Colloquium of the Spatial Information Research Centre.[S.l.]:[s.n.], 2002:149-156.
[12] CAMERON S. Approximation hierarchies and S-bounds[C]//Proceedings of the first ACM Symposium on Solid Modeling Foundations and CAD/CAM Applications. New York:ACM, 1991:129-137.
[13] 徐义春, 董方敏, 刘勇, 等. 带平衡约束矩形布局优化问题的遗传算法[J]. 模式识别与人工智能, 2010, 23(6):794-800. XU Y C, DONG F M, LIU Y, et al. Genetic algorithm for rectangle layout optimization with equilibrium constraints[J]. Pattern Recognition and Artificial Intelligence, 2010, 23(6):794-800(in Chinese).
[14] 黎自强, 田茁君, 王奕首, 等. 求解平衡约束圆形Packing问题的快速启发式并行蚁群算法[J]. 计算机研究与发展, 2012, 49(9):1899-1909. LI Z Q, TIAN Z J, WANG Y S, et al. A fast heuristic parallel ant colony algorithm for circles packing problem with equilibrium constraints[J]. Journal of Computer Research and Development, 2012, 49(9):1899-1909(in Chinese).
[15] TENG H, SUN S, LIU D, et al. Layout optimization for the objects located within a rotating vessel-A three-dimensional packing problem with behavioral constraints[J]. Computers & Operations Research, 2001, 28(6):521-535.
[16] WANG Y S, TENG H F. Knowledge fusion design method:Satellite module layout[J]. Chinese Journal of Aeronautics, 2009, 22(1):32-42.
[17] ZHANG W H, ZHU J H. A new finite-circle family method for optimal multi-component packing design[C]//WCCM VII.[S.l.]:[s.n.], 2006.
[18] GAO H H, ZHU J H, ZHANG W H, et al. An improved adaptive constraint aggregation for integrated layout and topology optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 289:387-408.
[19] 单鹏. 镶嵌多个部件的结构拓扑优化设计[D]. 大连:大连理工大学, 2008:33-34. SHAN P. Optimal embedding objects in the topology de-sign of structure[D]. Dalian:Dalian University of Technology, 2008:33-34(in Chinese).
[20] KANG Z, WANG Y. Integrated topology optimization with embedded movable holes based on combined description by material density and level sets[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 255:1-13.
[21] COURANT R. Variational methods for the solution of problems of equilibrium and vibrations[J]. Bulletin of the American Mathematical Society, 1943, 49:1-23.
[22] FIACCO A V, MCCORMICK G P. Extensions of SUMT for nonlinear programming:Equality constraints and extrapolation[J]. Management Science, 1966, 12(11):816-828.
[23] CHEN Y L, HE P L, ZHANG Y H. Combining penalty function with modified chicken swarm optimization for constrained optimization[C]//First International Conference on Information Sciences, Machinery, Materials and Energy. Pairs:Atlantis Press, 2015:1899-1907.
[24] HUANG X X, YANG X Q, TEO K L. Convergence analysis of a class of penalty methods for vector optimization problems with cone constraints[J]. Journal of Global Optimization, 2006, 36(4):637-652.
[25] JAYSWAL A, CHOUDHURY S. Convergence of exponential penalty function method for multiobjective fractional programming problems[J]. Ain Shams Engineering Journal, 2014, 5(4):1371-1376.
[26] YU C, TEO K L, BAI Y. An exact penalty function method for nonlinear mixed discrete programming problems[J]. Optimization Letters, 2013, 7(1):23-38.
[27] ZHU J H, GAO H H, ZHANG W H, et al. A multi-point constraints based integrated layout and topology optimization design of multi-component systems[J]. Structural and Multidisciplinary Optimization, 2014, 51(2):397-407.
[28] 何坚勇. 最优化方法[M]. 北京:清华大学出版社, 2007:349-416. HE J Y. Optimization methods[M]. Beijing:Tsinghua University Press, 2007:349-416(in Chinese).

A penalty function based method for dealing with overlap constraints in integrated layout and topology optimization design of multi-component systems

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