Nonprobabilistic reliability oriented topological optimization for multi-material heat-transfer structures with interval uncertainties
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This study presents a nonprobabilistic reliability-based topology optimization (NRBTO) framework that combines a multi-material interpolation model and interval mathematics to achieve an optimal layout design for heat-transfer structures under unknown but bounded (UBB) uncertainties. In terms of the uncertainty quantification (UQ) issue, the interval dimension-wise method (IDWM) based on set collocation theory is first proposed to effectively determine the bounds of nodal temperature responses. For safety reasons, the interval reliability (IR) index corresponding to the thermal constraint is defined, and then a new design policy, i.e., the strategy of nonprobabilistic reliability oriented topological optimization is established. To circumvent problems of large-scale variable updating in a multi-material topology optimization procedure, theoretical deductions of the design sensitivity analysis are further given based on the adjoint-vector criterion and the chain principle. The validity and feasibility of the developed methodology are eventually demonstrated by several application examples.
KeywordsNonprobabilistic reliability-based topology optimization (NRBTO) Interval mathematics Multi-material heat-transfer structures The interval dimension-wise method (IDWM) The adjoint-vector criterion
The authors would like to thank the National Nature Science Foundation of China (11602012, 11432002), the Pre-research Field Foundation of Equipment Development Department of China (61402100103), the Aeronautical Science Foundation of China (2017ZA51012), and the Defense Industrial Technology Development Program (JCKY2016204B101, JCKY2017601B001) for the financial supports. Besides, the authors wish to express their many thanks to the reviewers for their useful and constructive comments.
- Bae K, Wang S (2013) Reliability-based topology optimization, in: Aiaa/issmo Symposium on Multidisciplinary Analysis and OptimizationGoogle Scholar
- Bendsøe BP, Sigmund O (2003) Topology optimization: theory, methods and applications, springer science and business media, BerlinGoogle Scholar
- Ben-Haim Y, Elishakoff I (1990) Convex models of uncertainty in applied mechanics, ElsevierGoogle Scholar
- Riedi PC 1976 Thermal physics: an introduction to thermodynamics, Statistical Mechanics and Kinetic Theory PalgraveGoogle Scholar
- Tritt TM 2010 Thermal conductivity: theory, properties, and applications, SpringerGoogle Scholar
- Wang L, Liu DL, Yang YW, Wang XJ, Qiu ZP (2017) A novel method of non-probabilistic reliability-based topology optimization corresponding to continuum structures with unknown but bounded uncertainties. Comput Methods Appl Mech EngGoogle Scholar
- L. Wang, Q. Ren, Y. Ma, D. Wu (2018a) Optimal maintenance design-oriented nonprobabilistic reliability methodology for existing structures under static and dynamic mixed uncertainties. IEEE Trans ReliabGoogle Scholar
- Wang L, Xiong C, Wang X, Xu M, Li Y (2018b) A Dimension-wise Method and Its improvement for multidisciplinary interval uncertainty analysis. Appl Math Model, 59Google Scholar
- Wang L, Liang J, Wu D (2018c) A non-probabilistic reliability-based topology optimization (NRBTO) method of continuum structures with convex uncertainties. Struct Multidiscip Optim1–20Google Scholar
- Zhu JH, Zhang WH, Xia L (2015) Topology optimization in aircraft and aerospace structures design, Arch Comp Methods Eng 1–28Google Scholar