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Acta Mechanica Sinica

, Volume 34, Issue 2, pp 315–326 | Cite as

Concurrent topology optimization for minimization of total mass considering load-carrying capabilities and thermal insulation simultaneously

  • Kai Long
  • Xuan Wang
  • Xianguang Gu
Research Paper

Abstract

The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously. Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the load-carrying capabilities and the thermal insulation properties. The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved.

Keywords

Concurrent design Topology optimization Homogenization Thermal insulation Nodal displacement Independent continuous mapping method 

Notes

Acknowledgements

The project was supported by the National Natural Science Foundation of China (Grants 11202078, 51405123) and the Fundamental Research Funds for the Central Universities (Grant 2017MS077). We are thankful for Professor Krister Svanberg for MMA program made freely available for research purposes.

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Beijing Key Laboratory of Energy Safety and Clean UtilizationNorth China Electric Power UniversityBeijingChina
  2. 2.State Key Laboratory for Alternate Electrical Power System with Renewable Energy SourcesNorth China Electric Power UniversityBeijingChina
  3. 3.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering MechanicsDalian University of TechnologyDalianChina
  4. 4.School of Automobile and Traffic EngineeringHefei University of TechnologyHefeiChina

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