Concurrent topology optimization for minimization of total mass considering load-carrying capabilities and thermal insulation simultaneously
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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.
KeywordsConcurrent design Topology optimization Homogenization Thermal insulation Nodal displacement Independent continuous mapping method
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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