強制熱対流場における多目的形状最適化

概要

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This paper presents a numerical solution to multi-objective shape optimization problems of steady heat-convection fields. In previous study, it has been dealt with a shape optimization problem for total dissipated energy minimization in the domain of a viscous flow field and a shape determination problem of temperature distribution prescribed problem in sub-domains of heat-convection fields. In this study, a multi-objective shape optimization problem using normalized objective functional is formulated for the total dissipated energy minimization problem and the temperature distribution prescribed problem in steady heat-convection fields. In addition, another multi-objective shape optimization problem is formulated for the temperature distribution prescribed problem, while the total dissipated energy is constrained to less than a desired value, in the steady forced heat-convection fields. Shape gradients of these multi-objective shape optimization problems are derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the traction method proposed as an approach to solving shape optimization problems. The validity of proposed method is confirmed by results of 2D numerical analysis.
一般社団法人日本機械学会の論文