120 強制熱対流場における多目的形状最適化

抄録

This paper presents a numerical solution to multipurpose shape optimization problems of steady heat-convection fields. In previous study, it has been dealt with a shape optimization problem for total dissipation 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, multipurpose shape optimization problem using normalized objective functional is formulated for the total dissipation energy minimization problem and the temperature distribution prescribed problem in steady heat-convection fields. Shape gradient of the multipurpose shape optimization problem was derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping was carried out by the traction method proposed as an approach to solving shape optimization problems. The validity of proposed method was confirmed by results of 2D numerical analysis.