Topology Optimization Of Heat Transfer Structures Under Design-dependent Heat Load

Topology optimization has conceived a tremendous development since its introduction in 1988. Its application has been extended from the mechanical problems to thermal problems and multi-physics problems, etc. In the conventional topology optimization, the load exerted on the structure is fixed during the iterative optimization process. However, in engineering practice, there are some kinds of load, whose location, size and direction are change as the topology changes. Namely, these loads are design-dependent.Based on finite element method, the present paper investigated topology optimization of heat transfer problems under design-dependent heat load with point-wise density method using the COMSOL with MATLAB and MATLAB platform. The contends of this paper are organized as follows:(1) The application of topology optimization in the COMSOL with MATLAB platform is introduced, which includes a detailed description about deriving the sensitity of objective function based on density method with adjoint method on this platform.(2) The influences of uniform heat sources and design-dependent heat sources on topology optimization of heat transfer problems are discussed respectively, including heat conduction problems and fluid-solid conjugate heat transfer problems. The nonlinear heat conduction coefficient of solid material is considered in solid heat conduction problems in order to make the simulation more realistic.(3) The design-dependent heat convection load in heat conduction problems is investigated. The boundaries where the design-dependent heat convection load is act on are not fixed but changing with the topology of structure during optimization iterations. Using the point-wise density method, the boundaries are identified as isolines of material field. In order to address the slender feature frenquently appeared in thermal problems, the central symbol method from the field of computer graphics is introduced to identify the isolines. The sensitivity of the objective function is derived semi-analytically, which improve the computational efficiency significantly compared with the finite difference method. Numerical examples are presented to show the avalibility of the proposed method.