Combination of Isogeometric analysis and level-set method in topology optimization of heat-conduction systems

In this paper, an isogeometrical approach for topology optimization in two-dimensional heat-transfer problems, including a concentrated heat flow and uniformly distributed heat generation has been developed using the level-set method and reaction-diffusion equation for the evolution of the design variables. The NURBS surface illustrates the exact geometry representation and the level sets lead to the identification of topological variation in the NURBS surface. The level-set surface is extended based on the value of the design variables at the control points of the NURBS surface as an implicit dynamic hyper-surface in higher dimension. The same basis functions are employed to approximate the unknown temperatures and geometry modeling. Since the coordinates of the level-set grids are similar to the coordinates of the control point grids, the sensitivity analysis of the control point grids is obtained and used as a velocity field, to evolution the reaction-diffusion equation. Then, any change in the coordinates of the level-set grids is mapped over the physical domain which Is parameterized using NURBS. In the optimization formulation, the heat transfer potential capacity is considered as the objective function. Also, the constraint is the maximum volume fraction of the material. Finally, several numerical examples are presented to demonstrate the optimal topology described in CAD systems and its sensitivity to various loading.