渗流问题的拓扑优化

Topology Optimization of Seepage Flow Problems

分析拓扑优化中的密度惩罚函数插值法SIMP(Solid isotropic material with penalization model),将结构力学中的拓扑优化方法应用到渗流问题的拓扑优化设计中,用有限元的方法建立了简单的理想状态下的渗流问题的拓扑优化数学模型,并采用基于剃度法的数值解法-优化准则法(OC系列算法),以设计具有最小能量损耗情况下的流体最佳流动路径的拓扑分布。以一组二维渗流问题为例,说明了该模型的有效性,为渗流问题的优化设计提供了一种有效的新思路和方法。

The SIMP method used in topology optimization is analyzed.The topology optimization method is applied into the topology optimization design of seepage flow.The finite element method is used to model the simple flow problems under the ideal conditions.And the optimization problem is solved with a gradient-based math-programming algorithm（OC） that is driven by analytical sensitivities.The topology optimization model for seepage flow is established,which is used to minimize the energy dissipation in the system and find the optimal flow route.Several two-dimensional examples were tested.The results show the model is effective.A new approach for the design of seepage structure is presented.