The automatic optimal design of feeding system in the shape casting process is considered in the present work. In fact, the goal is to find the optimal position, size, shape, and topology of risers in the shape casting process. This problem is formulated as a minimum weight topology optimization problem subjected to a non-linear transient PDE and space-time state dependent pointwise constraints. An elegant bi-level reformulation of the optimization problem is introduced which makes it possible to manage the infinite number of design parameters and state constraints efficiently. The computational cost of this algorithm is independent of the number of constraints. The validity and efficiency of the presented method are supported by several examples, from simple benchmarks to complex industrial castings. According to numerical results, the presented approach makes a complete solution to the problem of automatic optimal riser design in the shape casting process.

在目前的工作中，考虑了形状铸造过程中的进料系统的自动优化设计。实际上，目标是在形状铸造过程中找到冒口的最佳位置，大小，形状和拓扑。该问题被公式化为最小加权拓扑优化问题，该问题受到非线性瞬态PDE和时空状态相关的点状约束的约束。引入了对优化问题的优雅的双层重构，这使得有可能有​​效地管理无限数量的设计参数和状态约束。该算法的计算成本与约束的数量无关。从简单的基准测试到复杂的工业铸件，该示例的有效性和效率得到了多个示例的支持。根据数值结果，