The paper proposes a heat-flux based approach to optimize build orientation and topology simultaneously for self-supported enclosed voids in additive manufacturing. The enclosed overhangs that require supports in additive manufacturing are removed from the optimized design by constraining the maximum temperature of a pseudo heat conduction problem. In the pseudo problem, heat flux is applied on the non-self-supported open and enclosed surfaces. Since the density-based topology optimization involves no explicit boundary representation, we impose such surface slope dependent heat flux through a domain integral of a Heaviside projected density gradient. In addition, the solid materials and the void materials in the pseudo problem are assumed to be thermally insulating and conductive, respectively. As such, heat flux on the open surfaces can be successfully conducted to external heat sink through the void (or conductive) materials. However, heat flux on the non-self-supported enclosed surfaces is isolated by the solid (or insulating) materials and thus leads to locally high temperature. Hence, by limiting the maximum temperature of the pseudo problem, self-supported enclosed voids can be achieved, and the slope of the open surfaces would not be affected. Due to the differentiability of the heat flux loading in the pseudo problem, the calculated temperature and constraint on it are differentiable to both the build orientation and the density field. Numerical examples on 2D and 3D linear elasticity problems are presented to demonstrate the validity and effectiveness of the proposed approach in the design of self-supported enclosed voids.

该论文提出了一种基于热通量的方法，可以同时优化增材制造中自支撑封闭空隙的构建方向和拓扑结构。通过限制伪热传导问题的最高温度，在增材制造中需要支撑的封闭悬垂从优化设计中移除。在伪问题中，热通量应用于非自支撑的开放和封闭表面。由于基于密度的拓扑优化不涉及明确的边界表示，我们通过 Heaviside 投影密度梯度的域积分来施加这种依赖于表面坡度的热通量。此外，伪问题中的固体材料和空隙材料分别被假定为绝热和导电。像这样，开放表面上的热通量可以通过空隙（或导电）材料成功地传导到外部散热器。然而，非自支撑封闭表面上的热通量被固体（或绝缘）材料隔离，从而导致局部高温。因此，通过限制伪问题的最高温度，可以实现自支撑的封闭空隙，并且开放曲面的斜率不会受到影响。由于伪问题中热通量载荷的可微性，计算出的温度和对它的约束对于构建方向和密度场都是可微的。给出了 2D 和 3D 线性弹性问题的数值例子，以证明所提出的方法在自支撑封闭空隙设计中的有效性和有效性。