This paper studies additive manufacturing oriented structural topology optimization with SIMP approach and aims at 3D high-resolution printable structural topology design with overhang and horizontal minimum length control for minimum compliance.

To start with, we construct a hyperplane in ${ℝ}^4$ by fitting a local element density distribution in the 18 Elements Scheme, use its gradient to estimate the overhang angle, the directional-dependent overhang angle and formulate the corresponding constraints. Next, we propose a Horizontal Square Scheme and four support sets around the concerned element. The horizontal minimum length is controlled by forbidding the concerned element’s density to be larger than the average density of the elements in one of the support sets. By combining these two constraints, the hanging feature is well suppressed.

A new implementation scheme with an improved weight function is proposed to meet these element wise AM constraints well. To get high resolution structural boundaries with low computational efforts, this paper applies the multiresolution topology optimization (MTOP) method.

The structural TO problem is solved by MMA. A number of numerical examples and AM experiments show the effectiveness of this method. The present approach works efficiently when the building direction is in slight misalignment with the vertical direction.

本文使用SIMP方法研究面向增材制造的结构拓扑优化，并针对具有悬垂和水平最小长度控制以实现最小顺应性的3D高分辨率可打印结构拓扑设计。

首先，我们在 ${ℝ}^4$通过在18 Elements方案中拟合局部元素密度分布，使用其梯度来估算悬垂角，方向相关的悬垂角并制定相应的约束条件。接下来，我们提出了一个“水平正方形方案”，并在相关元素周围设置了四个支撑集。通过禁止相关元素的密度大于支撑组之一中元素的平均密度，可以控制水平最小长度。通过结合这两个约束，可以很好地抑制悬挂特征。

提出了一种具有改进权重函数的新实现方案，以很好地满足这些逐元素AM约束。为了以较低的计算量获得高分辨率的结构边界，本文采用了多分辨率拓扑优化（MTOP）方法。

MMA解决了结构化TO问题。大量数值示例和AM实验证明了该方法的有效性。当建筑物方向与垂直方向略有偏离时，本方法可以有效地工作。