The majority of topology optimization methods for porous infill designs is based on the assumption of deterministic loads. However, in practice, quantities such as positions, weights, and directions of applied loads may change accidentally. Deterministic load-based designs might deliver poor structural performance under loading uncertainties. Such uncertain factors need to be taken into account in topological optimization to seek robust results. This paper presents a novel robust concurrent topology optimization method for the design of uniform/non-uniform porous infills under the accidental change of loads. A combination of moving morphable bars (MMBs) and loading uncertainties is proposed to directly model multiscale structures and seek robust designs. The macro- and microscopic structures can be simultaneously optimized through the minimization of the weighted sum of the expected compliance and standard deviation. The geometries of adaptive geometric components (AGCs) are straightforwardly optimized. The AGCs consist of two classes of geometric components: macroscopic bars describing the overall structure and microscopic bars describing the material microstructures. Automatic mesh-refinement is utilized to enhance computing efficiency. Numerical examples demonstrate that robust porous design can be obtained with only one global volume constraint while the material continuity of neighboring unit cells and the structural porosity can be maintained without additional constraints. The robust designs yield a more robust structural performance along with a smaller standard deviation compared with deterministic porous designs under loading uncertainties.

多孔填充设计的大多数拓扑优化方法都是基于确定性载荷的假设。但是，实际上，诸如位置，重量和所施加负载的方向之类的量可能会意外更改。确定性基于载荷的设计可能会在载荷不确定性下提供较差的结构性能。为了寻求可靠的结果，在拓扑优化中需要考虑这些不确定因素。本文提出了一种新颖的鲁棒并行拓扑优化方法，用于在载荷意外变化下设计均匀/非均匀多孔填充物。提出了结合使用移动可变形钢筋（MMB）和载荷不确定性的方法，以直接对多尺度结构进行建模并寻求可靠的设计。宏观和微观结构可以通过最小化预期柔量和标准偏差的加权总和来同时优化。自适应几何组件（AGC）的几何结构可以直接进行优化。AGC由两类几何组成：描述整体结构的宏观条和描述材料微观结构的微观条。自动网格细化可提高计算效率。数值示例表明，仅通过一个整体体积约束就可以实现鲁棒的多孔设计，而相邻晶胞的材料连续性和结构孔隙率可以保持不变而没有其他约束。