Gradient additive manufacturing techniques are capable of implementing multiple materials with graded compositions into the fabrication of a single component. This provides a unique opportunity to control the properties of materials, such as thermal expansion, Young’s modulus, and yield stress, and create a structure that otherwise would be infeasible. To utilize this capability, a density-based topology optimization framework is developed to optimize the spatial distribution of different materials, their interfaces, and the structural layout in order to enhance both the stiffness and the stress. Interpolation schemes to achieve these objectives are proposed, and the three levels of complexities, i.e., multi-material designs, design-dependent thermal loads, and stress constraints, are addressed. The framework is evaluated using three numerical examples, and the optimized stiffness and strength-based topology and material composition are demonstrated. Finally, the single-material and multi-material optimized designs are compared. The results show that the low compliance of the multi-material designs, while satisfying the failure constraint, was either infeasible or was achieved with a significantly higher weight for single-material structures.

梯度增材制造技术能够将具有渐变成分的多种材料应用到单个组件的制造中。这提供了一个独特的机会来控制材料的特性，例如热膨胀、杨氏模量和屈服应力，并创建一个否则将不可行的结构。为了利用这种能力，开发了一个基于密度的拓扑优化框架来优化不同材料的空间分布、它们的界面和结构布局，以提高刚度和应力。提出了实现这些目标的插值方案，并解决了三个层次的复杂性，即多材料设计、与设计相关的热载荷和应力约束。该框架使用三个数值示例进行评估，并展示了优化的刚度和基于强度的拓扑结构和材料成分。最后，比较了单材料和多材料优化设计。结果表明，多材料设计的低顺应性在满足失效约束的同时，要么是不可行的，要么是通过单材料结构的明显更高的重量来实现的。