Permitting multiple materials within a topology optimization setting increases the search space of the technique, which facilitates obtaining high-performing and efficient optimized designs. Structures with multiple materials involving fluidic pressure loads find various applications. However, dealing with the design-dependent nature of the pressure loads is challenging in topology optimization that gets even more pronounced with a multi-material framework. This paper provides a density-based topology optimization method to design fluidic pressure loadbearing multi-material structures. The design domain is parameterized using hexagonal elements as they ensure nonsingular connectivity. Pressure modeling is performed using the Darcy law with a conceptualized drainage term. The flow coefficient of each element is determined using a smooth Heaviside function considering its solid and void states. The consistent nodal loads are determined using the standard finite element methods. Multiple materials is modeled using the extended SIMP scheme. Compliance minimization with volume constraints is performed to achieve optimized loadbearing structures. Few examples are presented to demonstrate the efficacy and versatility of the proposed approach. The optimized results contain the prescribed amount of different materials.

翻译：在拓扑优化中允许使用多种材料增加了技术的搜索空间，从而有助于获得高性能且高效的优化设计。涉及流体压力载荷的多材料结构具有多种应用场景。然而，处理压力载荷的设计依赖性在拓扑优化中颇具挑战性，在多材料框架下这一问题尤为突出。本文提出了一种基于密度的拓扑优化方法，用于设计承受流体压力载荷的多材料结构。设计域采用六边形单元参数化，以确保非奇异连接性。利用达西定律及概念化的排水项进行压力建模。每个单元的流动系数通过考虑其固体与空隙状态的平滑Heaviside函数确定。一致节点载荷采用标准有限元方法计算。多材料模型通过扩展SIMP方案实现。以体积约束下的柔度最小化为目标，完成承重结构的优化设计。通过若干算例展示了所提方法的有效性与通用性。优化结果中包含了预设比例的多种材料。