Novel Topology Optimization Methods for Designing Multifunctional Heterogeneous Material Systems

增材制造的新进展使得能够在单个打印作业中快速且廉价地制造包含多种材料（例如金属、陶瓷和聚合物）的复杂设计。这种能力使制造商能够生产不需要装配的异构、多组件设计，从而消除了装配过程所带来的成本和设计约束。它还允许设计人员生产比传统方法更高性能和/或更轻重量的组件。然而，我们目前制造这种设计的能力超过了我们优化它们的能力。本研究项目将研究新的算法，为多功能，异构系统生成最佳的结构几何形状和材料布局。 这些算法将考虑设计中使用的不同类型材料的行为以及材料之间的相互作用。通过这种方式，我们将实现多组件设计的系统级优化，这些设计的成本和性能远远超过使用传统方法创建的组件。这种新颖的设计方法有可能对多个研究社区和行业产生影响，其应用范围从生物医学设备到消费电子产品。通过这项研究，我们将介绍一种新的设计公式，用于处理包含几类材料的多功能设计问题。这一目标将通过开发基于拓扑优化的新算法来实现，该算法将联合收割机非线性有限元分析与专门为异构问题创建的原始参数化设计表示方案相结合。数值优化问题将使用基于梯度的方法来解决，其中函数梯度将指导设计空间的优化搜索。 这些梯度将使用伴随灵敏度分析进行计算，并将考虑正在研究的各种非线性来源，包括超弹性，塑性和材料损伤。 将使用优化设计的高保真计算建模以及对类似市售设计的分析沿着来验证所得到的设计算法，以量化每个算法产生的性能增益。

New advances in additive manufacturing have enabled rapid and inexpensive fabrication of complex designs containing multiple classes of materials, such as metals, ceramics, and polymers, all within a single print job. This capability allows manufacturers to produce heterogeneous, multi-component designs that do not require assembly, thereby eliminating the cost and design constraints imposed by the assembly process. It also can allow designers to produce higher-performing and/or lighter-weight components than is possible through traditional means. However, our capacity to manufacture such designs currently exceeds our capability to optimize them. This research project will investigate novel algorithms for generating optimal structural geometries and material layouts for multifunctional, heterogeneous systems. These algorithms will consider the behavior of the different types of materials used in a design and the interactions among the materials. In this way, we will enable system-level optimization of multicomponent designs that will exhibit cost and performance properties far exceeding components created using traditional approaches. This novel design approach has the potential for impacts across multiple research communities and industries, with applications ranging from biomedical devices to consumer electronics.Through this research, we will introduce a new design formulation for handling multifunctional design problems containing several classes of material. This objective will be achieved through the development of novel topology optimization-based algorithms that will combine nonlinear finite element analysis with an original parametric design representation scheme, created specifically for heterogeneous problems. The numerical optimization problem will be solved using gradient-based methods in which function gradients will guide the optimization search of the design space. These gradients will be computed using adjoint sensitivity analysis, and will take into account the various sources of nonlinearity being investigated, including hyperelasticity, plasticity, and material damage. The resulting design algorithms will be validated using high-fidelity computational modeling of the optimized designs, along with analysis of analogous commercially-available designs, to quantify the performance gains generated by each algorithm.