Shape and Topology Optimization
Topology and shape optimization determine the optimal distribution of material within structures, as well as the shape of structures to provide the best performance possible while minimizing costs (e.g. mass) and satisfying constraints (e.g. maximum stress, cost, manufacturability, material use). Many optimized structures try to balance strength-to-weight ratios, such as a drone chassis, which needs to be strong enough to carry motors and cargo but light enough to fly. Computer-driven topology and shape optimization accelerates the design process and often produces structures that have nonintuitive geometric features and material distributions.
The CDO applies topology and shape optimization to large-scale problems, developing new shape control mechanisms and accommodating complex physical phenomena. The center also works to extend applications to design sentient devices, solve inverse and identification problems, generate reduced order models (ROMs), and more.
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Metamaterial Design
Optimization plays a key role in designing metamaterials—composite material systems that exhibit effective mechanical, thermal, and electromagnetic properties that don’t exist in nature. The CDO’s software efficiently traverses massive design spaces to determine the best layout of material constituents to optimize properties like structural stiffness, thermal conductivity, and refractive index. These designs can be quickly fabricated, tested, characterized, and validated through partnerships with the Center for Engineered Materials and Manufacturing (CEMM) and the Non-destructive Characterization Institute (NCI).
The CDO team can maximize hierarchical structures like the Eiffel Tower through multiscale optimization, designing both the unit cells (building blocks) and macroscopic structures that they fill. This has led to unique structures with extreme stiffness-to-weight ratios, responsiveness to external stimuli, negative thermal expansion behavior, and more.
Design for Additive Manufacturing
Fully taking advantage of additive manufacturing (AM)’s potential means designing and optimizing with the technology’s fabrication capabilities in mind. Every AM process has different constraints that influence designs and need to be considered to ensure optimized designs can be readily fabricated. The team also develops workflows to quickly and efficiently translate optimized designs into print-ready instructions that the AM machines can execute. In addition, the team develops digital twins—virtual models of real 3D printing process—to ensure that optimized designs are accurately fabricated.
Read more:
- https://str.llnl.gov/str-december-2025/designing-new-era-manufacturing
- https://www.llnl.gov/article/49351/new-hpc4ei-project-create-digital-twin-models-aerospace-manufacturing
Reduced Order Modeling for Shape Optimization
Reduced Order Modeling (ROM) provides efficient approximations to otherwise computationally intensive simulations for shape optimization, as fully-resolved finite element simulations are prohibitively expensive in iterative design optimization workflows and traditional homogenization methods lack the accuracy for predicting structural responses in practical applications.
ROM approximates the deformation of unit cells via high-order "super elements,” which ensures displacement continuity across the interfaces that separate dissimilar unit cells. ROM also leverages machine learning to interpolate the unit cell behavior over the design space. This innovative technique makes it possible for researchers to efficiently model and optimize complex multiscale structures like truss lattices.
Heat & Mass Transport Optimization
CDO researchers use optimization to develop and improve materials and devices for heat and mass transport systems, such as batteries, carbon sequestration heat exchangers, electrochemical reactors, fuel cells for hydrogen-powered energy, and targets for fusion energy. The team is also working to better understand material degradation and interfacial interactions to improve the accuracy of their simulations and hence, the effectiveness of their designs.
The team has developed a framework that generated designs with geometric features that match the diffusion length scale of batteries, thus maximizing material use. Other work has involved designing electrochemical reactors across the atomic, nano-, micro-, and meso-scales and helped design graphene aerogels: porous, high-surface-area conductive materials for energy storage and desalination applications.
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