Adaptive Design of Additively Manufactured Lattice Structure through Position-Dependent Parametric Analysis on Strut Cross-section Geometry

Abstract

Lattice structures are architected materials composed of periodically repeating unit cells that form a porous, lightweight framework. Their exceptional strength-to-weight and stiffness-to-weight ratios, high energy absorption capacity, and finely tunable mechanical properties have led to widespread interest across engineering disciplines where lightweight, mechanical efficiency, and precise tunability are critical. Applications in aerospace, automotive engineering, and biomedical implants increasingly rely on the unique performance advantages of lattice structures, leveraging their capacity to achieve mechanical behaviors unattainable through traditional solid components. Despite these advantages, the practical implementation of lattice structures was historically constrained by the limitations of conventional subtractive and formative manufacturing techniques, which could not reliably produce the intricate and interconnected strut networks of lattice structures. The emergence and advancement of additive manufacturing (AM), particularly laser-based powder bed fusion (PBF-LB), has dramatically transformed this landscape. PBF-LB enables the fabrication of highly complex three-dimensional geometries with micro-level precision by selectively melting metal powders in a layer-by-layer manner. This capability has liberated the geometric design space of lattice structures, allowing engineers to exploit topological freedom and fine-scale structural variation that were previously inaccessible. As a result, PBF-LB has acted as a catalyst for rapid advancement in the design, optimization, and functional deployment of lattice structures. A strut-based lattice is governed by geometric parameters at two distinct scales: the unit-cell scale and the strut scale. Unit-cell parameters, such as topology, cell size, and relative density, have been studied extensively, given their influence on global stiffness, failure mechanisms, and structural resolution. In contrast, strut-level geometric parameters, particularly those defining the shape and dimensional characteristics of the strut cross-section, have only recently drawn attention as critical determinants of performance. Cross-section geometry directly regulates the second moment of area, shear stiffness, lateral buckling resistance, and stress-distribution behavior of individual struts. In addition, the longitudinal mass distribution along the strut affects local stress concentration at nodes, regions known to be mechanically vulnerable. These strut-level parameters often exert influence comparable to unit-cell parameters, offering a powerful means to tailor mechanical behavior precisely. However, the design potential of strut cross-section geometry remains largely underexplored. Theoretically, an infinite number of cross-section shapes and dimensions are possible. Furthermore, the mechanical effect of a given strut geometry is inherently position-dependent: the same cross-section modification can appear differently, depending on its orientation within the lattice and its relationship to local loading paths. This vast design space, coupled with complex positional interactions, renders systematic investigation extremely challenging. Previous studies have relied heavily on isolated experimental tests or case-specific numerical analyses, which only capture limited subsets of the design space and fail to provide a continuous or generalizable understanding of geometry–mechanics interactions. As a result, the true opportunity for cross-section-level optimization, potentially the most influential degree of freedom in designing high-performance lattice structures, remains insufficiently realized. This dissertation addresses these critical gaps by proposing a comprehensive framework for the parametric analysis, predictive modeling, and adaptive optimization of strut cross-section geometries in additively manufactured lattice structures. The research progresses through three interconnected stages. First, a mathematical analytical model based on the direct stiffness method is formulated to evaluate continuous correlation between cross-section geometry and mechanical response. This formulation captures stiffness contributions of struts with various geometric parameters and reflects orientation-dependent, connectivity-dependent, and topology-sensitive behaviors. By enabling continuous parametric variation of cross-section dimensions, the analysis reveals mechanical trends that cannot be observed through discrete simulations alone. The model also demonstrates the position-dependent mechanical effects that arise within lattice unit-cells. Second, leveraging the data generated through the analytical model, machine-learning algorithms are developed to predict the mechanical performance of lattice structures across geometric combinations. This approach greatly reduces computational cost by eliminating the need for repetitive numerical simulations or physical testing for each new design. Instead, the trained machine-learning model provides generalized data acquisition fundamental to analyze mechanical trends across the entire continuous design space. The resulting predictive capability enables rapid evaluation of lattice configurations under various loading conditions and geometric design. Third, upon the enlarged data obtained from predictive model, data-driven systematic optimization process that inversely derives the strut cross-section geometry required to achieve specific mechanical targets is developed. Using the predicted mechanical trends, the optimization framework identifies the cross-section geometric parameter values that maximize performance metrics such as compressive strength or stiffness, while considering orientation-dependent and topology-dependent conditions of each strut. This adaptive design capability enables the creation of lattice structures whose cross-sections vary across positions to suit local loading environments, achieving a level of tailored performance unattainable with uniform cross-section designs, verifying the practical effectiveness of the proposed framework. Through this integrated methodology, combining parametric analysis based on theoretical mechanics, machine learning, finite element analysis, and experimentally informed calibration, this dissertation establishes a rigorous and scalable framework for the design of strut cross-section geometries in lattice structures. The resulting approach expands the geometric design space and enhances structural efficiency. Ultimately, this investigation contributes a significant advancement toward the systematic and adaptive optimization of lattice structures, strengthening their industrial applicability across a wide range of engineering demands.