Bingshan Liu

To overcome the bottlenecks of soaring computational overhead, boundary distortion at complex boundaries, and fragile heterogeneous interfaces when designing variable-density lattices from discrete unstructured meshes, this paper proposes a geometry-physics dual-field-driven implicit modeling method for multi-morphology functional lattices. First, a spatial implicit sampling probe (SISP) is constructed to continuously decouple and characterize complex fields. Second, an intelligent decision mechanism adaptively coordinates the co-allocation of solid, triply periodic minimal surface (TPMS), and random strut structures. To resolve C^0 discontinuities across heterogeneous topologies, an implicit dilation blending operator (IDBO) is introduced to achieve seamless blending of multi-morphology structures through local non-uniform geometric dilation. Computationally, CPU-GPU parallel framework significantly accelerates generation while minimizing memory footprints. Benchmarks demonstrate that the total execution time is merely 66.7 s for a case with 2.62 million struts at a 7683 resolution. Compared with conventional operators, the IDBO-enhanced lattices improve peak compressive load and elastic modulus by 111.3% and 150.1%, respectively. This method provides an efficient, precise, and general paradigm for the intelligent, lightweight engineering of multi-morphology functional lattices structures in demanding service environments.

Lattice structures offer exceptional performance in additive manufacturing, yet ensuring their geometric validity under complex design constraints poses a significant computational geometry challenge. This paper addresses the scalability bottleneck in processing million-scale lattice models by proposing a high-performance framework based on Hybrid Spatial-Topological Index. Our approach leverages a priority-driven heuristic solver integrated with a local topology update strategy, decouples computational cost from the total topological complexity of the model. Besides, the framework introduces a series of atomic operators to resolve coupled DfAM constraints, such as overhang angle, pillar ratio, and connectivity. Compared to isotropic remeshing, our framework strictly enforces physical DfAM constraints rather than merely pursuing topological regularity, preventing the inadvertent introduction of new geometric violations. Furthermore, against state-of-the-art self-supporting topology optimization methods, our approach achieves higher overhang correction rates while avoiding the severe boundary distortion and secondary dimensional violations caused by global scaling. The proposed framework can resolve complex geometric violations within tens of seconds for models exceeding 106 elements, maintaining a high degree of geometric fidelity and structural integrity, provides a scalable computational foundation for the next generation of CAD tools capable of handling extreme-scale lattice designs.

This study conducts a systematic investigation of four representative truss-based lattice structures (SC, RBCC, CB, and BCC) and analyzes their tensile and shear mechanical responses across different volume densities. The numerical results reveal pronounced topology dependence and density sensitivity in lattice performance. The SC lattice exhibits the highest stiffness and the smallest deformation under both loading conditions. The BCC lattice shows the largest strain in the low-to-medium density range due to bending–torsion coupling in its inclined struts. The CB and RBCC lattices display comparable overall performance, with the CB configuration performing slightly better owing to its more uniform load-transfer pathways. To validate the accuracy of the numerical model, uniaxial tensile tests were conducted on SC and BCC specimens with a volume density of 0.44. The experimentally measured ratio of equivalent elastic moduli closely matches the numerical predictions, confirming the model’s ability to capture the topology-dependent load-bearing mechanisms. Based on the simulation results, performance–density maps incorporating volume density, global deformation, and local stress metrics were constructed. In addition, a multi-constraint lightweight lattice-design method was proposed. This method enables the determination of the minimum feasible lattice density and the corresponding optimal topology under simultaneous strength, stiffness, and volume constraints. The proposed approach provides an intuitive, efficient, and generalizable framework for lattice selection and infill design. Overall, this work offers a reliable theoretical foundation and methodological support for lightweight design, multiscale optimization, and additive manufacturing of lattice structures.

Addressing manufacturing failures and computational bottlenecks caused by overhang constraints in lattice additive manufacturing, this paper presents an efficient incremental geometric correction method. We propose a hybrid index enabling O(1) complexity for non-manifold wireframe queries and spatial-attribute synchronization. An incremental correction mechanism leveraging a version-controlled priority-queue strategy is established to mitigate performance losses from high-frequency heap deletions, ensuring data consistency and rapid convergence during massive-scale topological updates. During the correction phase, a hierarchical strategy dispatches local operators to satisfy manufacturing constraints while preserving original design intent. Quantitative evaluations demonstrate the method's robustness, achieving second-level convergence and correction rates exceeding 98%. Commercial software validation confirms substantial reduction in overhang regions, providing a high-performance preprocessing solution for reliable industrial-grade fabrication.

Point cloud models of industrial parts are characterized by an unordered distribution of points and locally similar structures. Traditional point cloud classification methods have limited capability in modeling local neighborhood relations and are insufficient in representing local geometric differences, which restricts their performance in industrial part classification tasks. To address this issue, a point cloud classification method fusing vectorized local relation modeling and geometric enhancement is proposed. Specifically, a Vector-Edge Local Aggregation Block is designed to reconstruct the conventional local feature extraction unit. First, vectorized local relation modeling is introduced to construct hybrid local descriptors, generate vector features, and perform aggregation as well as scalar projection, thereby explicitly encoding the geometric and structural relations between the centroid point and its neighboring points. Then, edge features are extracted to supplement local differential geometric information. Finally, residual fusion is employed to achieve collaborative representation of multiple features, enabling the network to jointly capture local relational patterns and differential geometric information, thus improving its ability to represent complex local structures and fine-grained inter-class differences. Experiments on ModelNet40, the industrial part dataset MCB, and S3DIS demonstrate that the proposed method improves local feature representation for point clouds, effectively distinguishes fine-grained structural differences among industrial parts, and achieves strong performance, robustness, and generalization ability in point cloud tasks.

Lattice structures offer exceptional performance in additive manufacturing, yet ensuring their geometric validity under complex design constraints poses a significant computational geometry challenge. This paper addresses the scalability bottleneck in processing million-scale lattice models by proposing a high-performance framework based on a novel Hybrid Spatial-Topological Index (HSTI). Unlike traditional global optimization methods, our approach leverages a priority-driven heuristic solver integrated with a local topology update strategy. By confining geometric revalidation to the 1-ring neighborhood, we achieve O(1) atomic complexity, effectively decoupling the computational cost from the overall topological complexity of the model. The framework introduces a set of atomic operators—including vertex shifting and edge reconfiguration—to resolve coupled constraints such as overhang angles, strut proportions, and connectivity. Experimental results on massive datasets demonstrate that the proposed framework can resolve complex geometric violations within tens of seconds for models exceeding 106 elements, maintaining a high degree of geometric fidelity and structural integrity. This work provides a scalable computational foundation for the next generation of CAD tools capable of handling extreme-scale lattice designs.

To address the significant accuracy loss in high-curvature regions caused by conventional uniform sampling in the preprocessing stage, this paper proposes a geometric curvature-based adaptive sampling method for trajectory planning of multi-degree-of-freedom robotic arms in additive manufacturing. The strategy dynamically adjusts the sampling density according to the path curvature, preserving more points in high-curvature regions to maintain trajectory accuracy while reducing redundant points in low-curvature regions to decrease computational load. A local error evaluation method is proposed to assess the path error of the trajectory planning results for the sampled point sets. Experimental results within the TOPPRA framework demonstrate that, compared to uniform sampling, the proposed approach reduces errors in high-curvature regions by 21.68%–30.06% without affect the errors in low-curvature regions. This improve ment enhances the overall trajectory quality while maintaining the same point set size.

This study aims to optimize the formulation of vat photopolymerization resin for digital light processing (DLP) three‐dimensional (3D) printing of Si₃N₄ ceramics to address the challenges posed by their high refractive index. Initially, we evaluated nine commonly used monomers and selected acryloyl morpholine, propoxylated neopentyl glycol diacrylate, and trimethylolpropane ethoxylated triacrylate based on their quantitative performance. We then employed a formulation experimental design to determine the optimal monomer ratio of 25:60.9:14.1. Furthermore, we optimized the prepolymer (epoxy acrylate) and plasticizer (2,2,4‐trimethyl‐1,3‐pentanediol diisobutyrate) contents to minimize monomer shrinkage, selecting optimal values of 20 wt.% and 10 wt.%, respectively. Based on these optimizations, we determined the ideal concentrations of photoinitiator, dispersant, and thixotropic agent to be 3, 2, and 2 wt.%, respectively. Finally, using the optimized resin formulation, we prepared a high‐solid‐content Si₃N₄ slurry and successfully printed high‐precision, complex Si₃N₄ green structures. This demonstrates the practical applicability of the optimized vat photopolymerization resin formulation, laying a solid foundation for the development of Si₃N₄ ceramics in DLP 3D printing.