materials selection

This work addresses the limitations of black-box optimization in structural design, which often yields suboptimal or physically implausible solutions due to its neglect of problem modeling and domain knowledge. Focusing on the topology optimization of laminated composite structures, the study proposes an explicit decoupling of topological and fiber orientation design variables, combined with a physics-informed sequential optimization strategy. This approach departs from conventional context-agnostic black-box paradigms by leveraging domain-specific insights. Compared to concurrent optimization of all variables, the proposed sequential method significantly improves compliance minimization under volume constraints, yielding superior and physically interpretable designs. The results underscore the critical role of integrating domain knowledge into the optimization process to enhance both performance and solution plausibility.

Large-scale mechanical systems face significant challenges in parametric design—including geometric constraint handling, variable loading conditions, performance deviations, over-specification, and cost-performance trade-offs. To address these, this paper proposes a modular mechanism design optimization framework based on Kriging surrogate modeling. Departing from conventional predefined design schemes, the method uniquely integrates geometry-constrained kinematic parameter optimization with manufacturability-aware cost modeling. It employs NSGA-II for multi-objective optimization to dynamically cluster components, enable customized grouping, and embed cost sensitivity analysis with decision support. The framework significantly improves motion performance consistency and component interchangeability while reducing over-specification rates. In validation on representative industrial systems, it achieves an average 12.7% reduction in manufacturing cost and a 9.4% decrease in carbon footprint.

Addressing the challenge of simultaneously achieving structural performance and manufacturability in two-dimensional topology optimization, this paper proposes a multi-thickness density-based optimization method. The approach integrates hierarchical penalization, smoothed Heaviside projection, parameter continuation, and adaptive mesh refinement to effectively suppress spurious thin features. With only three discrete thickness levels, it closely approximates the performance of continuous thickness-varying designs. The method inherently accommodates both additive manufacturing and conventional machining constraints, significantly enhancing convergence stability and geometric resolution. Benchmark tests on cantilever and MBB beams demonstrate compliance errors below 2% and stiffness values nearly matching those of variable-thickness optimization—substantially outperforming the standard SIMP method in both accuracy and manufacturability.

In large-scale laminated composite manufacturing, overlapping seams arising from roll-based cutting degrade structural quality. Method: This paper proposes an automated ply segmentation method tailored for developable surfaces. It formulates global ply decomposition as a sequence of one-dimensional piecewise linear optimization problems, integrating greedy global search with local linear programming to achieve efficient, constraint-satisfying segmentation. Constraints include thickness tolerance, obstacle-avoidance zones, sub-ply geometric continuity, and material utilization. Contribution/Results: This work pioneers the integration of developable surface modeling with piecewise linear optimization, significantly improving computational efficiency while ensuring process feasibility. Validation on aerospace (wing surface) and defense (armored vehicle panel) case studies demonstrates robust performance. The method seamlessly integrates into mainstream composite design workflows, replacing conventional trial-and-error approaches with a rigorous, optimization-driven solution.

This study investigates how the choice of norm in compliance-based objective functions influences structural topology in topology optimization. While the form of the objective function is known to significantly affect optimization outcomes, the mechanistic differences among compliance formulations derived from various norms—specifically ℓ², √ℓ², and spectral ℓ¹ norms induced by the stiffness matrix—remain unclear. Through systematic numerical experiments within a finite element framework, the work reveals that the classical quadratic (ℓ²) compliance promotes uniform load paths, whereas the spectral ℓ¹ norm yields sparse and highly localized structural members. These findings demonstrate that, under identical physical constraints, distinct norm-based formulations can produce markedly different optimization landscapes and topological configurations, offering a principled pathway toward tailoring structural performance to specific design requirements.

This work addresses key challenges in multi-material topology optimization—namely, limitations on the number of candidate materials, redundant design spaces, and difficulties in ensuring physically valid material interpolation—by introducing a generalized shape function (gSF) method. The approach employs an n-dimensional linear shape function to map the multi-material simplex domain onto a compact design space, using natural coordinates as design variables to determine material densities. By integrating density filtering with a barycentric-projection strategy, the method rigorously enforces barycentric coordinate properties. For the first time, it establishes a generalized n-linear shape function applicable to arbitrary dimensions, thereby overcoming conventional constraints on material count and enabling a highly scalable optimization framework. The method successfully optimizes 2D and 3D structures—including compliant mechanisms—with up to 24 and 15 materials, respectively, achieving smooth convergence of objective functions and demonstrating its efficiency, generality, and engineering applicability.

This work addresses the lack of systematic evaluation frameworks for inverse design algorithms in materials science, as existing machine learning benchmarks are largely confined to forward property prediction. To bridge this gap, we introduce MatFormBench—the first unified benchmark for goal-driven materials formulation. Built upon a physics-informed synthetic data generation pipeline, MatFormBench features five tiers of task difficulty and a multidimensional scoring metric, MatFormScore, which evaluates performance across target achievement, search efficiency, exploration capability, robustness, and stability. Through standardized evaluations of 39 algorithms—including diffusion models, variational autoencoders (VAEs), genetic algorithms, and large language models—across 1,170 trials, we demonstrate MatFormBench’s effectiveness: diffusion models emerge as overall top performers, while VAEs and genetic algorithms excel in specific scenarios, underscoring the benchmark’s value in algorithm assessment, diagnostic analysis, and reproducibility.

This work addresses the reliance on expert knowledge in multi-stage decision-making within topology optimization, which hinders full automation. To overcome this limitation, the authors propose TopOptAgents—a six-agent system powered by large language models (LLMs)—that introduces, for the first time in this domain, a multi-agent collaborative framework integrated with an iterative self-refinement mechanism. Through closed-loop iterations encompassing problem modeling, validation, code generation and execution, and solution quality assessment, the system enables end-to-end automated decision-making. The approach substantially enhances the reliability and generalization capability of LLMs in low-prior-knowledge scenarios, successfully generating convergent design solutions for complex problems where literature and open-source resources are scarce, and significantly outperforming single-LLM baselines.

This work addresses the lack of a unified, open-source, and modular platform for collaboratively exploring shape and topology optimization methods in both teaching and research. The authors present an object-oriented, MATLAB-based open-source framework that employs abstract base classes to define core interfaces, enabling seamless integration of parametric and level-set-based shape optimization alongside density-based, level-set, and topological sensitivity approaches to topology optimization. By directly mapping mathematical formulations to executable code, the framework allows users to extend objective functionals or constraints simply by deriving new classes without modifying the core implementation. Highly modular and reproducible, the framework bridges the gap between shape and topology optimization, offering a continuous research pathway. Its effectiveness and flexibility are demonstrated through diverse numerical examples in both educational and research contexts.

This work addresses a critical gap in functionally graded additive manufacturing, where existing approaches focus predominantly on geometric or material distribution while neglecting the coordinated control of slicing and process parameters, thereby forcing users to manually configure slicer region settings—an inefficient and error-prone practice. To overcome this limitation, the authors propose a novel slicer project compilation pipeline that, for the first time, automatically maps implicit heterogeneous designs to the slicing layer. By leveraging spatial attribute partitioning, submesh extraction, and slicer-dialect serialization, the method generates syntactically compliant .3MF project files embedding submeshes, parameter recipes, and process states. It supports calibration from high-order properties—such as those of thermally responsive foaming materials—to process parameters, integrating three parameter systems: setting meshes, virtual extrusion, and color/material halftoning. Experimental validation demonstrates successful fabrication of specimens featuring gradient toolpaths, performance tuning, texture-process co-control, and color blending, replacing over 2,500 manual operations, with an open-source framework enabling extensible functionally graded manufacturing.