Structures composed of spatially-varying architected materials have great potential for targeted mechanical and/or multifunctional behavior, but lack of structural integrity at the interfaces between different architecture geometries can degrade the expected performance. While smooth transitions between functionally-defined architected materials can be designed easily using mathematical interpolation, a robust transitioning scheme is less apparent for architectures without a simple mathematical description. Here we focus on periodic, strut-based lattices exhibiting cubic symmetry of their nodes and propose an algorithm that automates the design of smoothly-varying transitions between any finite set of these lattices embedded in a macroscale structure. The algorithm takes in lattice existence and relative density fields indicating which lattice and associated relative density exists at each point in the macroscale structure, and an ordered set of m key lattices to be embedded. We define a transitional skeleton (i.e., nodes and connectivity) that encapsulates all m key lattices via a continuous morphing between different nodal configurations, and use it to spatially transition between the different lattice geometries. Material is added after manipulating the skeletons according to the given relative density distribution. We explain details of the algorithm in 2D using a multi-lattice design obtained from topology optimization and show the flexibility and robustness of the algorithm by generating a lattice-embedded rendering of The Starry Night by Vincent Van Gogh. In 3D, we explore the effect of the transition radius and demonstrate manufacturability of the spatially-varying lattice-embedded structures by 3D printing a multi-lattice canopy obtained from topology optimization.
We introduce a generative artificial intelligence (AI) algorithm trained to generate realistic three-dimensional microstructures of polymer-bonded explosives (PBX). We idealize PBX as a two-phase composite with anisotropic crystals as inclusions in a polymer matrix. To improve memory efficiency, we introduce a two-stage hierarchical algorithm in which a deep generative graph model captures the grain topology in the PBX, while a latent diffusion model generates the 3D geometry of individual grains. This approach enables us to idealize each grain as a simply connected body embedded in three-dimensional space. This divide-and-conquer strategy enables us to bypass the challenging task of generating manifolds of complex topology and to avoid wasted computations when applying convolutions to grids dominated by constant values. To generate PBX microstructures with realistic grain topology, we sample sub-domains of segmented micro-computed tomography (CT) images of a mock PBX with Idoxuridine (IDOX) grains to form a dataset. Each sub-domain is represented by a node-weighted graph with the position, size, and shape descriptors stored as node features. The topological dataset is then used to train a graph recurrent neural network (GraphRNN) that learns to add nodes and edges sequentially to form a weighted graph describing the IDOX granular network, consisting of nodes with features connected by edges. With the global topology prescribed, the individual grains are generated by a conditional denoising diffusion probabilistic model that takes node features as inputs and produces grains that match the prescribed node features. Numerical examples assess the similarity between the actual and synthetic microstructures.
Surrogate modeling is widely used to reduce the computational cost of Monte Carlo simulation (MCS)-based reliability analysis involving expensive performance functions. However, the relative effectiveness of different surrogate construction strategies in reliability applications remains insufficiently understood. This study compares two major paradigms for surrogate modeling: optimization-based and active learning-based strategies, referred to as oMMs and iMMs. Three representative techniques—artificial neural networks, Gaussian process regression, and support vector regression—are implemented within these frameworks. To assess surrogate performance from a reliability perspective, a probability-aware sign-penalized limit-state accuracy (SPLA) index is proposed. The index emphasizes prediction accuracy near the limit-state surface and penalizes sign misclassification that directly affects failure probability estimation. Four structural and geotechnical examples are investigated. The results show that high global surrogate accuracy achieved by oMMs does not guarantee reliable failure probability estimates and often requires substantially higher computational cost. In contrast, iMMs consistently provide more accurate and stable reliability predictions by adaptively enriching training data near the limit-state surface, as reflected by higher SPLA values. Furthermore, SPLA is employed to guide the selection of reliable models in bootstrap-based bagging ensembles, enhancing the robustness of surrogate predictions while maintaining high reliability estimation accuracy.
To address the problem of time-dependent reliability analysis for high-cost engineering structures under mixed random–fuzzy uncertainty, a novel multi-fidelity framework is proposed by integrating a serial multi-layer latent mapping model (SMLM) with hyper-rectangular constrained subset simulation (HCSS). The proposed method employs SMLM to provide a unified characterization of the correlation structure among data of different fidelity levels, thereby enhancing the response approximation capability for mixed inputs involving random continuous variables and fuzzy state variables. Meanwhile, HCSS generates critical candidate samples layer by layer within constrained hyper-rectangular regions, enabling sequential surrogate updates in the vicinity of the failure boundary and thus improving the efficiency and accuracy of interval estimation for time-dependent failure probabilities. Numerical examples and the engineering case of a wing box structure demonstrate that the proposed method can effectively fuse multi-fidelity information and maintain high accuracy and stability in boundary estimation while significantly reducing the number of high-fidelity model evaluations.
Fractional viscoelastic shell simulations are expensive because the finite-element system must be solved repeatedly at the complex frequencies used for numerical Laplace inversion. The difficulty is greater when membrane and bending deformation relax at different rates. We show that, after scaling by the membrane relaxation function, all material-frequency dependence of the modal problem enters through the single ratio r=f_b/f_m , where f_m and f_b are the membrane and bending relaxation functions. The resulting eigenvalue curves depend on geometry but not on the fractional material parameters. This reduction is exact for any compatible finite-element assembly and is demonstrated on non-separable shell operators and a real blade-airfoil section. We approximate the one-dimensional eigenvalue curves spectrally and interpolate their geometry dependence cubically. The approximation has a conservative a-priori error bound when the complex inversion points lie inside an admissible Bernstein ellipse and remain separated from the system poles. The frequency-domain error is then propagated to a time-domain quantity of interest. In the reported tests, the operator agrees with an independent full-shell finite-element solution to 3.4× 10^-4 , while its online evaluation is approximately 10^4 times faster than a converged preconditioned iterative solve. A permutation-invariant point-cloud encoder is used only as a geometry interface for wind-turbine blades; its measured error is propagated deterministically rather than claimed as an a-priori neural-network certificate. The blade calculations reproduce reference frequencies for the NREL 5-MW and IEA-15-MW configurations and provide geometry derivatives for design studies and digital-twin updates.
