structural engineers

Abstract: Rigidity and global rigidity are fundamental graph properties in discrete geometry, with applications to structural engineering and network localization. In two dimensions, both admit combinatorial characterizations in terms of the rigidity matroid and graph connectivity. We study the computational complexity of finding minimum-cost sets of edges or vertices whose deletion destroys either property in a finite simple graph. With unit costs, we give deterministic polynomial-time algorithms for edge deletion destroying global rigidity and vertex deletion destroying either property. We prove that edge deletion destroying rigidity is NP-hard and that, with positive integer costs, all four problems are NP-hard. These results resolve, in dimension two, the open questions on recognizing robustness under edge and vertex deletions posed by Jordán and Whiteley (2017), as well as the minimum edge-deletion problem for rigidity recorded in EGRES Open.

Abstract: System identification, namely the inference of mathematical representations of dynamical systems from measured data, is fundamental to engineering diagnostics, prognostics, and decision-making. Bayesian filtering offers a principled framework for probabilistic state estimation but traditionally relies on prescribed transition and observation models. Recent advances in deep Bayesian filtering address this limitation by embedding learnable representations within probabilistic state-space formulations, enabling data-driven identification of unknown dynamics while retaining physical structure and uncertainty-aware inference. This tutorial provides a systematic introduction to deep Bayesian filtering for nonlinear structural system identification, focusing on the interplay between learned dynamics, physical inductive biases, and posterior inference. The Deep Markov Model serves as a data-driven reference, while the Physics-guided Deep Markov Model (PgDMM) and Neural Extended Kalman Filter (Neural EKF) illustrate complementary approaches based on amortized variational inference and differentiable Kalman filtering, respectively. Their capabilities are examined through dynamic state estimation and joint dynamic state and parameter estimation on a three-dimensional shear-frame benchmark with hysteretic Bouc-Wen connections and sparse acceleration measurements. The results highlight important distinctions between measurement-conditioned reconstruction and open-loop forecasting, demonstrate how physical structure can improve latent-state interpretability without necessarily ensuring predictive fidelity, and reveal differences in the robustness of response and parameter estimation. Practical guidelines for model construction, training, evaluation, and deployment are provided, together with an outlook on remaining challenges in uncertainty calibration, identifiability, and real-world validation.

Abstract: A converged topology optimization can solve the wrong problem when loads, supports, or the domain are underspecified. Assuming defaults, or asking the problem's author about every detail, ignores how much each answer changes the design. We propose consequence-guided clarification (CGC), which bases acceptance on computed mechanical consequences. CGC computes a reference design for each of a finite list of complete specifications, called readings. A design is accepted only if its compliance is at most 5% above the reference at every reading consistent with the answers. Otherwise, CGC asks the question whose worst answer leaves the smallest worst-case excess, and withholds acceptance at its question limit. To save optimizations, the screening variant CGC-S postpones some references until a candidate must be checked. We developed and evaluated both on 36 arXiv-derived tasks, treating each of 134 readings in turn as intended and simulating correct answers. In 26 tasks, the default-reading design failed another reading. Apart from always-asked questions on load direction, sign, and material budget, asking everything took 188 questions; CGC and CGC-S each took 105. The acceptance test supplied most of this saving: applying it to the default design alone took 117. Relative to asking everything, CGC-S requested 4.6 extra reference designs per avoided question, each from two optimization starts, counting optimization time only. References are not certified optima: better ones pushed three accepted cases above tolerance, and finer meshes changed some decisions. Within these limits, the test shows which readings a design covers and which details block acceptance.

Abstract: Slender concrete columns reinforced with fiber-reinforced polymer (FRP) bars fail at medium to high axial load levels either by concrete crushing or by loss of stability, while the tensile strains in the reinforcement remain far below the rupture strain. Each non-linear finite element (FE) analysis yields only the capacity of the governing failure mode, and the governing mode changes over a broad zone in which both capacities are nearly equal. Both characteristics conflict with active-learning Kriging-assisted Monte Carlo simulation (AK-MCS), which assumes a single, smooth limit-state function. This paper proposes a piecewise, two-branch AK-MCS framework in which each failure mode is represented by its own Kriging model, trained only on the FE analyses in which that mode governs, and the governing prediction is the minimum of both. Safeguards against data starvation keep rarely governing branches usable. After convergence, additional FE analyses are placed based on a leave-one-out calibration check and on the width of the confidence interval on the reliability index. A design-point search on the surrogate and importance sampling at the design points provide the reliability index even where direct Monte Carlo simulation finds no failure. For an FRP-reinforced concrete column example with mixed failure, 79% and 62% of the training points lie near the mode boundary. The reliability index from the design-point search agrees with the Monte Carlo estimate to within 0.05, and an FE analysis at the design point confirms the surrogate to within 0.6%.

Abstract: Constitutive models for history-dependent, path-dependent materials typically encode this dependence in prescribed functional forms through internal variables such as damage or plastic strain that are phenomenological, model-dependent, and not directly observable. These rigid forms lack flexibility to match observations, make calibration potentially non-unique, and complicate uncertainty quantification. This paper develops a Gaussian-process state-space model (GP-SSM) that replaces the fixed form of the constitutive model with a flexible GP regression, and the prescribed internal variables with latent state variables learned directly from observable stress-strain histories. As a GP, the model is naturally endowed with a measure of uncertainty and can be constrained to satisfy physical principles. We demonstrate this framework for quasi-brittle materials under triaxial compression, where the latent variable evolution is driven by the current-state stress invariants and the increment of equivalent strain to reflect irreversible, pressure-sensitive history. A sparse multi-output GP then maps the latent state and current strain tensor to the six-component stress response, trained by variational sparse inference. The trained model is exported into Abaqus/Explicit through a user material subroutine. Four verification cases are reported: (1) offline rollout on validation and test histories; (2) a single element under changing confinement; (3) a frozen-memory unloading-reloading extension; and (4) a multi-element structural model compared against the Karagozian and Case Concrete (KCC) model. These results show that the learned state-space update reproduces held-out RVE-scale histories in closed-loop rollout, tracks evolving confinement, supports unloading without violating the irreversibility of the learned history state, and reproduces structural-level behavior consistent with KCC.

Abstract: Resonance-induced excessive vibrations can degrade performance, reduce reliability, and shorten the service life of engineering structures. To reduce the risk of resonance, structural natural frequencies are generally engineered to be shifted away from excitation frequencies. To achieve these frequency shifts, topology optimization provides a systematic approach to tailor structural stiffness and mass as an effective inverse design approach. Multi-material topology optimization exploits the high-dimensional design space of spatially varying material constituents by simultaneously optimizing material selection and spatial distribution over the design domain, offering great flexibility in controlling natural frequencies. This study proposes a multi-material topology optimization that attenuates excessive structural dynamic vibrations in free-vibration scenarios via a novel multivariate weight-based interpolation method. Additionally, to address non-smoothness due to mode switching amid optimization, we employ a bound formulation with an auxiliary scalar design variable to replace the max-min eigenvalue objective with constraints on individual eigenvalues. Furthermore, we study and compare three optimization formulations for multi-material design to attenuate vibrations, including maximizing fundamental eigenfrequency, maximizing the gap between adjacent eigenfrequencies, and excluding frequencies from targeted frequency bands, which are smoothly approximated by a proposed rational polynomial formulation. Numerical examples are presented to demonstrate the effectiveness and applicability of our proposed method.

Abstract: Finite element model updating is among the most general approaches to discover constitutive models from structural experiments: since the displacement field is computed rather than measured, it accommodates arbitrary geometries, boundary conditions, and sparse or noisy data. However, every loss evaluation requires a nonlinear finite element solve per load step, and training neural materials requires many such evaluations. Intrusive model order reduction lowers this cost while retaining boundary conditions and variational structure. How can a reduced model remain accurate while the network weights change at every training step? We combine proper orthogonal decomposition and energy-conserving sampling and weighting with adjoint sensitivities of the reduced model, and adapt both the trial space and the sampled elements along the optimization path. The constitutive law is a polyconvex neural network: a logarithmic normalization term, together with a zero-anchored input convex architecture and a growth term, renders the energy polyconvex, coercive, and non-negative by construction, independent of the trained weights. We demonstrate the approach on two experimental datasets and one synthetic three-dimensional example. For a two-phase specimen, training time decreases from nine hours to 41 minutes compared with a full-order identification, without loss of accuracy. In the three-dimensional example, six modes replace 48 672 degrees of freedom, 116 of 15 625 elements suffice to evaluate the internal forces, and training takes 13 minutes. In all cases, the identified material reproduces the measured reaction force and predicts the displacement field from the force alone. Hyperreduction makes the discovery of neural materials from structural data affordable while retaining the advantages of finite element model updating.

Abstract: Recent advances in large language models and agentic workflows offer a new paradigm to early-stage structural design translating design intent into structural models. Although text-to-3D approaches have demonstrated that natural language can be used to produce visual, mesh-based geometric models, structural design requires domain-specific geometric arrangements and semantically rich data types. This paper introduces a proof-of-concept workflow for prompt-to-structure generation using an AI agent connected to a COMPAS-based structural modelling API through a Model Context Protocol (MCP) server. Through controlled modelling operations, the agent creates and modifies a graph-based structural data model composed of explicit building elements. The resulting artifacts can be inspected, modified, serialised, and further connected to downstream AEC workflows. The approach is demonstrated through selected prompt-to-structure examples and by progressive and editable design sequences that resemble typical iterative structural design workflows. The results are preliminary, but demonstrate the possibility of combining natural language, agentic workflows, and domain-specific structural data structures as a first step toward AI-assisted structural co-design.

Abstract: Shipboard equipment must survive the transient loads of underwater explosions. The U.S. Navy certifies such equipment with the Dynamic Design Analysis Method (DDAM), a modal response analysis driven by Navy shock design spectra. DDAM is well established as a verification tool, yet it is rarely used as a design driver in topology optimization. The design spectrum depends on the modal mass, a non-smooth coupling that classical sensitivity formulations do not address. This paper presents a complete differentiable formulation of the DDAM criterion for gradient-based topology optimization. Eigenvalue sensitivities follow the Fox-Kapoor method, and eigenvector sensitivities follow Nelson's method. The chain rule covers a spectral displacement that depends on both the natural frequency and the modal participation factor. Automatic differentiation assembles the sensitivity, and the engineer can certify components inside the optimization loop rather than after design. Three certification problems on a representative shipboard equipment frame demonstrate the workflow. In each, the optimizer removes 43.2% to 46.1% of the design-domain material and holds the certifying NRL Sum within 0.41% of the Navy allowable. Two companion studies follow. A compliance-optimized frame of nearly the same mass has a 5.2 Hz fundamental, outside the range the certification can qualify. Its nominal response also exceeds the allowable by a factor of 2.75. A lower bound on the mean of the two lowest eigenvalues separates the repeated pair that the demonstrations drive onto the frequency floor. The response then stops oscillating across the acceptance boundary. It ends at most 0.5% above the allowable, at a cost of under two percentage points of volume fraction.

Abstract: Deep generative design can produce complex geometries, but unconstrained representations may create undercuts that prevent release from a two-part mold. We present CAST, which reformulates three-dimensional shape generation under a selected mold-opening constraint as a two-dimensional image generation problem using paired top and bottom depth images. Each valid depth pair defines one material interval along a selected mold-opening direction, so reconstructions exclude undercuts in that direction by construction. Diffusion models generate candidate shapes in this representation, and a finite element analysis (FEA) guided optimizer refines the same two boundaries. We evaluate diffusion-based generation with limited training data comprising 211 SimJEB bracket designs. On SimJEB brackets, FEA-guided refinement with a volume penalty reduced compliance in 193 of 200 generated candidates. The median reduction across all candidates was 36.8 percent in the optimization FEA model. Reconstruction of existing brackets revealed a mass--stiffness trade-off: filling occluded regions increased material volume and reduced displacement under the evaluated loads. Paired depth images thus connect generative exploration and structural refinement in a shared design space that preserves the selected pull-direction restriction.

Abstract: The current paper introduces the GraphNARX model, a graph-based nonlinear autoregressive exogenous model for structural dynamics. The model is built to account for the geometry of structures and to model dynamic behaviour as the interaction between elements of the structure. Similar to other types of NARX models, GraphNARX is used for system identification. Nodal attributes of the graph encode past displacements and nodal forces, and the output of the model is the next-timestep displacement. The graph formulation of the model allows it to generalise to structures of different dimensions and degrees of freedom. Moreover, because graph-learning is performed locally between the nodes, the GraphNARX model can also learn to infer displacements of nodes for which data are not available, i.e.\ to perform virtual sensing. The proposed model's performance is evaluated in a system-identification framework and a virtual-sensing framework, and achieves good accuracy and exhibits generalisation capabilities to structures of different sizes.

Abstract: Here, we study an undamped Rayleigh beam subjected to a concentrated transverse impulse applied at a point far from the boundaries. For a simply supported finite beam struck at its midpoint, using the modal expansion of the impulse response, a short-time asymptotic series for the response of the struck point is derived. The infinite beam impulse response is obtained as a spectral integral in two ways. The spectral integral is evaluated exactly in terms of modified Bessel functions via Laplace transform calculations. The corresponding short- and long-time asymptotics of the exact integral are consistent with the power series developed earlier and the Euler-Bernoulli beam, respectively. Direct numerical evaluation of the integral with a pre-specified error bound and numerical contour integration is also presented for verification. An ad hoc approximation is given which matches the response well for all times. The relationship between finite and infinite beam responses is examined in some detail. There are three consequences of finite length. First, the coefficients in the power series expansion contain components that decay exponentially with increasing length of the beam. Second, a smooth deviation from the infinite beam response is observed, consistent with the greatest group velocity in the beam, wherein a small precursor is detected which is consistent with broader theory. Third, a slope discontinuity is observed, corresponding to the high-frequency limit of group velocity. The full time series plot from modal expansion satisfactorily shows both the arrival and passage of these high frequency components. This paper opens the door to impact studies that are envisaged in future work.

Abstract: Cumulative energy fields in irreversible evolution depend on the loading path, even when terminal states and global work agree. We derive a posteriori bounds for these fields in scalar gradient damage with a prescribed driving density. A perturbation estimate for the incremental obstacle map yields a continuous loading history, which is enclosed by nondecreasing residual supersolutions. A primitive identity transfers this enclosure to the cumulative field. An exact endpoint-rule defect and outward arithmetic certify the output delivered by the numerical method. The analysis separates spatial, loading, and algebraic errors and gives sufficient conditions for certificate decay. Computable realizations use splines and verified supersolutions in one dimension and on two-dimensional rectangles. The production bounds cover the independently enclosed errors of all 417 saved histories from 28 adaptive calculations and all 25 fixed-parameter controls. In a narrow-localization case, the verified relative error decreases from approximately 158.78\% to below 2.125\% at a 5\% certified target. Source-oriented marking reduces accumulated matrix--vector work by 35.9\% and 51.9\% in two comparisons. A mechanically generated two-dimensional benchmark shows how auxiliary supersolutions sharpen constant barriers and enable acceptance of both loading orders.

Abstract: Elastic buckling remains a critical concern in the design of deep spherical shell caps, given that experiments reveal a significant reduction of critical loads from those predicted by linearized eigen-buckling analysis. This discrepancy has been attributed to initial geometric imperfections and is often reconciled through a dimensionless parameter, namely the knockdown factor (KDF). However, conventional KDFs (NASA SP-8007; Eurocode 3) are highly conservative, as they represent the lower bound of an extensive body of experimental data. This study aims to narrow the conservatism in the KDFs for spherical shell caps through machine learning (ML) regression models trained on experimental data on spherical shell buckling. A hybrid model is proposed by combining Gaussian Process Regression (GPR) with Extreme Gradient Boosting (XGBoost), and its improved performance is demonstrated over conventional ML algorithms, i.e., the Artificial Neural Network (ANN), Support Vector Regressor (SVR), Random Forest Regressor (RFR), and Histogram-based Gradient Boosting (HGBoost). Each of these models uses six input features and a single output, i.e., the KDF. The most critical feature affecting the KDF is ascertained through a sensitivity analysis. The study concludes with a reliability-based design framework that relies on the predictive ML model to obtain safety-consistent, yet less conservative, KDFs.

Abstract: Bifurcations are ubiquitous in physical systems, from structural buckling to fluid and climate dynamics, yet they remain largely unexplored in deep learning. At a symmetry-breaking bifurcation, a single input admits multiple equally valid solutions, violating the one-to-one assumption underlying most learned physical surrogates. We introduce Bi-FORK, a generative framework for learning these one-to-many solution maps in high-dimensional systems. Bi-FORK generates complete trajectories through latent flow matching, preserving space and time coherence, and uses repulsion-guided sampling to recover distinct solution branches in a single amortized pass. We evaluate Bi-FORK on buckling beams, mechanical metamaterials, and Allen-Cahn phase separation, spanning continuous, discrete, and field-valued bifurcations with discretizations up to 260,000 points. Bi-FORK recovers the multimodal solution structure while scaling several orders of magnitude beyond prior approaches, opening generative modeling to high-dimensional bifurcating physical systems.

Abstract: Solving high-dimensional structural model updating problems requires an algorithm capable of navigating complex, non-convex landscapes with correlated parameters. Existing hybrid evolutionary algorithms typically rely on static architectures or fixed switching rules, resulting in disjointed search phases. To address this, this study proposes a Deep Reinforcement Learning-governed dynamic DE-CMAES Orchestration (DRL-DCO) algorithm, in which a Deep Deterministic Policy Gradient (DDPG)-based actor-critic agent continuously governs the evolutionary process as a single, unified system rather than a mechanical concatenation of algorithms. Guided by a progression-aware state representation and a diversity-informed reward, the agent fluidly reallocates computational resources between the differencevector-based exploration of Differential Evolution (DE) and the covariance-guided exploitation of CMA-ES, while jointly regulating population size, elite preservation, and a restart mechanism to escape local optima. This allows DRL-DCO to autonomously transition between exploration-dominant, exploitation-dominant, and mixed-strategy regimes across generations. Beyond the training phase, the trained actor can operate in a supervision-free inference mode, where the internalized policy autonomously orchestrates DE and CMA-ES control from observed search states through forward inference alone, without critic evaluation or weight updates, enabling faster deployment while retaining full effectiveness. Validated on high-dimensional single-objective optimization benchmarks and the IASC-ASCE structural health monitoring benchmark, DRL-DCO achieves superior convergence accuracy and robustness compared to state-of-the-art adaptive and hybrid evolutionary algorithms, as well as single-operator DRL-governed baselines.

Abstract: Thermo-mechanical fracture couples transient heat conduction on a cracked domain with a crack that grows as the temperature and the displacement evolve. Neural energy solvers have been proposed for phase-field fracture and later extended to represent a sharp crack through the network input, but heat conduction on the cracked domain and crack propagation under the resulting thermal stresses have not yet been treated together in these solvers. We present an extended deep energy method for thermo-mechanical crack propagation in which the crack remains a sharp polyline. Two networks represent the temperature and the displacement and receive the crack through a scalar embedding function, discontinuous across the crack and smooth elsewhere, so that both fields can jump across it without a regularization length, and the displacement is enriched near the tip by the Williams expansion with trainable amplitudes. The two fields are obtained by minimizing an incremental conduction functional and the thermoelastic potential energy in a staggered sequence, with Monte Carlo integration on points stratified over background elements, densified near the tip and redrawn during training. The stress intensity factors are extracted by the interaction integral with the area term of Wilson and Yu and checked by a sweep of the contour radius, and the crack advances at the maximum hoop stress angle when the energy release rate of the kink reaches the critical value at the crack-tip temperature. On a stationary thermal edge crack the extracted stress intensity factor agrees with the published value to 0.11%, in a functionally graded shear test initiation agrees with an independent sharp-crack finite element solution to within one load step, and on a notched cruciform specimen the crack paths follow the published solutions under mechanical, thermal and combined loading.

Abstract: The increasing use of lattice-like architectures in load-bearing members, facilitated by advances in additive manufacturing, calls for efficient multiscale approaches to their structural analysis. For slender lattice-like structures, beam models provide a computationally efficient macroscopic representation while retaining the ability to account for the underlying lattice architecture through an homogenization approach. Although finite element squared (FE2) approaches combining beam models at the macroscopic scale with continuum models at the microscopic scale have been established, an FE2 framework combining a beam-based macroscopic model with a truss-based microscopic model of a lattice structure has not yet been reported. To address this gap, an FE2 framework is developed for three-dimensional shear-deformable beams with periodically repeated lattice-like microstructures and periodic displacement boundary conditions. The proposed FE2 framework introduces constraint equations that (a) prevent rigid-body translations and rotations of the representative volume element (RVE) without imposing additional kinematic restrictions and (b) ensure that the homogenized stress resultants and material matrix are independent of the selected RVE length. To mitigate artificial boundary effects arising at the boundaries of the lattice-like RVE, local correction factors are introduced. The framework is assessed through numerical studies of two- and three-dimensional lattice-like structures with different geometries, considering both geometric and material linearity and nonlinearity. The results demonstrate the independence of the homogenized stress resultants and material matrix from the selected RVE length and show good agreement with the corresponding reference models in all investigated cases.

Abstract: Yield point phenomena in metals, anticracks in soils and snows, or planewise collapses in lattice metamaterials, are different manifestations of plastic instabilities characterized by stress softening and strain localization. Several independent constitutive descriptions exist and suffer from similar challenges: experimental difficulties to link local events to global measurements, and computational lack of convergence, spurious localization and mesh sensitivity. This work proposes a minimal field-agnostic constitutive framework where plastic softening is represented by a damage-like internal variable which explicitly separates stable hardening behavior from unstable softening. The resulting formulation admits a variational structure and can leverage regularization tools originally developed by the ductile fracture community. The framework aims at emphasizing similarities within plastic instability phenomena and establishing a bridge with continuum damage mechanics, to open a path towards regularized variational formulations of localized plastic flows.

Abstract: We present a space-time finite element formulation for the transient analysis of geometrically exact shear-deformable beams. The formulation treats space and time within a unified finite element framework and employs a mixed approach in which translational and angular velocities are introduced as independent fields. The rotation field is parametrized using nodal rotation (pseudo-)vectors and a suitable objective interpolation of the triad field is employed. The resulting formulation supports generally curved beam structures, including geometric kinks and rigid joints. Furthermore, time-dependent material domains can be represented directly through the geometry of the space-time surface, enabling the treatment of non-material boundaries without modifying the underlying beam formulation. Numerical examples demonstrate convergence to solutions obtained with classical time-stepping schemes, objectivity of the formulation, and the influence of the space-time stabilization. Finally, the sliding spaghetti problem illustrates the applicability of the proposed approach to axially moving continua.

Abstract: Deep learning has emerged as an efficient alternative for predicting high-performance material distributions in topology optimization. Existing methods struggle to accurately capture load-transfer information, limiting out-of-distribution generalization, while their model architectures often incur high computational costs. To address these challenges, this paper proposes TopoMamba, a topology prediction framework incorporating a load-support relation-guided multi-directional state-space model. Coupling physical fields with load-support relations enables more effective modeling of mechanical dependencies. A load-support relation-guided spatially adaptive fusion mechanism dynamically adjusts multi-directional scan features according to spatial conditions. Mamba is coupled with the solid isotropic material with penalty method to enhance structural mechanical performance while maintaining computational efficiency. Results on two-dimensional topology optimization benchmarks demonstrate that TopoMamba achieves superior topology prediction accuracy, out-of-distribution generalization, and computational efficiency over state-of-the-art models. The proposed load-support physics-guided framework enables efficient optimization of more complex structural systems.

Abstract: Machine learning plays an increasingly vital role in engineering, but the corresponding increase in compute time is not without environmental cost. Physics-informed machine learning or "grey-box" models have been developed to overcome some of the limitations of traditional black-box learners, utilising the physical insight that an engineer would have about the structure they are modelling and have shown promising results in the structural engineering field among many others. This work explores whether an additional advantage could be a reduced environmental impact, considering the relationship between training data quantity and training time, linking this duration to carbon emissions from computing. In a structural health monitoring context, four physics-informed machine learning approaches - spanning Gaussian processes and neural networks - are evaluated: residual modelling, input augmentation, hybrid modelling, and constrained learning. The emissions for training each of the models to reach a given error threshold is compared, and in most examples, shown to be lower for the physics-informed models (with input augmented models being an exception). This reduction in training emissions further compounds the environmental savings achieved by collecting and storing less data. Although promising results, we cannot expect a silver bullet and the case studies demonstrate that a trade-off is needed between the increased complexity that comes from introducing physics into a machine learner, against the gain from reduced training data requirements.

Abstract: In solid mechanics, finite element discretization of large-scale static problems produces large sparse linear systems whose solution requires substantial computation time and memory. The variational quantum linear solver (VQLS) offers a hybrid quantum-classical route, but its use in quantum finite element analysis is limited by the decomposition of nonunitary matrices, barren plateaus, and the measurement cost of expectation values. We propose a voxel-based block variational quantum linear solver (Voxel-BVQLS) that combines structured matrix decomposition, the principle of minimum potential energy, and batched quantum tests. First, we construct an LCU decomposition of the stiffness matrix from the recursive block-banded structure of voxel-grid finite element matrices, with the number of unitary terms bounded independently of the problem size. Second, we optimize the ansatz parameters using a minimum-potential-energy objective in place of a conventional VQLS loss function, thereby mitigating barren plateaus in the studied problems. Third, we introduce a block-Hadamard test whose circuit directly estimates weighted sums of multiple inner products, reducing the number of circuit configurations required per iteration. We assessed the proposed method in noiseless classical simulations using three examples. These examples show that the method reduces both the number of unitary terms in the LCU decomposition and the number of iterations required to converge, while still yielding solutions of finite accuracy. Voxel-BVQLS thus provides a structured hybrid quantum-classical framework for quantum finite element analysis on regular grids.

Abstract: The linearized buckling load of a stiffened panel depends on the stress stiffness its shell element assembles. We read it from exported operators against three truncations of one second variation. The classic pass of ANSYS SHELL181 carries a rotation-rotation block pairing the drilling freedom with the bending rotations and its perturbation pass does not; removing the block recovers the perturbation load factor to 0.02%. SHELL281 carries block and couplings in both passes. Abaqus S4 matches the critical mode of the complete second variation to 1.0000 on the translations and its load factor to 1.7%, against 17% and 34% for the other two forms. On an optimized panel under cantilevered shear a 20-node continuum lies 3% to 6% above that form, S4 and SHELL281, 11% and 23% below both SHELL181 passes and 25% above Abaqus S8R, at the finest meshes. On a conventionally stiffened panel the SHELL181 passes stand 1.0% and 3.5% above the complete form, 9% and 21% at half the rib pitch; under a shear flow, on cylinders, open beams and under axial compression the three forms coincide and no pass parts by more than 0.3%.

Abstract: Multimodal large language models, or MLLMs, perform well at visual understanding and structured generation, yet these capabilities do not establish whether an engineering design will work when executed. Existing benchmarks assess spatial reasoning, structural validity, or physics-grounded construction, but they do not determine whether MLLMs can synthesize complete load-bearing structures and repair them after simulator execution exposes a failure. We introduce PolyBridgeBench, an executable benchmark for multimodal bridge design. A model receives a visual scene and structured engineering constraints and generates a complete node--member--material topology. Deterministic legality checks gate execution in a native dynamic physics simulation. Following an execution failure, the benchmark returns temporal visual evidence from the failed rollout and evaluates repair under a fixed interaction budget. Separate measurements of deterministic validity, dynamic functional success, and post-failure recovery identify the stage at which design fails. Experiments with six representative MLLMs across 189 levels expose a substantial gap between deterministic validity and dynamic success, pronounced sensitivity to material budgets, and limited post-failure recovery under the primary strict-budget setting.

Abstract: This paper presents novel approaches to tackle two key challenges in topology optimization problems with buckling constraints: determining how many eigenvalues to aggregate and identifying the eigenvalue modality at the optimal design. We demonstrate the mathematical inconsistencies that arise when choosing an arbitrary fixed number of eigenvalues for aggregation. Specifically, if the multiplicity of the critical eigenvalues is smaller than the chosen subset size, coalescence with higher-order eigenvalues can occur. Neglecting these during aggregation causes incorrect sensitivities, while simply increasing the preselected eigenvalue count unnecessarily raises computational costs. To resolve this issue, we propose an approach that dynamically determines the exact number of eigenvalues required at each optimization iteration. The proposed approach reduces computation time significantly while maintaining competitive performance relative to the conventional method across the numerical experiments presented. Additionally, accurately predicting modality at the optimal point is crucial for understanding the buckled mode shapes of optimized designs. A new optimization formulation is proposed using the difference between eigenvalues to capture the true eigenvalue modality. This formulation is first validated on a classical 1D clamped column, successfully predicting both the bimodal solution and the optimal eigenvectors. The approach demonstrates that the optimal solutions for the wall reinforcement and shear-loaded hinged plate problems for the given set of parameters are trimodal and tetramodal, respectively.

Abstract: Density-based topology optimization is typically structured as a nested sequence of material updates, structural analyses, and sensitivity assessments. While neural density parameterization and dual-field physics-informed approaches provide data-free alternatives, most existing methods represent density and displacement as coordinate fields and make limited use of the discrete relationships inherent in the finite element mesh. The present study introduces HGTO, a unified graph-based formulation that extends complete neural topology optimization from coordinate space to finite-element graph space. Element densities are parameterized on the element graph derived from the mesh, and the structural state is determined on the corresponding node--element hypergraph. Finite element kinematics, numerical quadrature, constitutive response, and force assembly remain explicitly defined operations within the differentiable computation. The material field and equilibrium state are therefore coupled through a common finite-element incidence structure. Numerical studies show compliance comparable to conventional density-based optimization at substantially lower computational cost than a representative coordinate-based dual-field neural method. The same coupled formulation accommodates high-resolution and irregular meshes, three-dimensional structures, finite deformation, and elastoplastic response.

Abstract: Although the impact resistance of concrete has been studied extensively, a framework linking mesoscale heterogeneity to full-field stress-tensor prediction has been lacking. Data were generated with a full-scale aggregate-resolved LS-DYNA model (projectile diameter 45 mm, mass 2.13 kg, target diameter 500 mm x thickness 200 mm, mesh 10 mm), verified against published penetration experiments (Frew 2006, Hanchak 1992, Forrestal 1996) by configuration similarity. The dataset contains six-component stress-tensor fields on the X-Z mid-plane for 400 cases (4 impact velocities x 100 aggregate seeds). Three contributions are reported. First, case-by-case verification of the terminal penetration state delimited the rest-state validity of penetration depth and anchored reliable observables to rigid-body motion and field-level stress evolution. Second, a field-level graph neural operator surrogate learned the time-varying stress-field evolution and evaluated cross-velocity leave-one-out extrapolation. Third, the full-scale, aggregate-resolved, cross-velocity, per-seed database was established as a reproducible resource. Cases at 100, 135 and 200 m/s still moved at window end (negative velocity, i.e. rebound), and only one 165 m/s case arrested. Penetration depth is therefore not reported as a rest-state scalar except for the single arrested case (69.33 mm); nose-node depth differences were confirmed as numerical artifacts of displacement integration after erosion. The single-step relative L2 error was 0.6977, reported honestly; autoregressive rollout from frame 11 to 39 took about 144 ms, a speedup of about 3.6x10^3 to 4.3x10^3 relative to single-core LS-DYNA, reported as application value. Validation is bounded by configuration similarity and field-level self-consistency; the framework is a simulation-trained decision-support method within the studied parameter space.