Nonlinear fluid viscous dampers are highly effective devices for passive control of structural systems. Their reliable analysis and design optimization require robust computational tools capable of accurately evaluating the nonlinear dynamic structural response. A robust time integration approach based on the mixed Lagrangian formalism (MLF) is presented for dynamic response analysis and optimization. MLF has demonstrated strong robustness in nonlinear transient analysis, but its use in gradient-based optimization of structures equipped with nonlinear fluid viscous dampers has been largely unexplored. Structures exhibiting elasto-plastic behavior with kinematic hardening and equipped with nonlinear fluid viscous dampers are considered. The dampers are modeled through a Maxwell representation combined with a fractional power-law constitutive relation. The proposed approach addresses the numerical challenges posed by nonlinear velocity-dependent damper forces, which are characterized by fractional exponents and rate-sensitive dissipation mechanisms. The proposed framework is assessed through numerical examples involving seismic retrofit with nonlinear fluid viscous dampers, including a three-dimensional irregular frame structure with a double setback. The results show that the proposed MLF-based approach provides accurate and stable response predictions and efficient optimized designs. As a direct sensitivity-analysis approach, the present formulation is computationally convenient when the number of design variables is less than or equal to the number of response functions to be differentiated. Moreover, unlike an adjoint sensitivity approach, it can be carried out concurrently with the forward response analysis, without requiring a subsequent backward-in-time solution.
Rolling noise, arising from the complex interaction between vehicle wheels and the rail, is the dominant noise source in railway traffic across a wide range of speeds. This paper presents a novel time-domain approach for modeling structure-borne sound generation and propagation in railway tracks. The proposed model provides a comprehensive structural representation by incorporating the Timoshenko beam theory for vertical and lateral bending waves as well as longitudinal waves, torsional waves and warping effects, allowing for arbitrary excitation and track composition. A complex frequency-shifted perfectly matched layer approach is developed using auxiliary differential equations in order to simulate an infinite track. The resulting system of 27 differential equations is solved by an explicit finite-difference method. Validation against an existing semi-analytical model shows a strong alignment, verifying the numerical implementation. Finally, moving source simulations demonstrate that the approach is able to successfully capture key dynamic phenomena, including the sleeper-passing frequency and the Doppler shift of the pinned-pinned frequency in both vertical and lateral directions.
The integration of neural network–based methods into scientific modeling has opened new opportunities for tackling complex challenges in constitutive modeling within computational mechanics. In practical settings, however, challenges arise due to the privacy constraints, distributed nature of data, and the difficulty of transferring large datasets. Federated learning offers an effective solution by enabling decentralized training of a global model while keeping data localized. In this work, we present, for the first time, a physics-guided Federated Scientific Machine Learning (FedSciML) framework for both inverse parameter identification of a constitutive model and direct approximation of polycarbonate material behavior under heterogeneous and decentralized data conditions. To systematically study data heterogeneity, we introduce controlled data generation strategies that produce non-independent and identically distributed (non-IID) datasets and employ the 1-Wasserstein distance to quantify distributional differences. We further examine how varying the number of participating clients influences the level of heterogeneity. The results show that the proposed FedSciML framework effectively calibrates the constitutive model by identifying a unified parameter set that accurately reproduces experimental observations. In addition, the framework demonstrates strong predictive capability in learning material behavior even under severe data scarcity and highly non-IID conditions. Overall, both the global federated model and the local client models achieve accurate extrapolation across unseen regimes, without requiring direct data sharing. This highlights the robustness and practical relevance of the proposed approach.
Large-span spatial structures are widely used in critical public facilities, but conventional incremental dynamic analysis (IDA)-based seismic fragility assessment is computationally intensive. This study proposes a multimodal deep learning framework to improve efficiency and interpretability. An IDA-based database was developed for three representative systems: a spherical reticulated shell, a cylindrical reticulated shell, and a flat grid structure. The framework integrates normalized time-domain waveforms, frequency-domain spectrograms, and physical intensity measures through a multi-branch fusion architecture. A two-stage classification–regression strategy and quantity-weighted loss are adopted to address imbalanced damage-state distributions. Fragility predictions are evaluated using the median parameter θ, logarithmic dispersion β, percentage errors, and curve agreement. With 40% of the dataset (480 samples), the multimodal feature model achieves R2 values of 0.9116, 0.8990, and 0.8757 for the three structures, with average θ and β errors of 6.41% and 20.81%, respectively. Increasing the training proportion to 80% further improves accuracy and highlights the benefit of multimodal fusion. SHAP analysis identifies physical measures, particularly Sa(T1), as the dominant contributors, while time- and frequency-domain features provide complementary information. Compared with full IDA, the proposed framework reduces computational time by approximately 59.98% while maintaining acceptable accuracy.
The force density method is an equilibrium-based form finding approach commonly used to define the geometry of funicular and anti-funicular structural networks. This study revisits form finding of compressive reticulated shells by extending the standard equilibrium equations with additional constraints that incorporate both kinematic relations and the constitutive law. The result is an enhanced formulation capable of capturing linear elastic equilibrium through constrained optimization. Using mathematical programming, a unique set of force densities is determined that governs both the structural shape and its elastic response, while naturally ensuring control over deflections. This framework enables the design of elastic no-tension configurations, which are relevant for applications such as 3D concrete printing. Numerical simulations are carried out to optimize compressive gridshells with fixed plan geometry under vertical loads. Two objectives are investigated: minimizing the maximum reaction force and minimizing structural compliance. For the first objective, results are compared with those from a traditional equilibrium-based approach, while for the second, comparisons are made with a combined force density and finite element method. The sensitivity of the resulting forms to the underlying modeling assumptions is highlighted.
This work presents an efficient finite element model for simulating the mechanical behavior of synthetic stranded sub-ropes under large deformation. The model first simulates the shape of the sub-rope obtained starting from straight strands, then the sub-rope’s response to a tensile loading. The model represents the volume of the strands and takes into account the contact and friction between strands. A detailed 3D model representing four lay-lengths is first developed, to serve as a reference for validating a more efficient reduced model. The influence of the stresses generated when the strands are twisted into a helix to form the sub-rope is demonstrated. To reduce computational cost, a simplified model using periodic and symmetry conditions over one quarter of a lay-length is proposed. This reduced model shows excellent agreement with the reference model, both in terms of global response (force, torque and elongation) and mechanical fields. It also enables a very significant reduction in computation time. The reduced model is therefore particularly well-suited for parametric studies (typically construction parameters). The model allows for the rapid calculation of the global response of the sub-rope and the intra-strand and inter-strand mechanical fields.
Violent sloshing in partially filled tanks is strongly nonlinear and poses a safety-critical problem in many engineering applications since large impact pressures can be imposed on tank structures. Although internal baffles are widely adopted as suppression devices and have been investigated in some studies, the identification and quantitative assessment of optimal configurations across both rigid and elastic designs remain limited, probably because exhaustive exploration of a high-dimensional design space is computationally prohibitive. Traditional mesh-based methods often require coupling treatments to deal with free surface evolution and large deformations, whereas smoothed particle hydrodynamics, as a fully Lagrangian mesh-free method, can naturally capture violent sloshing flows. Therefore, to address the computational bottleneck of exhaustive exploration, a simulation-driven design framework is developed by integrating smoothed particle hydrodynamics with Bayesian optimization where a probabilistic surrogate model guides the search under a limited computational budget and enables the identification of an optimal baffle configuration. Both rigid and elastic baffle designs are tested, and the results show that for the rigid case, the suppression rate reaches 63.6% after only 40 simulations selected from a total of 441 candidate configurations. As for the elastic case, the suppression rate achieves 59.1% using only 45 simulations from a much larger design space of 6006 candidates. These results confirm that Bayesian optimization can identify optimal baffle configurations to effectively suppress the sloshing within a limited number of expensive simulations, even when the underlying design space is high-dimensional.
This work presents a geometry-consistent decomposition–migration framework for constructing strictly non-overlapping periodic representative volume elements (RVEs) of composites containing concave inclusions while preserving the target concave geometry and prescribed in-plane orientation statistics. Each inclusion is first reduced to a compact set of convex primitives by hybrid triangulation followed by topology-preserving convex merging, enabling robust convex–convex interaction queries for highly non-convex boundaries. Periodic overlap detection and penetration-depth evaluation are performed using the Gilbert–Johnson–Keerthi algorithm together with the Expanding Polytope Algorithm under a minimum-image convention. A symmetric penetration-based migration update then aggregates multi-contact corrections to separate overlapped inclusions and stabilize relaxation in dense configurations. Efficiency is improved through circumscribed-polygon preprocessing, a periodic cell-list broad phase, and hierarchical enclosing-circle and bounding-box filters at both the inclusion and convex sub-polygon levels. The framework avoids artificial truncation of boundary-crossing inclusions and therefore produces cells directly compatible with periodic boundary conditions. Numerical examples show that the method generates dense periodic configurations with morphology-dependent packing limits exceeding 70%, and the generated configurations are characterized using statistical descriptors of orientation and spatial distribution. The resulting microstructures are further used in finite-element homogenization and damage simulations, demonstrating their suitability as reliable geometric inputs for microstructure-resolved solid mechanics.
Nature-inspired triply periodic minimal surface structures offer breakthrough potential for ultra-lightweight aerospace applications. However, their aeroelastic behavior under the combined influence of structural and aerodynamic damping remains insufficiently understood. This study aims to elucidate the flutter instability boundaries of functionally graded triply periodic minimal surface plates subjected to supersonic airflow, focusing specifically on the interactions between structural and aerodynamic damping mechanisms. To accurately capture intricate aeroelastic responses, an efficient computational model is established using isogeometric analysis coupled with higher-order shear deformation theory. Based on a linear aeroelastic formulation, numerical results reveal a pronounced nonmonotonic dual-damping effect, whereby increasing structural damping initially reduces the critical flutter pressure in the low-damping regime before reversing this trend and significantly improving aeroelastic stability at higher damping levels. The results further show that transverse shear deformation reduces the flutter boundary for moderately thick plates, whereas its influence gradually diminishes as the plate becomes thinner, leading the flutter boundary to asymptotically approach a constant value. Moreover, among the evaluated configurations, the symmetric I-Graph-Wrapped Package architecture emerges as the best configuration among the considered cases for enhancing flutter resistance. These findings provide a systematic evaluation of damping-dependent flutter trends for the nature-inspired lattice plate configurations, offering valuable qualitative insights into their aeroelastic instability in high-speed environments.
The first-order hyperbolic {p,F} formulation of nonlinear elastodynamics, with p as the linear momentum and F as the deformation gradient, enables finite volume methods from computational fluid dynamics (CFD) to be applied to solid dynamics. Dual time-stepping (DTS), the CFD standard for time accuracy, extends to the solid solver, offering a unified infrastructure for fluid–structure interaction (FSI). The nearly incompressible neo-Hookean (NINH) model adopted here makes convergence challenging, as its eigenstructure varies with deformation and its pressure wave speed approaches infinity near incompressibility. Yet no systematic assessment of DTS inner solvers exists for this system. This work characterizes, for the first time, three inner solvers within a second-order BDF2 DTS formulation: explicit multistage Runge–Kutta (MRK), lower-upper symmetric Gauss–Seidel (LU-SGS), and FGMRES with LU-SGS preconditioning. Sweeps over time step, CFL number, Krylov parameters, Poisson’s ratio, and mesh topology show only preconditioned FGMRES converging across the range. The augmented {p,F,J} system, which adds the volume map J as a conserved variable, restores convergence where {p,F} fails. Our earlier angular momentum correction is recast for BDF2 and conserves momentum to machine precision independently of the inner solver. The results provide solver selection guidelines for DTS, with extension to time spectral methods (TSM) as future work.
This paper presents a refined 4-node quadrilateral shell element with 6 degrees of freedom per node. Developed based on the original DKMQ24 element [53], the refined DKMQ24 uses smoothed pseudo-normal vectors at the corner nodes to ensure normal continuity across neighbouring elements in a discretised shell model. These pseudo-normals are employed to compute pseudo-curvatures, which enable full coupling between membrane and bending behaviours, and are further utilised to compute the constant kinematic transverse shear strain along the element sides. This formulation stays within the modified Reissner-Mindlin-Naghdi framework. It incorporates MITC4-type assumed shear strains to suppress shear locking and applies artificial drilling stiffness to maintain matrix rank in coplanar configurations. Numerical validation proves that the refined DKMQ24 element passes all patch tests, is locking-free, maintains proper rank, and converges rapidly throughout benchmark problems. Additionally, the element demonstrates consistent convergence with mesh refinement in Scordelis-Lo’s roof and pinched cylinder, and, most importantly, it shows reliable performance in Raasch’s hook, where the original formulation diverges. Collectively, these improvements confirm the effectiveness of using pseudo-normals in kinematic transverse shear strains and pseudo-curvatures in bending strains.
This paper presents the first extension of the Parametric High-Fidelity Generalized Method of Cells (PHFGMC) to fully transient elastodynamic analysis. The PHFGMC is a well-established micromechanical method that uses second-order parametric displacement expansions within arbitrary-shaped subcells for modeling linear, nonlinear, and multiphysics behaviors in composites featuring periodic microstructure. Inertial terms, together with optional Rayleigh (physical) damping, are incorporated into the volume-averaged virtual work formulation. Two time-integration schemes are implemented: (i) an implicit Hilber–Hughes–Taylor algorithm, and (ii) an explicit central-difference scheme employing the Hinton–Rock–Zienkiewicz mass-lumping procedure. The scientific contribution is not the parametric mapping (already established in the quasi-static PHFGMC) but the first transient micromechanical formulation that resolves full local field histories on arbitrarily shaped subcells; this requires resolving a specific obstacle—standard row-sum lumping of the second-order subcell shape functions yields non-physical negative masses—that does not arise in the rectangular dynamic HFGMC. The framework is rigorously verified against elastodynamic benchmark problems possessing established analytical, experimental, or finite-element reference solutions: (1) surface impact on an elastic half-space; (2) pulse propagation through a periodically bilaminated composite; (3) transient unloading waves from the sudden formation of a circular hole in a prestressed plate; (4) instantaneous initiation and sub-Rayleigh propagation of a semi-infinite crack under Mode I, Mode II, and Mode III loading; (5) dynamic expansion of a pressurized spherical cavity in an infinite elastic medium; (6) two-dimensional Lamb problem under strip impulse loading; (7) wave propagation normal to long fibers in a unidirectional fiber-reinforced composite; and (8) wave propagation in tri-orthogonally fiber-reinforced composites. In all cases, implicit and explicit PHFGMC predictions show excellent quantitative agreement with the reference data, here quantified by a relative L2 error norm rather than by visual inspection alone, and benchmarked against high-order (20-node tri-quadratic) finite elements in addition to standard linear ones.
This study presents a computationally optimized framework for predicting the effective thermal conductivity tensors of three-dimensional heterogeneous composites through an enriched Fast Fourier Transform (X-FFT) solver. The framework is implemented by developing and validating an efficient Abaqus plug-in. The classical spectral solvers are extended to capture anisotropic interfacial thermal resistance and temperature-dependent material behavior with an enriched augmented Lagrangian (AL) formulation at the interface. The framework combines a level-set representation of material interfaces with strong-discontinuity enrichment to capture temperature jumps associated with Kapitza thermal resistance on structured voxel grids. Temperature-dependent anisotropic conductivity is integrated through a consistent nonlinear Newton framework. Optional surface-gradient regularization and calibrated morphology-dependent interface conductance are introduced as stabilization and extension capabilities without altering the underlying physical interface model. The resulting X-FFT framework is then verified against analytical benchmarks and validated with asymptotic expansion homogenization (AEH), conjugate gradient FFT (CG-FFT), and classical FFT schemes. Numerical results demonstrate the robustness and accuracy of the proposed method for nonlinear conductivity variations and high-resolution unit cells, and achieve marked reductions in computational time compared to AEH. This ensures a reliable and integrated platform within the commercial finite element environment that accelerates multiscale composite analysis.
This paper presents a Machine Learning taxonomy-based framework for deriving fragility curves of bridge portfolios under exogenous hazards, with application to multi-span simply supported prestressed concrete girder bridges with single-shaft reinforced concrete piers. A tailored taxonomy is created to account for two main hazards: traffic and seismic loads. Different finite element numerical models are created for substructure and superstructure, aimed at performing parametric analyses accounting for material degradation (i.e., corrosion). The results are used as input dataset to train and test Machine Learning algorithms to derive fragility curves for different collapse limit states. Statistical metrics and eXplainability approaches are used to identify the best surrogate model and the most critical input features. The comparison with finite element-based fragility curves shows median differences generally lower than 5% for traffic hazard and lower than 10% for seismic hazard. The proposed approach is tested on a real-life case study to assess the accuracy of prediction against numerical analyses for rapid portfolio-scale screening and prioritization. The main innovation of the work is a tangible and quantitative set of Machine Learning taxonomy-based fragility curves, which can be used for supporting prioritization of bridge portfolios.
Application of fractional calculus in the formulation of basic viscoelastic models is reviewed. Attention is focused on efficient and memory-low implementation of two fundamental theoretical approaches to the modelling of a polymer interlayer in laminated glass plates. In particular, the convolution integral-based formulation is compared to the one arising from the solution of differential equation of an underlying constitutive model. The role of approximation of fractional derivative is examined with reference to the Gr & uuml;nwald-Letnikov and the so-called L1 schemes adopted in the prediction of the response of simple rheological models such as springpot, Maxwell unit, and three-element Maxwell chain to discontinuous as well as smooth loading scenarios. The results show several compelling properties of the L1 scheme particularly in conjunction with the gradual memory reduction procedure and promote this method when advancing the modelling to computationally intensive large scale structural analyses.
