Search Results (120)

U.S. renewable energy consumption has expanded substantially over the past five decades, but this transition cannot be adequately characterized by aggregate growth alone. This study developed an integrated empirical, forecasting, uncertainty, reconciliation, scenario, and planning framework for U.S. renewable energy consumption using a complete monthly multisector panel from January 1973 through December 2025. The analytic dataset contained 3180 sector–month observations across 636 monthly periods and five reporting sectors: Commercial, Electric Power, Industrial, Residential, and Transportation. The framework combined data harmonization, mutually exclusive source-family construction, long-run trend analysis, source-mix diversification metrics, structural-regime diagnostics, sector–source panel analysis, rolling-origin forecast benchmarking, probabilistic interval assessment, hierarchical reconciliation, future scenario analysis, and decision-focused planning evaluation. Annual reported total renewable energy consumption increased from 2475.547 trillion Btu in 1973 to 7050.214 trillion Btu in 2025, equivalent to approximately 2.476 quadrillion Btu and 7.050 quadrillion Btu, respectively. The results show that U.S. renewable energy growth was also a source-mix transformation: the portfolio became less concentrated as wind, solar, transportation biofuels, renewable diesel, waste, and other emerging sources gained importance alongside legacy wood and hydroelectric power. Sector–source heterogeneity was substantial, with Electric Power, Industrial, and Transportation showing distinct renewable-source profiles. Forecasting performance depended strongly on model family, horizon, validation window, target group, and evaluation lens. Strong statistical baselines and feature-based tree models remained competitive or superior to several deep learning architectures, while time-series foundation models provided useful modern comparators but required calibration and horizon-specific interpretation. All five selected foundation model comparators completed successfully. ChronosBolt was the fastest and strongest completed foundation model comparator, followed in runtime by TimesFM, Moirai/Uni2TS, TimeGPT, and LagLlama; however, foundation model forecasts remained too smooth for peak-sensitive planning and did not displace the strongest feature-based tree models in point-forecast benchmarking. Probabilistic diagnostics showed that nominal coverage alone was insufficient because interval width, Winkler score, CRPS, and visual inspection revealed target-specific miscalibration, underforecast bias, and weak peak coverage. Hierarchical and decision-focused evaluation changed the model-selection narrative: bottom-up and reconciled hierarchical forecasts produced stronger planning-loss and planning-value profiles than many nominally advanced alternatives, while selected tree-based models were particularly useful for preserving source-share allocation. Scenario analysis showed that solar acceleration increased projected totals but also increased concentration and coherence divergence, whereas diversification reduced concentration but required wider uncertainty buffers. Overall, U.S. renewable energy consumption should be analyzed as a dynamic, diversified, hierarchical, and planning-sensitive system. The proposed framework provides a reproducible basis for evaluating renewable energy growth, source-mix evolution, forecast reliability, uncertainty, source allocation, scenario trade-offs, and planning value beyond single-model forecasting claims. Full article

This study presents the nonlinear seismic analysis of a large-scale suspension bridge under multiple sequential earthquake records. A detailed 3D finite element model is developed in SAP2000, incorporating CFST pylons, a composite deck, and a main cable suspension system. The novelty of this work lies in the combined treatment of two critical and often independently studied factors: nonlinear pile foundation behavior and sequential seismic loading. A Winkler-based nonlinear pile foundation model is established through depth-dependent p-y, t-z, and Q-z nonlinear spring curves implemented as Multi-Linear Plastic Link elements, capturing the full nonlinear lateral and axial response of the 1.8 m diameter, 60 m long pile group. Simultaneously, the structural response is evaluated under real seismic sequences rather than single events, addressing the cumulative damage that conventional analyses systematically underestimate. The results demonstrate that the combination of foundation nonlinearity and repeated seismic loading significantly amplifies internal forces and deformation demands on critical structural components, highlighting the inadequacy of standard single-event, fixed-base design assumptions for long-span bridges. Full article

The present study deals with the nonlinear forced vibration of an axially functionally graded beam subjected to an electromagnetic actuator, moving load, and Casimir force, considering the curvature of the beam and it resting on a nonlinear elastic Winkler–Pasternak foundation. The presence of an electromagnetic actuator and Casimir force besides the presence of mechanical impact (moving load) and nonlinear elastic foundation is a characteristic of a real system, but this has not been studied in this form until now, currently representing a remaining gap. The governing differential equations of motion in the considered system are based on Euler–Bernoulli beam theory and von Kármán geometric nonlinearity. The material properties are expressed according to a power law function through the thickness direction. We point out that the present study is the first to consider the curvature in combination with electromagnetic actuation, Casimir force, an elastic foundation, and moving load. Unlike in other works, axial inertia is not assumed to be negligible in our investigation. The Optimal Homotopy Asymptotic Method is employed to obtain an approximate analytical expression for the nonlinear dynamic response and the nonlinear frequency. The solutions obtained are very accurate in comparison with numerical solutions, and our procedure is simple and easy to implement for nonlinear problems. The local stability near the primary resonance and internal resonance is analyzed by means of the variable expansion method, the homotopy perturbation method, equilibrium points, the Jacobian matrix, and the Routh–Hurwitz criterion. Full article

The present study provides a comprehensive investigation into the hydrodynamic performance of grooved rubber journal bearings (GRJBs) employed as shaft supports in various rotating systems, with particular emphasis on marine applications. These bearings are lubricated with non-Newtonian fluids such as modern oil containing additives and viscoelastic water-based lubricant, which—owing to its complex composition including hydrocarbon chains, metal oxides, and impurity particles and contaminants such as salts, organic substances, microalgae, biopolymers, and microorganisms—deviates from the ideal Newtonian fluid model and demonstrates non-Newtonian rheological behavior. By examining various theories used in the analysis of non-Newtonian fluid behavior, the power-law model, which has a high degree of generality, has been employed in the present study. Also, to improve modeling accuracy, the elastic deformation of the rubber bush in this study is characterized using the Winkler foundation approach and analyzed via the finite element method (FEM). This advanced mechanical formulation, integrated with non-Newtonian lubrication modeling of lubricant using the power-law fluid model, and the parametric assessment of groove number and dimensions on steady-state bearing performance parameters, constitutes the core of this research. The investigation focuses on groove configurations of 4, 6, 8, and 10 channels. The findings indicate that increasing the groove count partitions the convergent pressure film zone into discrete segments, thereby reducing the maximum hydrodynamic pressure while intensifying the overall energy dissipation within the bearing. Additionally, the influences of rheological properties of the fluid—namely the power-law index (n) and the consistency index (m)—on key performance characteristics are thoroughly examined. An increase in both parameters enhances the effective viscosity and load carrying capacity; however, the exponential amplification due to the power-law index exhibits a more pronounced effect on load capacity and peak pressure compared to the consistency index. Full article

Seismic loading can significantly affect the safety and serviceability of structures supported by piles, making seismic performance a key consideration in pile foundation design. The coupling between slope effect and dynamic loading can significantly alter pile–soil interaction and consequently influence the response of laterally loaded piles. In the present study, a dynamic extension of the static p-y curve model for piles near clay slopes is developed for analyzing the response of laterally loaded piles under dynamic loading, based on adjustment of the real stiffness component, and the spring and dashpot model. A computational program based on the Beam on Dynamic Winkler Foundation (BDWF) model is developed for analyzing the dynamic response of piles near a slope. Comparison with finite element simulation results shows that the complex stiffness scheme provides accurate response predictions, thereby validating the effectiveness of the proposed model. Finally, parametric analyses are carried out to investigate the effects of loading parameters (excitation frequency and load amplitude), pile parameters (pile diameter, pile length, and adhesion coefficient), boundary conditions (pile-head and pile-tip constraints), and slope parameter (slope angle). The pile–soil system exhibits a characteristic frequency governed by the soil shear-wave velocity and pile diameter, while being essentially independent of slope angle and pile length. Near this frequency, the pile-head stiffness and damping ratio change significantly. The proposed method provides a practical tool for steady-state dynamic analysis of laterally loaded piles near clay slopes. Full article

Rail infrastructure plays an important role in freight and passenger mobility, and the assessment of rail track structure depends critically on understanding how the rail interacts with the supporting foundation. When rail support degrades (e.g., due to ballast fouling, settlement, etc.), the rail exhibits greater localized deformation that can lead to serious deleterious conditions. Track modulus represents a fundamental diagnostic measure of rail support, encompassing the vertical stiffness characteristics of the foundation and its resistance against downward rail movement. Existing track modulus characterization methodologies typically comprise deflection measurements of railway track (e.g., tie deflections) under known loads. Track modulus estimations result from analyzing deflection and load under assumptions of a traditional Winkler foundation, which can oversimplify mechanic relationships. Specifically, in the context of rail–ballast–subgrade interaction, a tensionless foundation permits gap development which can occur as track structure separates from the supporting ballast; additionally, track modulus may vary along the track length as conditions vary spatially. This paper presents a general analytical solution of ballasted track support characterization based on an iterative algorithm for the static response of a finite beam resting on a tensionless Winkler foundation. The method relates to multiple loads (e.g., concentrated axle loads and distributed self-weight), deflection along the track, and track condition through singularity functions, superposition of discrete support springs, and moment–curvature relationships. The model estimates rail deflections, lift-off points and shear and moment diagrams along the track. The technique permits: (1) validations against benchmark solutions and previously published results, (2) estimations of track modulus from known loads and measured deflections, and ultimately, (3) a framework for designing and processing sensor data streams for use in analyses and evaluations of railway track structure. Full article

This study presents an analytical investigation of the dynamic behavior of concrete beams reinforced with different types of nano-clay (NC) particles and resting on a Winkler–Pasternak elastic foundation. The equivalent elastic properties of the nanocomposite were determined using an Eshelby-based homogenization model. An improved quasi-three-dimensional beam theory was applied to formulate the governing equations of motion, which were subsequently then analytically solved using Navier’s method. The analysis shows that NC reinforcement systematically elevates the natural frequencies of the beam, with the magnitude of improvement varying by particle type and concentration. Increasing the NC volume fraction to 30% leads to a significant rise in the fundamental frequency, reaching about 30% for hectorite (SHca-1) compared with the unreinforced beam, whereas montmorillonite (SWy-1) produces a more moderate increase of approximately 13%. This reinforcing effect remains consistent across different span-to-depth ratios, indicating that the influence of nano-clay content on the dynamic response is largely independent of beam slenderness. Furthermore, increasing the Winkler foundation stiffness results in an almost linear rise in frequency of approximately 18–22%, whereas the Pasternak shear parameter produces a stronger effect, reaching around 25% enhancement depending on the reinforcement type. These results indicate that incorporating nano-clay platelets can be an effective strategy for enhancing the vibrational stiffness of concrete beams and improving their dynamic performance when interacting with supporting soil media. Full article

This work investigates trapped modes induced by localized inhomogeneities in semi-infinite elastic waveguides in the form of a point mass or a meta-spring attached to the edge. Explicit relations linking the parameters of the meta-spring and the mass are presented with a string or beam resting on a Winkler foundation. Asymptotic expansions are derived to describe the limiting behavior of the obtained solutions, including small- and large-mass regimes. Special emphasis is placed on the less-studied trapped modes in an elastically supported beam, providing new insights into the peculiarities of wave localization phenomena, e.g., the analysis of the associated frequency equation. Full article

This study presents an analytical investigation into the free vibration behavior of perforated nanobeams resting on a Kerr-type elastic foundation within the framework of Eringen’s nonlocal elasticity theory. Specifically, Eringen’s nonlocal elasticity theory is employed to inherently capture small-scale effects, while the three-parameter Kerr model is utilized to provide a mathematically consistent representation of shear continuity and realistic surface interactions. In this context, the governing equations of motion for a perforated Euler–Bernoulli nanobeam are derived using Hamilton’s principle, incorporating both the nonlocal parameter and perforation geometric factors, namely, the filling ratio and the number of holes. The resulting equations are solved analytically via the Navier method for simply supported boundary conditions. The results indicate that the Kerr foundation model exhibits an intermediate behavior between the Winkler and Pasternak models, owing to the stiffness-reducing effect of its upper spring layer connected in series. A key finding is the “masking effect,” where high foundation stiffness significantly suppresses the frequency reduction caused by nonlocal small-scale effects. Furthermore, it is observed that in the absence of foundation support, the vibration behavior is governed by the competition between mass reduction and stiffness loss depending on the number of holes; however, foundation dominance stabilizes the system regardless of perforation geometry. Full article

Functionally graded materials (FGMs) are widely applied in spacecraft structural design, thermal protection systems, and planetary landing mechanisms, benefiting from their ability to resist large thermal, pressure, and force gradients. To assess structural response behaviors for lander missions, docking maneuvers, and force transfer in layered aerospace structures, analyzing the contacts subjected to heavily stressed areas becomes very important. This article investigates the receding contact between a functionally graded top layer and a uniform substrate lying on a Winkler elastic foundation using the elasticity theory. An analytical approach has been validated using a finite element method (FEM) implemented in ANSYS. Comparison between the analytical solution and the FEM solution has been conducted for different stamp radii, elastic foundation stiffnesses, and ratios of shearing modulus for various realistic materials in the aerospace field. The data indicate very good convergence between the two solutions for both the length of contacts and the normal stress distribution, where differences are always below 3%. An increase in stamp radius leads to an extension of the contacts as well as a reduction in normal stresses and elevated stiffness and shearing modulus ratio contribute to smaller contacts and higher stresses. The validated methodological approach offers a realistic means for predicting force transfer mechanisms in spacecraft landing pads, multi-layer insulation panels, adaptive space structures, and functionally graded parts subjected to localized loads. This work offers predictive capabilities for space material interface design and optimization for harsh mechanical environments. Full article

The application of steel–concrete composite structures in the pylons of long-span cable-stayed bridges can effectively address the issue of insufficient structural stiffness. Shear connectors are critical load-transfer components in steel–concrete composite segments, where they are typically arranged to ensure coordinated force transmission between steel and concrete. The stud–PBL composite shear connector, as a novel type of connector, has been implemented in engineering practice. However, the collaborative load-bearing performance between studs and PBL connectors remains unclear. Most shear connectors operate within the elastic stage during service, making their elastic stiffness a key evaluation metric. Based on the Winkler elastic foundation beam theory, plane strain theory, and the spring series–parallel model, this study derives the elastic stiffness calculation formulas for stud shear connectors and PBL shear connectors, respectively. The primary focus of this study was the single-layer stud–PBL composite shear connector within the steel–concrete composite section of bridge pylons. Embedded push-out tests were designed and conducted, comprising three main categories and eight subcategories. The load–slip curves for the three types of shear connectors were generated, and the stiffness calculation formula for the stud–PBL composite shear connector was verified through finite element analysis. The comparative push-out tests and finite element simulations demonstrate that the theoretical formula proposed in this study can effectively analyze the elastic stiffness of three types of shear connectors. The elastic stiffness of composite shear connectors can be regarded as the superposition of the elastic stiffness of studs and PBL shear connectors. Compared with single shear connectors, composite shear connectors exhibit superior elastic stiffness and shear resistance, meeting the application requirements of steel–concrete composite bridge pylons. The research findings provide a theoretical basis for the optimal design of shear connectors in large-span cable-stayed bridge composite pylons. Furthermore, the established formula has broad applicability. Full article

A thorough understanding of the effects induced by continuous curved pipe jacking on adjacent underground facilities is paramount for ensuring both safety and operational efficiency during construction. This study posits a three-stage analytical framework designed to calculate the displacement of existing objects resulting from sequential vertical curved rectangular pipe jacking. The methodology involves the following stages: first, the stresses at the object surface must be derived based on classical Mindlin’s solutions; second, the displacements at arbitrary points of the object must be determined using the Winkler foundation model, wherein soil–object interactions are modeled as elastic springs to transform displacements into normal and shear forces; and third, the rigid-body displacement and rotation of objects, caused by aggregate forces, must be calculated by kinematic analysis. The validity of the proposed method is confirmed through comparison with a reduced-scale experimental test, and a parametric study discussing the influence of key factors, including Poisson’s ratio and object geometry, is presented. Full article

Spherical caps exploit their intrinsic curvature to achieve efficient stress distribution, delivering exceptional strength-to-weight ratios. This advantage renders them indispensable for aerospace systems, pressurized containers, architectural domes, and structures operating in extreme environments, such as deep-sea or nuclear containment. Their superior load-bearing capacity enables diverse applications, including satellite casings and high-pressure vessels. Meticulous optimization of geometric parameters and material selection ensures robustness in demanding scenarios. Given their significance, this study examines the natural frequency and static response of bio-inspired helicoidally laminated carbon fiber–reinforced polymer matrix composite spherical panels surrounded by Winkler elastic foundation support. Utilizing a 3D elasticity approach and the finite element method (FEM), the governing equations of motion are derived via Hamilton’s Principle. The study compares five helicoidal stacking configurations—recursive, exponential, linear, semicircular, and Fibonacci—with traditional laminate designs, including cross-ply, quasi-isotropic, and unidirectional arrangements. Parametric analyses explore the influence of lamination patterns, number of plies, panel thickness, support rigidity, polar angles, and edge constraints on natural frequencies, static deflections, and stress distributions. The analysis reveals that the quasi-isotropic (QI) laminate configuration yields optimal vibrational performance, attaining the highest fundamental frequency. In contrast, the cross-ply (CP) laminate demonstrates marginally best static performance, exhibiting minimal deflection. The unidirectional (UD) laminate consistently shows the poorest performance across both static and dynamic metrics. These investigations reveal stress transfer mechanisms across layers and elucidate vibration and bending behaviors in laminated spherical shells. Crucially, the results underscore the ability of helicoidal arrangements in augmenting mechanical and structural performance in engineering applications. Full article

The study presents a stability analysis of an axially compressed column resting on a Winkler foundation with a stepwise variation in stiffness. The solution is based on an energy approach using the Rayleigh quotient, and the original buckling mode function is proposed to capture the localization of deformations in the region of foundation discontinuity. The theoretical model was verified numerically for rectangular-section columns by comparing the results with simulations performed in COSMOS/M and ABAQUS systems. The differences in critical load values did not exceed 1.7%. The investigation showed that increasing the stiffness contrast leads to stronger buckling localization within the weaker foundation segment. The developed model can be used for preliminary assessment of the load-carrying capacity of structural elements interacting with a non-homogeneous distributed foundation. Full article

Excavation of ultra-shallow pilot tunnels triggers surface settlement and endangers surrounding pipelines. The discontinuous settlement curve from traditional stochastic medium theory cannot be directly integrated into the foundation beam model, limiting pipeline deformation prediction accuracy. The key novelty of this study lies in proposing an improved coupled method tailored to ultra-shallow burial conditions: converting the discontinuous settlement solution into a continuous analytical one via polynomial fitting, embedding it into the Winkler elastic foundation beam model, and realizing pipeline settlement prediction by solving the deflection curve differential equation with the initial parameter method and boundary conditions. Four core factors affecting pipeline deformation are identified, with pilot tunnel size as the key. Shallower depth (especially 5.5 m) intensifies stratum disturbance; pipeline parameters (diameter, wall thickness, elastic modulus) significantly impact bending moment, while stratum elastic modulus has little effect on settlement. Verified by the Xueyuannanlu Station project of Beijing Rail Transit Line 13, theoretical and measured settlement trends are highly consistent, with core indicators meeting safety requirements (max theoretical/measured settlement: −10.9 mm/−8.6 mm < 30 mm; max rotation angle: −0.066° < 0.340°). Errors (max 5.1 mm) concentrate at the pipeline edge, and conservative theoretical values satisfy engineering safety evaluation demands. Full article