Displacement Boundary Research Articles

A novel finite element model for predicting the effective mechanical performances of graphene nanoplatelets and carbon nanotubes synergistically reinforced polymer nanocomposites

AbstractGraphene nanoplatelets (GNPs) and carbon nanotubes (CNTs) reinforced polymer nanocomposites have received great attention in the fields of aeronautics and astronautics due to their superior comprehensive performances. However, the random distribution configuration of GNPs and CNTs is complicated at the microscale and their synergistic strengthening mechanism is not disclosed clearly. Therefore, it is valuable to predict the equivalent elastic performances of nanocomposites by proposing a new high‐efficient mechanical model. First, this study proposes a new geometrical unit cell model describing the randomly distributed features of GNPs and CNTs by adopting an efficient nanofiller generation algorithm. Then, a micromechanical finite element model for predicting the effective elastic properties of nanocomposites is established by employing the periodical displacement boundary conditions. Especially, the effects of unit cell dimension and sample size on the predicted elastic constants are discussed from the perspective of probability and statistics in detail. To validate the effectiveness of the presented model, the effective elastic constants of GNPs and CNTs reinforced nanocomposites are analyzed, and good agreement is obtained between the predicted values and the available experimental results. The effects of nanofiller mass fraction and mass ratio on the mechanical properties are discussed, and the synergistic strengthening mechanism of GNPs and CNTs is studied in detail. The presented model contributes to conducting the optimization design of GNPs and CNTs reinforced polymer nanocomposites.Highlights Microscale modeling of GNPs and CNTs is crucial for the mechanical appraisal of nanocomposites. Unit cell dimension should be greater than 2500 nm and sample size is greater than 3. Periodical boundary conditions ensure obtaining accurate mechanical response of the unit cell. The elastic properties increase linearly with the increasing mass fraction of nanofillers. Synergistic strengthening mechanism of GNPs and CNTs on elastic properties is revealed.

Cross scale numerical simulation and experimental study on hydroforming of double-layer Y-shaped tube

Abstract During the hydroforming process of the double-layer Y-shaped tube, defects such as wrinkling and rupture severely affect the forming quality. In this study, for the first time, hydroforming of multi-pass pipes is combined with crystal plasticity finite element modeling (CPFEM). A cross-scale simulation approach is proposed, where the displacement boundary conditions of the macroscopic finite element model are applied to the Representative Volume Element (RVE) through the submodel function in ABAQUS. A macroscopic-microscopic finite element model for hydroforming of double-layer Y-shaped tube is established, and the deformation behavior in the representative region is systematically studied. The effects of non-uniform deformation on stress and strain are analyzed from the perspective of crystal plasticity finite element modeling, and the results are validated by hydroforming experiments. The results show that both macroscopic and microscopic finite element model exhibit good consistency with the experimental results. Considering the microstructure, initial stress concentrates on specific grains due to grain orientation differences. As work hardening occurs, slip systems in other grains are gradually activated, ultimately leading to a uniform stress distribution. The effect of stress state on the slip mode is also discussed. The stress state and slip mode in the same regions of the inner and outer tubes are identical. Moreover, the cross-scale simulation can accurately predict the macroscopic deformation in the critical regions of the hydroforming tube, thus compensating for the limitations of traditional finite element simulations. This cross-scale numerical simulation method also lays the foundation for further research on hydroforming of multi-pass pipes.

Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators

Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators

Energy Method for Deformation Analysis of Flexible Pile Composite Foundation Under Lateral Restriction

To limit the lateral extrusion and compression deformation of soft soil within the load-bearing range, and effectively control the settlement of soft soil foundations, a new technology for side-limited flexible pile composite foundation and energy method for deformation analysis has been proposed. Based on certain assumptions, the compo-site reinforcement area within the side limit and the natural foundation within the de-formation influence depth are considered as a whole, and the displacement component expressions that satisfy the displacement boundary conditions are constructed, leading to the formulation of the total potential energy equation for the system. Based on the principle of potential energy extremum, a displacement variational equation for the system is established, and an approximate analytical algorithm for deformation analysis of flexible pile composite foundation under side limit conditions is proposed. The rationality of the theoretical analysis method is verified by FLAC3D numerical simulation results and on-site monitoring results.

Multiscale dynamics analysis of lumbar vertebral cortical bone based on the Abaqus submodel finite element method

The direct effect of macroscopic loads on the microstructure of bone tissue in a vibration environment is not yet known. Therefore, this study aims to investigate the macro- and micro-biomechanical properties of the lumbar spine system under dynamic loading in such an environment. We analyzed the dynamic characteristics of osteon by establishing a macro- and micro-scale model of the lumbar spine, using a submodel-specific boundary displacement method based on St. Venant’s principle. Utilizing the results from the transient dynamic analysis of the entire lumbar spine as boundary conditions, this study simulates the dynamic behavior of osteon in each segment of the spine on a microscopic scale. The macroscopic results of the transient dynamic analysis showed that the rates of change in dynamic displacement amplitude relative to static displacement amplitude for the L1-L5 vertebrae were 212.60%, 242.11%, 314.80%, 1.17%, and 3.75%, respectively. The change in displacement amplitude under dynamic load relative to static load was highest for the L3 vertebra, as observed in the macroscopic model. The stress and strain values in the microscopic osteon of each lumbar spine segment under sinusoidal periodic loading were higher than those in the macroscopic osteon. In the microscopic bone unit, the maximum stress occurred at the cement line during the peak stress moment, while the minimum stress was observed at the innermost bone plate during the moment of minimum stress. Under dynamic loading, the microscopic bone osteon demonstrated a cyclic stress and strain response, with variations observed in different components of the osteon. These findings provide new insights into the biomechanical behavior of the lumbar spine in a vibration environment.

A Variational Bayesian Inference Theory of Elasticity and its Mixed Probabilistic Finite Element Method for Inverse Deformation Solutions in Any Dimension.

In this work, we have developed a variational Bayesian inference theory of elasticity, which is accomplished by using a mixed Variational Bayesian inference Finite Element Method (VBI-FEM) that can be used to solve the inverse deformation problems of continua. In the proposed variational Bayesian inference theory of continuum mechanics, the elastic strain energy is used as a prior in a Bayesian inference network, which can intelligently recover the detailed continuum deformation mappings with only given the information on the deformed and undeformed continuum body shapes without knowing the interior deformation and the precise actual boundary conditions, both traction as well as displacement boundary conditions, and the actual material constitutive relation. Moreover, we have implemented the related finite element formulation in a computational probabilistic mechanics framework. To numerically solve mixed variational problem, we developed an operator splitting or staggered algorithm that consists of the finite element (FE) step and the Bayesian learning (BL) step as an analogue of the well-known the Expectation-Maximization (EM) algorithm. By solving the mixed probabilistic Galerkin variational problem, we demonstrated that the proposed method is able to inversely predict continuum deformation mappings with strong discontinuity or fracture without knowing the external load conditions. The proposed method provides a robust machine intelligent solution for the long-sought-after inverse problem solution, which has been a major challenge in structure failure forensic pattern analysis in past several decades. The proposed method may become a promising artificial intelligence-based inverse method for solving general partial differential equations.

Configuration reconstruction investigation on submarine cable considering varied displacement boundary based on the inverse finite element method

ABSTRACT Submarine cables have become indispensable for the transmission of power and information. Cables are endangered due to the harsh marine environment such as floating platform motion, waves and currents. It is important to research cable health monitoring systems. A submarine cable configuration reconstruction model is proposed based on the Inverse Finite Element Method (IFEM) in this paper. The structural configurations are obtained based on a limited number of strain sensors by experimental results. The software Orcaflex is used to test the reconstruction accuracy of the large-scale cable configuration under a more complex marine environment and the monitoring sensor arrangement is analysed. Placing more sensors at both ends of the cable helps improve monitoring accuracy. Furthermore, a preliminary attempt at reconstruction in the time domain is made to prepare for investigations on dynamic monitoring. The results can provide certain guidance for the design of a cable health monitoring system.

Research on Non-Random Vibration Analysis of Concrete Pump Truck Boom Based on Dynamic Excitation

When pouring concrete overhead, a pump truck boom’s vibration has a big effect on how accurately the concrete is poured. This is especially true during fixed-point pouring, where the boom’s vibration is likely to cause the pouring position to deviate, which lowers the quality of the construction. It is difficult to forecast the dynamic reaction of the pump truck boom in a construction setting because of the constantly shifting external factors (wind speed, pipeline stress during pumping, etc.), which makes it difficult to guarantee casting accuracy. This study suggests a non-random vibration analysis technique for pump truck booms based on the interval process theory in order to address this issue. A dynamic excitation analysis method based on rigid–discrete coupling is proposed, taking into account the response influence of the material characteristics in the transportation process. The pumping process of concrete materials in the conveying pipeline is simulated using discrete element simulation technology to determine the system’s stress conditions under pumping conditions. The dynamic response characteristics of the pump truck boom under operating conditions are revealed by using non-random vibration analysis with the mathematical model that has been created based on the particular specifications of the pump truck boom. This study employs the Newmark-β technique for numerical computation to solve the dynamic equations and characterize the displacement response envelope under uncertain system parameter settings. The experimental findings demonstrate that the suggested approach may accurately capture the upper and lower bounds of the boom dynamic response, offering a trustworthy way to assess the dynamic behavior while pumping. The technique can reliably predict the dynamic displacement boundary and control the casting position deviation within a predefined range by accurately predicting the dynamic displacement range of the pump truck’s boom end and efficiently constructing the displacement envelope under uncertain dynamic excitation. For numerical computation, use the Newmark-β algorithm. This outcome confirms the substantial enhancement of the proposed method regarding pouring precision in construction settings, offering a novel solution and technical guidance for vibration control in engineering projects.

Efficient Contact Algorithm for 3D Finite Element Modeling of Bottomhole Assemblies: Validation and Application

Summary Static analysis of the lateral deformation of a bottomhole assembly (BHA) is essential for controlling borehole trajectories in directional drilling. A major technical challenge in static BHA modeling is efficiently determining the contact configuration between the BHA and the borehole wall. This configuration, including contact locations and orientations, is not known a priori and introduces nonlinearities into the analysis. Most algorithms addressing the contact problem in BHA modeling are proprietary and lack detailed descriptions. Explicit algorithms based on the Newton-Raphson iteration method and linear/nonlinear complementarity problem formulations have limitations, such as computational inefficiency and the need for predefined contact locations. In this paper, we derive governing differential equations for 3D BHA static deformation, incorporating nonlinear effects from borehole curvature, axial forces, and both discrete and continuous contacts. The finite element method (FEM) is used to solve these equations under appropriate boundary conditions. Within the finite element framework, the Lagrange multiplier method (LMM) is used to impose displacement constraints at contact points, while an innovative iterative process ensures the unilateral nature of the contacts. The algorithm typically converges in O(10) iterations, with each iteration involving the solution of approximately O(102) finite element equations, ensuring high computational efficiency. The algorithm, grounded in principles of structural mechanics, is robust across a wide range of conditions, and its accuracy is validated against a published algorithm. The proposed BHA model is further validated using downhole measurements. In one scenario, bending moment on bit (BOB) measurements from a BHA equipped with a rotary steerable system (RSS) shows strong agreement with the model results, both in magnitude and variation pattern, when a fixed displacement boundary condition is applied at the bit. In another scenario, the BHA model is integrated with a bit-rock interface law to predict borehole propagation trajectories, demonstrating alignment with survey data when the bit side-cutting efficiency is fine-tuned. Additional analyses, including an evaluation of whirling-induced downhole tool failure, are provided in the supplementary material. These validations underscore the versatility and accuracy of the proposed model across various stages of the drilling process. Its computational efficiency makes it suitable for both offline and real-time applications, including prejob BHA designs and the development of operational parameter roadmaps for borehole trajectory control and vibration suppression, real-time integration with downhole measurements to optimize drilling performance, and post-job analysis to diagnose the root causes of undesirable drilling dysfunctions.

From Wind Turbines to Energy Islands: Wind as Model Power in Denmark

This article explains how the fluctuating, ever-changing elemental entity of wind is constructed as a stable renewable energy resource through a global wind energy infrastructural model promoted by the Danish wind energy industry. Examining Denmark’s project to build the world’s first “Energy Islands,” or offshore wind energy hubs, the article accounts for how wind is shaped into “energy” as a media environment, just as wind as medium and milieu shapes the infrastructural forms of wind power. The article thinks through wind with the elemental orientations of “matter,” “molecule,” “milieu,” and “medium,” as well as the mediated conditions of its legibility, to explicate the global wind infrastructural model as a multimodal elemental media assemblage. Wind’s ontological qualities as an infrastructural medium are transduced through apparatuses of environmental data, such as graphical “island” figures and models of landscape featured on promotional websites, wind turbine test sites, and wind atlases that are constructed with numerical data and statistical models. The article argues that the metonymic visibility and invisibility of wind energy infrastructural components enable the territorialization as well as deterritorialization of wind through the strategic projection and displacement of spatial boundaries and geographical situatedness. This extends the infrastructural scope of wind power across various scales, which also contributes to a milieu of geopolitical and economic speculation. Although wind energy is projected as a stable resource, it should be described as a speculative milieu of long-term projections, intermittent changes, and sudden crises, which renders the “Green Transition” an uncertain landscape of environmental futures.

Exponential decay for displacement boundary value problems in nonlinear elasticity

Exponential decay for displacement boundary value problems in nonlinear elasticity

Improved artificial rabbits algorithm for global optimization and multi-level thresholding color image segmentation

The Artificial Rabbits Optimization Algorithm is a metaheuristic optimization algorithm proposed in 2022. This algorithm has weak local search ability, which can easily lead to the algorithm falling into local optimal solutions. To overcome these limitations, this paper introduces an Improved Artificial Rabbits Optimization Algorithm (IARO) and demonstrates its effectiveness in multi-level threshold color image segmentation using the Otsu method. Initially, we apply a center-driven strategy to enhance exploration by updating the rabbit’s position during the random hiding phase. Additionally, when the algorithm stalls, a Gaussian Randomized Wandering (GRW) strategy is utilized to enable the algorithm to escape local optima and improve convergence accuracy. The performance of the IARO algorithm is evaluated using 23 standard benchmark functions and CEC2020 benchmark functions, and compared with nine other algorithms. Experimental results indicate that IARO excels in global optimization and demonstrates notable robustness. To assess its effectiveness in multi-threshold color image segmentation, the algorithm is tested on classical Berkeley images. Evaluation metrics including execution time, Peak Signal-to-Noise Ratio (PSNR), Feature Similarity (FSIM), Structural Similarity (SSIM), Boundary Displacement Error (BDE), The Probabilistic Rand Index (PRI), Variation of Information (VOI) and average fitness value are used to measure segmentation quality. The results reveal that IARO achieves high accuracy and fast segmentation speed, validating its efficiency and practical utility in real-world applications.

Flexural Wave Bandgap Characteristics Analysis of Periodic Double-Span Beam Based on Spectral Geometry Method: A Unified Formulation

The bandgap characteristics of periodic double-span beams are analyzed using spectral geometry methods in this paper. The displacement function of the beam structure is represented in a unified form, supplemented by sine series in addition to Fourier cosine series to avoid discontinuities in displacement at the boundary positions. The introduction of artificial spring technology satisfies the strong coupling connection conditions between beams. Combining it with Bloch’s theorem allows the separation of boundary conditions and displacement functions, ensuring the convergence and accuracy of the method. The energy functional of the double-span beam under periodic boundary conditions is established. The bandgap characteristics of the double-span beam can be obtained using the Rayleigh–Ritz method. The bandgap characteristics calculated based on the proposed method are in good agreement with those obtained from the transfer matrix method, and the bandgap frequency range matches well with the vibration attenuation range obtained from the test results. The effectiveness of forced vibration analysis for finite periodic double-span beams is also validated through the finite element method. Additionally, the influence of material properties, geometric parameters and lattice constants on the bandgap characteristics of periodic double-span beams is presented, providing insights into the mechanisms for tuning bandgap characteristics.

Пространственное распределение авроральных высыпаний и сбоев в работе железнодорожной автоматики на севере европейской части России

We study the relationship between space weather disturbances and spatial distribution of failures in railway automatics at segments of Northern and October railways in 2001–2006. During the most intensive magnetic storms that caused numerous failures, latitude distribution of auroral electron precipitation and local geomagnetic disturbance, determined as mean absolute value of time derivative of the geomagnetic field horizontal component |dBH/dt|, are examined. We show that in magnetic storm main and recovery phases the segments, where the failures were recorded, correspond to the region of intense auroral precipitation and |dBH/dt| exceeded 5 nT/s. The relationship between position of auroral oval equatorial boundary and spatial distribution of failures is analyzed for individual magnetic storms and statistically for five years of observations. Both individual cases and statistic tests show that southward displacement of the auroral oval equatorial boundary correlates with increase in the proportion of failures at lower latitude railway segments.

Spatial distribution of auroral precipitation and failures in railway automatics at the north of European Russia

We study the relationship between space weather disturbances and spatial distribution of failures in railway automatics at segments of Northern and October railways in 2001–2006. During the most intensive magnetic storms that caused numerous failures, latitude distribution of auroral electron precipitation and local geomagnetic disturbance, determined as mean absolute value of time derivative of the geomagnetic field horizontal component |dBH/dt|, are examined. We show that in magnetic storm main and recovery phases the segments, where the failures were recorded, correspond to the region of intense auroral precipitation and |dBH/dt| exceeded 5 nT/s. The relationship between position of auroral oval equatorial boundary and spatial distribution of failures is analyzed for individual magnetic storms and statistically for five years of observations. Both individual cases and statistic tests show that southward displacement of the auroral oval equatorial boundary correlates with increase in the proportion of failures at lower latitude railway segments.

Accurate Nonlinear Bending Analytical Solutions Setting New Benchmarks for Rectangular Thin Plates with Four Clamped Edges

The von Kármán plate equations have been challenging to solve accurately, especially for two-dimensional problems. This paper presents more accurate nonlinear analytical solutions for rectangular thin plates with four clamped edges, providing a new benchmark beyond Lévy’s solutions. The main features of the present method are that the deflection is expanded by the double series of the classical beam eigenfunctions, the Airy stress function satisfying the geometric deformation compatibility equation corresponds to the nonlinear coupling relationships between the plate deflection and the in-plane force and/or displacement boundary conditions. These solutions can verify existing nonlinear numerical and approximate analytical solutions, offering a robust basis for engineering design. The central deflection error is less than 0.01%, and the central stress error is below 0.6%, exceeding the accuracy of the existing literature.

Frequency-Aware Feature Fusion for Dense Image Prediction.

Dense image prediction tasks demand features with strong category information and precise spatial boundary details at high resolution. To achieve this, modern hierarchical models often utilize feature fusion, directly adding upsampled coarse features from deep layers and high-resolution features from lower levels. In this paper, we observe rapid variations in fused feature values within objects, resulting in intra-category inconsistency due to disturbed high-frequency features. Additionally, blurred boundaries in fused features lack accurate high frequency, leading to boundary displacement. Building upon these observations, we propose Frequency-Aware Feature Fusion (FreqFusion), integrating an Adaptive Low-Pass Filter (ALPF) generator, an offset generator, and an Adaptive High-Pass Filter (AHPF) generator. The ALPF generator predicts spatially-variant low-pass filters to attenuate high-frequency components within objects, reducing intra-class inconsistency during upsampling. The offset generator refines large inconsistent features and thin boundaries by replacing inconsistent features with more consistent ones through resampling, while the AHPF generator enhances high-frequency detailed boundary information lost during downsampling. Comprehensive visualization and quantitative analysis demonstrate that FreqFusion effectively improves feature consistency and sharpens object boundaries. Extensive experiments across various dense prediction tasks confirm its effectiveness.

Identification of subwavelength microstructural information from macroscopic boundary measurements in elastodynamics

We present a method to obtain microstructural information from macroscopic boundary measurements exploiting scattering governed by the wave equation in a bounded linearly elastic domain in the long-wavelength regime. Applying a force to the outer boundary of the body on the macroscopic scale while measuring the resulting boundary displacement, we solve the inverse problem of identifying the geometry of the microstructure in the context of periodic homogenization minimizing a tracking-type objective functional as long as the geometry of the microstructure is parameterized by a finite set of parameters. Shape calculus is used to characterize the Gâteaux derivative of the objective function facilitating the use of gradient-based algorithms, and we present numerical experiments for a generic non-destructive testing problem for ellipsoidal microstructures showcasing the functioning of the identification method.

Changes in the soil and vegetation cover of the Kochubey biosphere station under global warming in recent years

Objectives: The study and long-term observations of changes in the spatial structure of vegetation cover of pasture landscapes of the Kochubey Biosphere Station (KBS) due to global climate warming. Arid pasture landscapes, due to the peculiarities of their spatial structure (the presence of semi-desert vegetation groupings) are a good indicator of modern climatic changes. To achieve this goal, the spatial structure and the current state of the arid landscapes of the Northwestern Caspian Sea in the territory of the KBS have been studied. The analysis of the biological diversity of species was carried out. Also the characteristics of the common features of seasonal dynamics of landscapes were studied. Moreover, trends of climatic changes in the landscape structure of the territory and trends in anthropogenic transformation of arid landscapes of the region were identified. It has been revealed that the main reasons for the reduction of biodiversity are habitat fragmentation, the introduction of alien species, the settlement of native species outside the range, ecotonization and “islandization” of pasture ecosystems, and the displacement of range boundaries. Since the goal of preserving the components of vegetation biodiversity is to reduce the pressures caused by climate change, adaptation measures should be aimed at reducing the rate of fragmentation and degradation of pasture landscapes. Monitoring observations have shown that over the last 20-century period there have been rhythmically repeating changes in climate and soil and vegetation cover, which indicates high mobility of vegetation. It has been established that the contribution of anthropogenic land degradation to desertification is confirmed by a significant linear trend in interannual fluctuations in indicators of pasture digression in the region. It has been established that the contribution of anthropogenic land degradation to desertification is confirmed by a significant linear trend in interannual fluctuations in indicators of pasture digression in the region. Due to excessive pasture digression, “islands” of anthropogenic desertification are formed here, the lifespan of which is determined by human influence and precipitation fluctuations.

Time-dependent behaviors of energy piles embedded in multilayered saturated transversely isotropic soils

Time-dependent behaviors of energy piles embedded in multilayered saturated transversely isotropic soils