Complex Loading Research Articles

Investigating dwell fatigue crack growth in welded titanium alloy structures

ABSTRACT In this paper, dwell-fatigue crack growth tests under complex loading spectra were conducted for a titanium alloy used in marine structures. The influence of upper and lower peak dwell time on the dwell-fatigue crack growth behavior of the welded structure were comprehensively investigated. The results show that the longer the upper and lower peak dwell times were, the faster the crack growth rate was. Still, the impact of the upper and lower dwell times on the crack growth rate of titanium alloy had a specific saturation value. Based on the above findings, a new model was developed that combined the fracture mechanics theory, considering the effects of welding and load dwell on crack growth. By predicting the dwell-fatigue behavior of titanium alloy welded structures using the model, it was confirmed that the model has a strong prediction ability for the dwell-fatigue behavior of welded structures under complex loads..

A data-driven underground gas storage production system string failure prediction model for time-varying reliability analysis

In underground gas storage (UGS) systems, the production tubing string system undergoes complex thermo-mechanical loading conditions, leading to fatigue damage accumulation and potential failure risks. To accurately assess the fatigue reliability and mitigate risks, it is crucial to develop a data-driven physics-informed uncertainty modeling approach that captures the coupled thermo-mechanical effects and accounts for various uncertainties. This study proposes a data-driven physics-informed modeling method based on thermo-mechanical coupling for fatigue reliability assessment and risk mitigation in critical UGS systems. A quantitative analysis method is introduced, which relies on small-scale multi-stage loading experiments and combines the stochastic degradation process with time-series reliability theory. To analyze the fatigue life of joints under complex loading conditions, a modified S-N curve model is developed. This model takes into account the influences of the dimension coefficient, stress concentration factors, surface finish coefficients, and thermal load. It considers the uncertainties associated with different temperature loads and surface finish on fatigue life. By integrating physics-informed modeling, uncertainty quantification, and fatigue damage accumulation analysis, this approach provides a comprehensive framework for fatigue reliability assessment and risk mitigation in critical UGS systems. It enables informed decision-making for safe and reliable operations, as well as optimized maintenance strategies, ultimately enhancing the overall system performance and mitigating potential failures.

A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory

The ionospheric F2 critical frequency (foF2) is one of the most crucial application parameters in high-frequency communication, detection, and electronic warfare. To improve the accuracy of spatial reconstruction of the ionospheric foF2, we propose a high-accuracy surface (HAS) modeling method. This method converts difficult-to-solve differential equations into more manageable algebraic equations using direct difference approximation, significantly reducing algorithm complexity and computational load while exhibiting excellent convergence properties. We used seven stations in Brisbane, Canberra, Darwin, Hobart, Learmonth, Perth, and Townsville, with one station as a validation station and six as training stations (e.g., Brisbane as a validation station and the other stations—Canberra, Darwin, Hobart, Learmonth, Perth, and Townsville—as training stations). The training stations and the HAS method were used to train and reconstruct the validation stations at different solar activity periods, seasons, and local times. The predicted values of the validation stations were compared with the measured values, and the proposed method was analyzed and validated. The reconstruction results show the following. (1) The relative root mean square errors (RRMSEs) of HAS method prediction in different solar activity epochs were 13.67%, 7.74%, and 9.19%, respectively, which are 13.57%, 7.41%, and 6.41% higher than the prediction accuracy of the Kriging method, respectively. (2) In the four seasons, the RRMSEs of the HAS method prediction are 9.27%, 13.1%, 8.81%, and 8.09%, respectively, which are 10.83%, 11.73%, 4.25%, and 12.00% higher than the prediction accuracy of the Kriging method. (c) During the daytime and nighttime, the RRMSEs of HAS method prediction were 9.23% and 11.17%, which were 5.92% and 11.99% higher than the prediction accuracy of the Kriging method, respectively. (d) Under the validation dataset, the average predictive RRMSE of the HAS method was 10.29%, and the average predictive RRMSE of the IRI prediction model was 12.35%, with a 2.06% improvement in the predictive accuracy of the HAS method. In general, the prediction effect of the HAS method was better than that of the Kriging method, thus verifying the effectiveness and reliability of the proposed method. In summary, the proposed reconstruction method is of great significance for improving usable frequency prediction and enhancing communication performance.

Study on instrumental coupler for heavy haul train

As a crucial load-bearing component, coupler’s safety is pivotal for sustainable railway industry development and is extensively scrutinized due to its complex loading environment. However, current research predominantly concentrates on the longitudinal dynamic behavior of couplers, neglecting factors such as nodding and shaking during traversals along curves and ramps. This study proposes an innovative method aimed at identifying multiple loads on couplers, which includes longitudinal tension and compression, lateral shaking, and vertical nodding forces. A theoretical load identification method based on strain sum and difference on coupler shank faces under various loading scenarios is established by finite element analysis. To facilitate accurate measurement, Wheatstone bridges are employed for three-dimensional force measurement, facilitating strain calculation and temperature compensation. The validity of the proposed approach is confirmed through comprehensive validation, encompassing finite element simulation, laboratory experimentation, and vehicle tests. Results demonstrate the robustness of the method, with maximum load deviations of 2.32% longitudinally, 22.52% horizontally, and 19.86% vertically observed during laboratory tests. Results indicate the proposed method’s accuracy and efficiency in heavy haul train coupler load assessment.

Wing-strain-based flight control of flapping-wing drones through reinforcement learning

Although drone technology has advanced rapidly, replicating the dynamic control and wind-sensing abilities of biological flight is still beyond reach. Biological studies reveal that insect wings are equipped with mechanoreceptors known as campaniform sensilla, which detect complex aerodynamic loads critical for flight agility. By leveraging robotic experiments designed to mimic these biological systems, we confirm that wing strain provides crucial information about the drone’s attitude angle, as well as the direction and velocity of the wind. We introduce a wing-strain-based flight controller that employs the aerodynamic forces exerted on a flapping drone’s wings to deduce vital flight data such as attitude and airflow without accelerometers and gyroscopic sensors. The present work spans five key experiments: initial validation of the wing strain sensor system for state information provision, control in a single degree of freedom movement environment with changing winds, control in a two degrees of freedom movement environment for gravitational attitude adjustment, a test for position control in windy conditions and a demonstration of precise flight path manipulation in a windless condition using only wing strain sensors. We have successfully demonstrated control of a flapping drone in various environments using only wing strain sensors, with the aid of a reinforcement-learning-driven flight controller. The demonstrated adaptability to environmental shifts will be beneficial across varied applications, from gust resistance to wind-assisted flight for autonomous flying robots.

Discrete differential geometry-based model for nonlinear analysis of axisymmetric shells

In this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical model leverages differential geometry principles to accurately capture the complex nonlinear deformation patterns exhibited by axisymmetric shells. By discretizing the axisymmetric shell into interconnected 1D elements along the meridional direction, the in-plane stretching and out-of-bending potentials are formulated based on the geometric principles of 1D nodes and edges under the Kirchhoff–Love hypothesis, and elastic force vector and associated Hessian matrix required by equations of motion are later derived based on symbolic calculation. Through extensive validation with available theoretical solutions and finite element method (FEM) simulations in literature, our model demonstrates high accuracy in predicting the nonlinear behavior of axisymmetric shells. Importantly, compared to the classical theoretical model and three-dimensional (3D) FEM simulation, our model is highly computationally efficient, making it suitable for large-scale real-time simulations of nonlinear problems of shell structures such as instability and snap-through phenomena. Moreover, our framework can easily incorporate complex loading conditions, e.g., boundary nonlinear contact and multi-physics actuation, which play an essential role in the use of engineering applications, such as soft robots and flexible devices. This study demonstrates that the simplicity and effectiveness of the 1D discrete differential geometry-based approach render it a powerful tool for engineers and researchers interested in nonlinear mechanics analysis of axisymmetric shells, with potential applications in various engineering fields.

Towards a Fracture Mechanics-Based Assessment for Fatigue Life Prediction of Ni–Ti Stents

The fatigue failure of Ni–Ti peripheral stents still represents an open issue of major concern due to the non-linear material behavior, the complex loads acting in vivo, and the manufacturing process. The fatigue assessment currently exploits total-life methodologies devoted to preventing crack nucleation. This work investigates a complementary fracture mechanics-based approach accounting for crack propagation from pre-existing manufacturing defects. Fatigue crack growth tests were performed on rolled Ni–Ti samples with a thickness and microstructure comparable to that of stents. A fracture mechanics-based assessment was implemented to predict the fatigue durability of surrogate samples tested at different mean and alternate strains. The fracture surfaces of the samples were inspected to determine a statistical distribution of defect size at the fracture origin. The cyclic J-integral was adopted as the crack driving force parameter, and it allowed to account for the complex response of the material, undergoing energy dissipations during phase transformation. Encouraging fatigue life predictions conforming to experimental data were obtained in the finite-life regime, whereas conservative estimates were computed below the fatigue threshold. This approach can be reverted to determine the maximum acceptable material defects for specific applications, providing a useful tool to manufacturing companies.

Dynamic Topology Optimization with Multiple Materials Based on Impedance Mismatching of Wave

Topology optimization with multiple materials studies were commonly adopted to address the issues of complex structures and dynamic loading cases. However, the perturbation excited from the transient load will be propagated and change the local stress level in the structure. Therefore, it is indispensable to consider impedance mismatching of waves at the interfaces of multi-materials layers in the optimization model. In this work, the wave impedance will be regarded as constraint conditions and assessment indicators in the optimization design. Firstly, a multi-material interpolation model using SIMP models is established based on the variable density method. Secondly, the optimization process is applied by combining using Newmark-[Formula: see text] method which is used to solve the dynamic response, an adjoint variable method for sensitivity study, and an optimization criterion method employed to update the design variables. Finally, the simulation examples are used to analyze the influence of impedance mismatching and volume fraction for multilayer dielectric on response. The results indicate that the position and content of the Polymethyl Methacrylate (PMMA) plays a key role in reducing vibration and buffering action.

Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Finally, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.

Physics-informed machine learning framework for creep-fatigue life prediction of a Ni-based superalloy using ensemble learning

Under extreme environments, critical components of nuclear power equipment suffer creep-fatigue damage accumulation due to the complex load, threatening the safety operation of equipment. Therefore, creep-fatigue life assessment is crucial to ensure the structural integrity and performance requirement of nuclear power equipment during service. To address the poor prediction accuracy under small data sets, this paper developed a physics-informed machine learning (PIML) framework to model the creep-fatigue interaction behavior of a Ni-based superalloy. In this work, an ensemble learning approach is considered to embed physical information into machine learning (ML) models for the creep-fatigue life prediction. The comparison of each model shows that PIML is capable of utilizing the strengths of purely data-driven models and physics-based models to provide excellent prediction accuracy and promote the generalization ability.

Joint input-state estimation of structures subjected to complex loads via augmented Kalman Filter with physics informed latent force models

Joint input-state estimation algorithms such as the Augmented Kalman Filter (AKF) rely on the assumption that the distribution of the input loads follows simple spatial patterns, which are either spatially distributed or sparse. However, in many real situations the spatial distribution of the loads is complex and time-varying, which poses a significant challenge. To tackle this issue, this paper introduces a novel method named the Augmented Kalman Filter with Physics Informed Latent Force Models (AKF-PILFM), which incorporates knowledge about the physics underlying the dynamics of the input loads in the estimation based on training data. In the paper, the general formulation of the AKF-PILFM is described, followed by its tailored application to structures subjected to loads with a complex spatiotemporal behavior such as wave loads. The dominant characteristics of the wave loads are identified from training data via the Dynamic Mode Decomposition, enabling the development of a state space model of the loads that can be integrated with the AKF-PILFM. To demonstrate the effectiveness of the proposed methodology, a numerical example is provided consisting of a 3D steel jacket structure subjected to nonlinear irregular waves. The AKF-PILFM shows accurate estimation results and, in the example, outperforms an existing method based on the Gaussian Process Latent Force Models and equivalent modal loads, signifying that the load’s spatiotemporal behavior substantially influences the structural response.

Recovering Mullins damage hyperelastic behaviour with physics augmented neural networks

The aim of this work is to develop a neural network for modelling incompressible hyperelastic behaviour with isotropic damage, the so-called Mullins effect. This is obtained through the use of feed-forward neural networks with special attention to the architecture of the network in order to fulfil several physical restrictions such as objectivity, polyconvexity, non-negativity, material symmetry and thermodynamic consistency. The result is a compact neural network with few parameters that is able to reconstruct the hyperelastic behaviour with Mullins-type damage. The network is trained with artificially generated plane stress data and even correctly captures the full 3D behaviour with much more complex loading conditions. The energy and stress responses are correctly captured, as well as the evolution of the damage. The resulting neural network can be seamlessly implemented in widely used simulation software. Implementation details are provided and all numerical examples are performed in Abaqus.

Quantitative Study on the Anticollapse Ability of Casing in Shale Gas Wells under Complex Load Conditions.

Implementing novel technologies, including the "well factory" model and zipper fracturing techniques, has become prevalent in shale gas development. During completion operations such as lowering casing and multistage fracturing, the casing is subjected to many complex loads, reducing its strength and increasing the risk of casing deformation. By establishing a casing wear model and conducting multistage cyclic loading experiments and numerical simulations, we analyzed the change rule of casing anticollapse strength under complex loads, developed a calculation method for casing comprehensive anticollapse ability under complex loads, and applied the method to an illustrative calculation. The study shows that the wear effect during completion has a negligible impact on the strength of the casing. The casing anticollapse strength exhibits a linear decline in correlation with the number of cycles. The zipper fracturing operation resulted in a nonuniform distribution of geo-stress around the well, and the casing anticollapse strength demonstrated a nearly linear decline in correlation with the nonuniformity of geo-stress. In the presence of both internal and external effects, the casing anticollapse strength exhibited a decline exceeding 15%, thereby increasing the risk of casing deformation. This research method can provide computational guidance for preventing casing deformation in field fracturing construction.

Non-Intrusive Load Monitoring Based on Dimensionality Reduction and Adapted Spatial Clustering

Non-invasive load monitoring (NILM) deduces changes in energy consumption patterns and operational statuses of electrical equipment from power signals in the feed line. With the emergence of fine-grained power load distribution, the importance of utilizing this technology for implementing demand-side energy management in smart grid development has become increasingly prominent. To address the issue of low load identification accuracy stemming from complex and diverse load types, this paper introduces a NILM method based on uniform manifold approximation and projection (UMAP) reduction and enhanced density-based spatial clustering of applications with noise (DBSCAN). Firstly, this paper combines the characteristics of user load under transient and steady-state conditions and selects data with significant differences to construct a load-characteristic database. Additionally, UMAP is employed to reduce the dimensionality of high-dimensional load features and rebuild a load feature database. Subsequently, DBSCAN is utilized to categorize typical user loads, followed by a correlation analysis with the load-characteristic database to determine the types or classes of loads that involve switching actions. Finally, this paper simulates and analyzes the proposed method using the electricity consumption data of industrial users from the CER–Electricity–Data dataset. It identifies the electricity load data commonly utilized by users in a specific area of Zhejiang Province in China. The experimental results indicate that the accuracy of the proposed non-invasive load identification method reaches 95%. Compared to the wavelet transform, decision tree, and backpropagation network methods, the improvement is approximately 5%.

Characterization on the impact load of a local corner region of a liquid tank entering water

This study conducts a detailed examination of the characteristics of impact loads in complex triangular areas within liquid tanks via the volume of fluids (VOF) method, with a general understanding of impact loads. By comparing the numerical results with previous experimental data of oblique wedge impacts on water surfaces, the effectiveness of the VOF method was confirmed. Complex dynamic phenomena such as fluid climbing, jet impact, and air cavity effects in corner areas were analyzed through 3D flow characteristics. By examining two types of impacts (a structure impacting fluid and a fluid impacting structure), the equivalence between them is verified. An in-depth exploration of the load characteristics in different areas is conducted by combining the free surface evolution. The multipeak characteristics of the load and synchronicity of the peak loads at different parts are closely related to the phenomenon of the climbing fluid being obstructed. Bubble flow also plays a crucial role in affecting the load characteristics. Further exploration of the effects of structural motion on load characteristics reveals complex load variability. These findings provide a valuable reference for understanding the impact loads in complex corner areas of liquid tanks.

Behaviour of yielding mechanical hybrid rockbolts under complex loading conditions

The original “hybrid bolt” was a pragmatic solution to address installation issues in the use of resin grouted rockbolts in heavily fractured ground and the inadequate capacity of friction rock stabilisers. The original hybrid rockbolt involved installing a resin rebar in a friction rock stabiliser. The development of Yielding Mechanical Hybrid Rockbolts has been driven by efforts to eliminate the use of resin in heavily fractured ground. A typical Yielding Mechanical Hybrid Rockbolt consists of a steel tendon mechanically anchored within a friction unit. The bolt is percussion driven by the rock drill and the mechanical anchor is subsequently activated using rotation. This installation process improves the rockbolt resilience to hole closures and avoids issues associated with the use of resin. Yielding Mechanical Hybrid Rockbolts are used in both squeezing and rockburst prone ground conditions.This paper addresses a significant knowledge gap related to the behaviour of Yielding Mechanical Hybrid Rockbolts under multiple quasi-static conditions. A comprehensive experimental program investigated the complete load displacement performance of Yielding Mechanical Hybrid Rockbolts under axial, shear, and a combination of tensile and shear loads. It was observed that the load capacity increases from axial (0°), combined axial and shear (30°), combined axial and shear (60°), and pure shear (90°). The displacement capacity, however, decreases under the same testing conditions. The results are consistent but there is a slightly greater variability as the loading angle increases from 0° to 90°. It was observed that beyond 60° loading angle there is greater variability in the results as the influence of the shear component manifests itself in greater disintegration of the concrete blocks at the shear interface.

In‐Plane Crashworthiness of Gradient Curved‐Walled Honeycombs: Experimental, Numerical Simulation, and Theoretical Analysis

Honeycombs are widely used in engineering protection, while the gap between peak and mean stresses remains to be narrowed, and the interaction effects among walls are weak. To break these limits, gradient curved‐walled honeycombs have been proposed recently. However, their in‐plane crashworthiness has never been studied, which restricts the actual applications in complex load environment. For this purpose, this article adopts experiments, finite‐element simulations, and theoretical analysis to reveal in‐plane crash performance of gradient curved‐walled honeycombs. Quasistatic and dynamic experiments are carried out for 3D‐printed honeycomb specimens made of 316L stainless steel, and numerical simulations are conducted by ABAQUS/Explicit. Compared to traditional straight‐ and curved‐walled honeycombs, gradient curved‐walled honeycombs display stabler deformation mode and more efficient mechanical response. Their EA and SEA are respectively 25.5% and 6.4% larger than straight‐walled honeycombs, and their energy absorption and force efficiencies are nearly 2.4 and 5.3 times larger, respectively. On this basis, plastic hinge model with high accuracy has been established, to derive the analytical solutions of their force–displacement relations. This work extends the comprehensive properties and application prospects of gradient curved‐walled honeycombs and sets an example to develop plastic hinge analysis with effective simplification and desirable accuracy on complex‐shaped structures.

Prediction method for re-damage behavior of the repaired CFRP bolted joint

Composite materials are widely used in various aircraft due to their high specific strength, stiffness, corrosion resistance, and robust design flexibility. However, when subjected to complex loading conditions, composite structures are susceptible to damage, necessitating prompt repair upon aircraft return. Analyzing the re-damage process of repaired structures is crucial for assessing aircraft structural reliability, lifespan, and determining whether a repeat flight is warranted. In this study, a prediction method was proposed for re-damage behavior through meso-modeling and energy analysis of the repaired composite bolted joint. First, this article established a meso-mechanical model for composite laminates, analyzed force transfer characteristics at the fiber − matrix interface, and derived equations for stress field. Additionally, a strain energy distribution model was developed for composite bolted repaired joint near fibers and repaired area, proposing a damage prediction method based on the strain energy criterion. This method could anticipate the location, type, sequence, and magnitude of damage. Finally, simulation calculations yielded mechanical characteristics of the repaired area under typical load conditions, while loading tests verified the feasibility of the prediction method. This study offered an effective means of predicting performance degradation in composite structures and provided a vital direction for optimal spacecraft structure repairing methods and parameters.

Minoxidil cyclodextrin complexes and their inclusion in transfersomes for the enhancement of therapeutic effect on androgenic alopecia

To further increase the drug loading (DL) of minoxidil (MXD) in transfersomes and fully utilize its role in the treatment of androgen alopecia (AGA), a strategy of drug in-cyclodextrin (CD)-in transfersomes was adopted and investigated. The sulfobutyl-substituted β-CDs (SBE-β-CD) with highest optimal binding energy was selected as the most suitable CD for MXD through molecular docking, which had high solubilization effect on MXD verified by phase solubility study. The transfersomes bearing inclusion complexes of MXD/SBE-β-CD was prepared by thin film hydration method, and the MXD/SBE-β-CD transfersomes (MXD/SCD@TFs) with the mass ratio of 10: 3: 2.5: 6 for phosphatidylcholine, cholesterol, Tween80 and MXD was selected as the optimal prescription through single factor screening, which had particle size of less than 100 nm, zeta potential of (−36.4 ± 0.11) mV. The DL of MXD/SCD@TFs was (44.02 ± 0.16)% (n = 3), which was increased nearly 3 times of MXD@TFs, resulting higher stability, in vitro skin permeation activity and drug skin retention. Importantly, the length of newborn hair and the length and number of hair follicles after 21 days of administration of MXD/SCD@TFs on AGA model C57BL/6 mice were significantly higher than those of MXD@TFs and commercial tincture (p < 0.01). Obviously, improving DL is an effective means to improve the therapeutic effect of MXD transfersoms on AGA, the screening of suitable CD for MXD and the loading of inclusion complex in transfersomes provide promising strategy to achieve it.

A New Cu-Alloyed Precipitation-Hardening Hot-Work Tool Steel

Abstract Hot-work tools for hot forming processes, such as die forging, are subject to complex loads that can often lead to premature tool failure. The present study attempts to reduce the main cause of failure of high-speed hot working tools, i. e., wear due to surface breakdown, with the aid of damage-tolerant microstructures. For this purpose, a hot-work tool steel is specifically alloyed with copper in order to form copper precipitations during the subsequent heat treatment, which increase the strength of the material and contribute to the reduction of dislocation movements. The aim is to close the property gap between the standardized direct-hardening and secondary-hardening hot-work tool steels.