External Load Research Articles

Identification of equivalent wind and wave loads for monopile-supported offshore wind turbines in operating condition

Wind and wave loads are critical to monopile-supported offshore wind turbines (OWTs) in determining whether OWTs are in safe conditions to generate electricity. However, these random and complex loads vary with time and location, and are difficult to measure directly. Theoretically, the loads can be identified based on structural responses. Nevertheless, it is challenging due to the complexity of external loads and the existence of harmonic loads generated by rotor rotation. This study proposes a new load identification framework using a limited amount of monitoring data to estimate the equivalent wind and wave loads of OWTs simultaneously. Both loads are modeled as Gaussian processes with exponential covariance function and incorporated into the augmented state-space model. Kalman filter is employed to identify the equivalent loads. The effectiveness and accuracy of the proposed method were validated based on a numerical OWT model and a scaled OWT test model. The results demonstrate that the framework can successfully identify equivalent wind and wave loads of OWTs in both parked and operating conditions. The probability distribution of identified load data is consistent with actual load data, with an error of less than 9.1 %. The proposed framework can find vast applications in operational management for OWTs.

Influence of local scour on the dynamic responses of OWTs under wind-wave loads

Offshore wind turbines (OWTs) often operate in complex marine environments, where they are not only subjected to wind and wave loads, but also adversely affected by scour. Therefore, it is of great significance to explore the effect of scour on the dynamic responses of OWTs under external loads to ensure structural safety, improve performance, and extend service life. In this study, a comprehensive numerical model of a 5-MW OWT, including tower, monopile, and soil-structure interaction (SSI) systems, is established by using ABAQUS platform. Aerodynamic loads is generated using blade element momentum, while wave loads is generated using the P-M spectral. The depth of scour is obtained based on on-site measured data. A comparative analysis is conducted between fixed foundations and SSI systems when conducting dynamic response analysis of OWTs under wave loads. Subsequently, the effect of scour on dynamic responses of OWTs under aerodynamic and wave loads is investigated. Results demonstrate that SSI can significantly influence the natural frequency and dynamic responses of the OWT. Therefore, it is essential to thoroughly consider SSI when evaluating the dynamic response of the OWT with local scour. The tower-top displacement and acceleration of the OWT with show a significant increasing trend compared to the non-scoured OWT. An increase in scour depth leads to higher maximum stress and stress amplitude in the steel monopile, which could potentially cause fatigue issues and should be given due attention.

Dynamic buckling active control of FGM spherical shell with piezoelectric sensor and actuator layers

The mechanical snap-through phenomenon represents one of the buckling modes inherent in shallow shells, exemplifying the shell's reaction to external loads, which can potentially have detrimental effects on structural performance. This article delves into the study of this phenomenon within the context of spherical shells. Leveraging functionally graded material (FGM) in the main layer of this structure proves instrumental in enhancing the shell's performance against rapid mechanical loads. Furthermore, the strategic placement of piezoelectric layers, both symmetrically and asymmetrically, coupled with the implementation of a proportional and derivative control system, facilitates the control of the shell's response. The formulation of displacement field and electric potential is grounded in the first-order shear deformation theory (FSDT) and second-order distribution, respectively. The strong form of nonlinear dynamic and electrostatic equations is derived using Hamilton's principle. Solving these equations is achieved through the implementation of the generalized differential quadrature (GDQ) method in the spatial domain and Newmark in the time domain. Additionally, the Newton-Raphson method is employed to tackle the inherent nonlinearity of the problem. The Budiansky's criterion is employed for the assessment of the load necessary for the buckling of the shell. Following the validation of results against numerical, analytical, and laboratory outcomes, a set of parametric results is presented. These results underscore the remarkable impact of the control system in mitigating shell deformation under time-dependent mechanical loads, as well as in postponing the occurrence of the snap-through phenomenon and damping the vibrations.

Stress Drives Soccer Athletes'Wellness and Movement: Using Convergent Cross-Mapping to Identify Causal Relationships in a Dynamic Environment.

Prediction of athlete wellness is difficult-or, many sports-medicine practitioners and scientists would argue, impossible. Instead, one settles for correlational relationships of variables gathered at fixed moments in time. The issue may be an inherent mismatch between usual methods of data collection and analysis and the complex nature of the variables governing athlete wellness. Variables such as external load, stress, muscle soreness, and sleep quality may affect each other and wellness in a dynamic, nonlinear, way over time. In such an environment, traditional data-collection methods and statistics will fail to capture causal effects. If we are to move this area of sport science forward, a different approach is required. We analyzed data from 2 different soccer teams that showed no significance between player load and wellness or among individual measures of wellness. Our analysis used methods of attractor reconstruction to examine possible causal relationships between GPS/accelerometer-measured external training load and wellness variables. Our analysis showed that player self-rated stress, a component of wellness, seems a fundamental driving variable. The influence of stress is so great that stress can predict other components of athlete wellness, and, in turn, self-rated stress can be predicted by observing a player's load data. We demonstrate the ability of nonlinear methods to identify interactions between and among variables to predict future athlete stress. These relationships are indicative of the causal relationships playing out in athlete wellness over the course of a soccer season.

Coupled Thermo-Electric-Elastic Piezoelectric Vibration Energy Harvester With Axial Movement: Modeling, Verification, and Analysis

Abstract In the field of rail transport and aerospace field, vibration energy harvesting is inevitably subjected to coupled excitations, including train wheel–track interaction induced friction heat and forced vibration, periodic thermal radiation, and vibration excitation. This paper investigates a coupled thermo-electric-elastic piezoelectric vibration energy harvester with axial movement under external heat flux and mechanical force load. The coupled forced vibration equation, coupled electric equation, and coupled thermoelastic heat conduction equation are derived and solved by Green's function theory. To analyze the effect of excitations on the response characteristics, the decoupled method is utilized to solve the coupled multi-field equations and obtain the displacement, electric, and temperature distribution closed-form solutions. The displacement coupling effect induced temperature distribution and the thermo-electric coupling effect triggered displacement are respectively decoupled and analyzed. The obtained closed-form temperature distribution and displacement solutions are verified by the finite element method. To further verify the obtained solutions, a numerical method is conducted by decoupling the coupled multi-field equations and comparing them with prior solutions. Additionally, the different height-to-length ratios, axially moving speeds, and external force load are analyzed in detail. The results indicate that the displacement, temperature distribution, and output voltage vary with external conditions due to the coupled multi-field effect. Overall, this work investigates the thermo-electric-elastic coupling effect on the axially moving piezoelectric energy harvesting, which is beneficial to promote theoretical investigations of the coupled multi-field energy harvesting system and accelerate the practical applications in the aerospace field.

Boosting tree with bootstrap technique for pre-stress design in cable dome structures

Tensegrity structures, known for their rigidity derived from feasible pre-stresses, present unique challenges in structural engineering. Traditional force-finding methods, though comprehensive, rely heavily on intricate matrix computations, making them computationally intensive and often uncomfortable for considering external loads in practical engineering scenarios. This paper introduces a novel approach to compute pre-stresses in cable dome structures by integrating machine learning and probability theory, collectively termed the boosting tree with bootstrap technique (BTWBT). This method reduces the sample size to as few as 100 per iteration, while improving computational efficiency by randomly generating internal forces. By reframing the force determination as an inverse problem, it ensures that structural displacement converges to zero under feasible pre-stresses. The effectiveness of BTWBT is demonstrated across three distinct cable dome structures: the Geiger dome, Kiewitt dome, and rotating hyperboloid cable dome. Results show that BTWBT achieves the preset displacement requirement (maximum nodal displacement below 0.01 mm) with fewer iterations and reduced computational cost compared to traditional machine learning methods. BTWBT's capability to manage complex structural configurations with minimal data, while incorporating random internal force generation ranges, highlights its potential as a superior alternative for force determination in tensegrity structures.

Stress evolution in rocks around tunnel under uniaxial loading: Insights from PFC3D-GBM modelling and force chain analysis

In underground engineerings, the evolution of the stress state in the surrounding rocks can effectively reveal its fracture mechanism. To precisely describe this microscopic information, the present study utilizes the three-dimensional Grain-based model based on Particle Flow Code (PFC3D-GBM) to construct a square numerical specimen with a pre-existing hole representing a tunnel and subjected it to uniaxial loading. In this model, different types of mineral structures and internal force chain networks are distinguished at a three-dimensional scale. Furthermore, the evolution of force chain networks in the top, bottom, left and right regions around the tunnel is quantitatively characterized. The anti-fracture capability depending on stress state of various structures is calculated and then the fracture mechanism from the point of anti-fracture capability is discussed. The research results indicate that at at the beginning of loading, some red force chains with higher level have appeared on both sides of the tunnel. As the load goes on, red force chain network extending from both sides of the tunnel to the upper and lower ends of the specimen have emerged. The average value and sum value of all force chains show an increasing trend before the peak load and a decreasing trend after the peak load. The average value of force chains within a specific structure can accurately reflect the microscopic mechanical properties of that structure. The average values of force chains on the left and right sides of the tunnel are higher, both in terms of starting points and ascending rates, than those in the upper and lower regions of the tunnel. The orientation distribution of all force chains is relatively uniform, but force chains with higher level are generally align with the loading direction. The fundamental reason for the high degree of fragmentation on the left and right sides of the tunnel is that these regions bear more external load than the upper and lower regions, rather than being inherently more prone to fracture.

Design and Optimization of Elliptical B-shaped Sleeve Configuration for Oil&Gas Pipeline

Abstract Affected by external loads or pipeline corrosion, oil & gas transmission pipelines may encounter safety hazards during service. In terms of defect repair, both domestic and foreign standards currently stipulate that the permanent repair method is B-type sleeve or tube replacement. Compared to the costly tube replacement, B-type sleeves are undoubtedly the preferred choice for economy and safety. However, due to installation size limitations, conventional sleeves are difficult to repair large deformation defects such as wrinkles and buckling in oil and gas pipelines. This study aims at developing, designing, and optimizing a B-type sleeve for welding repair of irregular defects in oil and gas pipelines. By designing irregular B-shaped sleeves with different curve configurations, the stress levels and concentration coefficients of irregular sleeves at different defect heights and sleeve lengths are calculated. The optimal pumpkin shaped and elliptical curve sleeve configurations are selected as the repair solutions for irregular sleeves. Under the existing limitations of machining and detection accuracy, pumpkin shaped irregular sleeves can be prioritized for application in engineering, while elliptical curve sleeves are considered as alternative solutions.

Bicortical Compression and Construct Stability With Variable Pitch Locking Screws in Cadaveric Specimens.

A variable pitch locking screw is intended to provide interfragmentary compression combined with fixed angle stability of locking plate constructs. The objective of this study was to compare variable pitch locking screws (3.5-mm KreuLock Ti locking compression screws, Arthrex Inc., Naples, FL) with standard locking screws (from the same manufacturer) in bicortical fixation scenarios in cadaver bone by assessing (1) interfragmentary compression and plate-bone compression and (2) construct biomechanical stability. Nine matched pairs of fresh-frozen cadaveric specimens with an average age of 67.2 years (range, 37-83) were used. Interfragmentary compression and plate-bone compression associated with insertion of single bicortical screws were compared between the variable pitch and standard locking screws at increasing levels of torque. The specimens tested were distal tibiae having a simulated longitudinal fracture. Additionally, fibulae were osteotomized to create a stable longitudinal fracture pattern and were fixed with a 5-screw plate construct with either all variable pitch or all standard locking screws. One of the 5 screws was placed across the osteotomy without lagging. Fibulae were tested cyclically with axial with torsional loading to compare displacements, rotation, and loads at failure or tested in 4-point bending to compare construct stiffness and maximum force to failure. Interfragmentary and plate-bone compression forces in the distal tibia model varied across specimens but were significantly higher with variable pitch locking screws compared with standard locking screws [512 N (SD = 324 N) vs. 79 N (SD = 64 N), P = 0.002, and 242 N (SD = 119 N) vs. 104 N (SD = 123 N), P = 0.028, respectively]. In cyclic loading of fibula constructs, no significant differences were detected in construct axial displacement or angular displacement (P > 0.05). In 4-point bending, no differences were detected in maximum force or bending stiffness (P > 0.05). Variable pitch locking screws produced interfragmentary compression between cortices and plate-bone compression that was greater than that produced by standard locking screws. In a stable bicortical fibula fixation scenario under external loading, the stability of variable pitch locking screw constructs was similar to constructs with standard locking screws.

Examining Pipe–Borehole Wall Contact and Pullback Loads for Horizontal Directional Drilling

Pipeline pullback load is a crucial basis for drill rig selection and pipeline strength design. This paper presents a new pullback load calculation model from the perspective of pipe–borehole wall contact. The pipe–borehole wall contact analysis includes the distribution of contact pressure and the relationship between the external load and compressive displacement. The friction force between the pipe and the borehole wall was calculated based on the pipe–borehole wall contact analysis and adhesion theory without depending on the empirical friction coefficient. The effects of the eccentricity were also considered when calculating the fluid drag force. Through case studies, we verified the applicability of the model and discussed the possible reasons for the errors between the theoretical and field-measured results. This study can provide a helpful tool for analyzing the pipe–borehole wall contact and pullback loads for horizontal directional drilling.

Strength analysis due to thermal loading and tensile loading when metals are bonded by heat-curing adhesives

Heat-curing adhesives are widely used after being cured by heating to a temperature higher than room temperature. To evaluate the adhesive strength, therefore, it is necessary to consider both the thermal stress generated during heat curing and external loads such as tensile stress. Butt joint specimens are essential for evaluating tensile adhesive strength but also thermal strength. The interfacial strength can be discussed from the stress intensity factor (SIF) of a fictitious edge interfacial crack assumed at the interface end. This is because the SIF is controlled by the intensity of singular stress field (ISSF) at the crack-free interface end and a constant term associated with the thermal load. In this paper, a useful thermal SIF solution is proposed by superposing the SIF under tensile stress and the SIF under uniform interface stress associated with thermal loading. This general SIF expression provided under arbitrary material combination can be applied for predicting the tensile strength σc and critical temperature change ΔT without performing new FEM calculations. The usefulness of the expression is confirmed through the adhesive strength of Aluminum/Epoxy butt joint experimentally obtained. Once the critical SIF K1C can be obtained from the tensile strength σc and the temperature change ΔT, the adhesive strength can be expressed asK1C = constant of an assumed fictitious interface, and this can be used to predict critical σc for various temperature change ΔT and for various adhesive bondline thickness h.

A study on load sharing characteristics of the planetary gear train system with cracked gears

Load sharing characteristic is very important for the reliability of the planetary gear train. Cracked gears can make the load sharing performance become worse. Nevertheless, previous studies have not paid enough attention to the influence of cracked gears on the load sharing behavior, when compared with the impact of multiple factors under healthy condition. An 18 degrees of freedom dynamic model for the spur planetary gear train is established based on the centralized parameters theory in this paper. The influences of cracked gears on the load sharing behavior are investigated, which include the cracked sun gear, the planet gear containing cracked side meshing with the sun gear, the planet gear having cracked side meshing with the ring gear and the cracked ring gear. Additionally, the sensitivity analysis of the external and internal load sharing behavior to different cracked components is conducted. The results indicate that the load distribution becomes more uneven with the propagation of crack in the sun gear and ring gear, while the change regulation is different for each cracked planet gear. Moreover, the load sharing characteristic of the external meshing is more sensitive to the cracked sun gear and the planet gear 1, which has the crack side meshing with the ring gear. While the load sharing characteristic of the internal meshing is more sensitive to the cracked ring gear and the planet gear 3, which owns the crack side meshing with the ring gear than others. The output of this paper will be useful for the crack fault diagnose and fault source identification of the planetary gear train system.

Thermal management of sodium-oxygen-hydrogen (Na-O-H) thermochemical water splitting for sustainable hydrogen production

Owing to environmental problems caused by the consumption of fossil fuels and the growing global demand for energy, interests in usage of hydrogen as a green energy carrier has grown. In particular, water is considered a prospect source for green hydrogen production. In this paper, a three-step sodium-oxygen-hydrogen (Na–O–H) thermochemical cycle, which is a newly developed cycle that can operate between 400 and 500 °C is implemented. Also, low number of steps, which results in less system complexity and easier system design is another advantage of the Na–O–H thermochemical cycle. In the first step of this study, a basic model of the three-step pure Na–O–H cycle is modeled in order to produce 1 kg/s of hydrogen. Moreover, output data from basic modeling is used for cycle energy management. Then, heat recovery is performed within the cycle streams to reduce the external energy demand and make the Na–O–H cycle more feasible. To achieve this objective, pinch method, which is an effective method for designing and optimizing plants is used. Several heat exchanger network designs have been developed and compared from different aspects. Finally, a design with the least heat requirement among others is selected and optimized based on total annualized cost objective function to introduce the optimum final design exchanger network. As a result of this work, it is found that using the final optimized design, external heating loads accounted for just 5.8% of the total load, while external cooling loads accounted for 19.3% of the total load. This implies that the Na–O–H thermochemical cycle recovered 74.7% of the energy required for heating and cooling of the streams. The implementation of the proposed heat exchanger network design boosts the overall energy efficiency of the Na–O–H thermochemical cycle. Using final heat recover scheme the overall efficiency of the cycle increased from 45.36% to 52.86%, representing an impressive 7.50% improvement. This significant achievement underscores the pivotal role of this study in developing an effective and optimized model for the Na–O–H thermochemical cycle, which holds great promise for future applications.

Three-, Four-, and Five-Day Microcycles: The Normality in Professional Football.

This study aimed to quantify training and match-day (MD) load during 3-, 4-, and 5-day microcycles in professional adult football, as well as to analyze the effect of the microcycle length on training load produced the day after the match (MD + 1) and the day before the match (MD - 1). The study involved 20 male professional football players whose external and internal loads were monitored for a whole season. The training exposure, total distance covered, high-speed-running distance, sprint distance (SD), individual SD above 80% of the individual maximum velocity (D > 80%), and the number of accelerations and decelerations were quantified, as well as rating of perceived exertion and session rating of perceived exertion training load. Microcycle length affected most of the variables of interest: high-speed-running distance (F = 9.04, P < .01), SD (F = 13.90, P < .01), D > 80% (F = 20.25, P < .01), accelerations (F = 10.12, P < .01), and decelerations (F = 6.01, P < .01). There was an interaction effect between the training day and microcycle type for SD (F = 5.46, P < .01), D > 80% (F = 4.51, P < .01), accelerations (F = 2.24, P = .06), and decelerations (F = 3.91, P < .01). Coaches seem to be influenced by shorter microcycles in their training proposal, preferring sessions with a reduced muscle impact during shorter microcycles. Independent of the length of the congested fixture microcycle, the daily load seems to decrease when MD approaches.

Dynamic Double Event-Triggered Anti-Disturbance Tracking Control for a 2-DOF Small Unmanned Helicopter.

This article devises a new dynamic double event-triggered anti-disturbance tracking control scheme for a 2-degree of freedom (DOF) laboratory helicopter subject to external time-varying disturbances and load fluctuation by using the generalized proportional-integral observer technique. The helicopter system is separated into two subsystems in the proposed control method, i.e., the pitch subsystem and the yaw subsystem. Each subsystem includes a discrete-time dynamic double event-triggering mechanism (DDETM), and the control laws of the two subsystems are independent of each other. There are two triggering conditions in the designed double triggering mechanism: one is designed based on the system states and the other is based on the lumped disturbance estimation. These two triggering conditions form a competitive relationship such that the controller updates the control signal as long as one of the triggering conditions is satisfied. Theoretical analysis is provided for achieving the better communication and control performance of the proposed DDETM-based robust control method. Through rigorous stability analysis, it is proved that the closed-loop hybrid system is globally ultimately bounded. At last, numerical simulations show that the suggested control strategy not only reduces the event-triggering number, but also improves the initial dynamic performance of the system.

Analysis of Cracking Causes of A Vibrating Screen Excited Beam

Abstract It was found that cracking occurred at the exciting beam of the vibrating screen produced by a mechanical equipment manufacturing Co., Ltd. In order to determine the reason for the cracking of the vibrating screen, the cracked vibrating screen samples were tested by appearance, physical and chemical properties, metallographic analysis, scanning electron microscopy(SEM) and energy spectrum analysis. The test analysis results show that the chemical composition analysis, tensile and flattening test results of the vibrating screen meet the requirements of GB/T 8163-2008 standard, the fillet weld at the vibrating screen exciting beam is not bevelled according to the requirements of the production design drawings. The main reason for the cracking of the vibrating screen is that the fillet weld cracking at the vibrating screen exciting beam originates from the welding defects in the weld, which accelerates the further expansion of the crack under the action of external vibration load, and finally leads to the complete cracking of the exciting beam weld.

Assessing External And Internal Loads Impacting Injury Odds In Male Collegiate Ice Hockey Players

Assessing External And Internal Loads Impacting Injury Odds In Male Collegiate Ice Hockey Players

Multi-task Gaussian Processes based transient aerodynamic load reconstruction for maglev vehicle using acceleration response

The accurate estimation of aerodynamic loads is crucial for developing high-speed maglev trains, which can reach speeds of up to 600 km/h. Traditionally, this estimation has been achieved through computational aerodynamic simulation or direct pressure measurement. In this paper, we propose a novel framework for reconstructing transient aerodynamic loads on maglev vehicles using on-board acceleration measurements. In the framework, an inverse mathematical model that correlates the measured acceleration and external aerodynamic loads is derived from a well-calibrated maglev vehicle model. To avoid the ill-posed problem when solving the inverse mathematical model, a multi-task Gaussian Processes method is proposed, in which all reconstructed transient aerodynamic loads are treated as Gaussian Processes and the closed-form posterior distributions of these aerodynamic loads could be calculated. To validate the proposed framework, a set of transient vibration data collected from an operational maglev train passing through a double-track tunnel is utilized for load reconstruction. The results demonstrate that the framework offers a cost-effective and efficient means to obtain aerodynamic loads, highlighting its practical relevance for aerodynamic field testing in the context of evolving high-speed maglev technologies.

Implementation and Evaluation of a 10-Week Kettlebell Training Load Distribution on Strength and Aerobic Capacity in Recreationally Trained Women

Objective: The purpose of this study was to characterize the dynamic distribution of training loads in a kettlebell program and evaluate its effects on muscle strength and aerobic capacity. MethodsFourteen recreationally active women with no kettlebell training experience (age: 25.86 ± 5.35 years; V̇O2max = 35.14 ± 5.58 mL/kg/min; body mass = 62.13 ± 13.40 kg; height = 164.75 ± 5.77 cm; body mass index = 22.68 ± 3.99 kg/m²) completed a 10-week kettlebell training program. The kettlebell training program was divided into three phases: Phase I (2 weeks), phase II (4 weeks), and Phase III (4 weeks). Maximum muscle strength (1RM) and aerobic fitness (V̇O2max) measurements were performed before (Pre) and after (Post) training. The external and internal loads were represented by the session's total volume and perceived exertion method. ResultsAn increase in maximum strength (P < .001; ∆% = 23.73; effect size = 0.87) and V̇O2max (P = .004; ∆% = 9.63; effect size = 0.57) was observed when comparing Pre and Post measurements. There was an increase in total volume when phases I and II (P < .001), phases I and III (P < .001), and phases II and III (P < .001) of the training were compared. The internal load values increased significantly between phases I and II (P < .001). However, there was no difference when comparing phases II and III (P = .796). ConclusionThe total volume increases during the training phases, and the training load was similar in phases II and III. Furthermore, were observed higher V̇O2max and strength (1 RM load) values.

Mechanical behavior and strengthening mechanism of loess stabilized with xanthan gum and guar gum biopolymers

Abstract The structural properties of loess are susceptible to change when subjected to external loads and complex environments, leading to various geological disasters. To investigate the mechanical behavior and strengthening mechanism of loess stabilized with biopolymers such as xanthan gum and guar gum, especially for soils with low bearing capacity and stability in engineering applications, we conducted research on the improvement of soil with xanthan gum and guar gum, tests including unconfined compressive strength, disintegration, direct shear, and microstructure tests were conducted. Among the four different dosages of biopolymers (0%, 0.5%, 1%, 2%) and four different curing ages (1 day, 3 days, 7 days, 14 days), the 2% content of biopolymer and 14 days had the greatest impact on the mechanical properties of loess, Both the compressive and shear strength, as well as the water stability of solidified loess, improve with higher content of xanthan gum and guar gum or prolonged curing time; however, the disintegration rate decreases. Microscopic analysis indicates that the biopolymers effectively fill the gaps between soil particles and attach to the particle surfaces, forming fibrous and reticular structures that improve the interparticle bonding and ultimately increase the strength and water stability of the loess. Xanthan gum and guar gum biopolymers can improve the mechanical properties and water stability of loess, enhance the erosion resistance and improve the water-holding capacity. These outcomes suggest that guar gum and xanthan gum biopolymers have the potential to serve as environmentally sustainable alternatives to conventional soil stabilizers.