Evolution Of Deflection Research Articles

Practical Formula for Predicting the Residual Deflection Evolution of Steel Plates Subjected to Repeated Impacts

Practical Formula for Predicting the Residual Deflection Evolution of Steel Plates Subjected to Repeated Impacts

Numerical simulations of the wake and deformations of a flexible rotor blade in a turbulent flow

We present, for the first time, the mean deflection evolution of a flexible rotor blade using a coupled model based on Navier–Stokes equations, for the fluid flow, and linear elasticity equations for the blade deformation. Three turbulence models are tested to reach Reynolds numbers as high as 8 104. The absolute tip speed ratios are in the range [0,25]. The numerical results are validated by comparisons with available tip displacements from experiments. For the parameter ranges, above mentioned, the elastic behavior of the flexible rotor is characterized, and the vorticity field is compared with results obtained for a rigid rotor. The effects of the pitch, the tip speed ratio (or frequency), and its sign on the blade deformation are reported. Typically, the blade deforms in the downstream direction, and it is shown that this deformation is a non-monotonic function of the rotation frequency and the pitch angle. Furthermore, it is found that, for particular values of the frequency and pitch angle, the blade is subject to deformations in the upstream direction. It is shown also that the flexible rotor could develop a vortex ring state, but not the rigid one, under the same conditions. It is found that there is a supercritical frequency associated with the apparition of this vortex ring state and this frequency occurs for negative pitches only, for the considered blade. The vorticity field revealed, as well, that the tip vortex changes sign with that of the blade deflection. Finally, we present the effect of the pitch and frequency on the twist angle of the blade and characterize its evolution along the span.

Probabilistic structural identification and condition assessment of prestressed concrete bridges based on Bayesian inference using deflection measurements

This paper presents a model-based probabilistic structural identification that uses the deflection of prestressed concrete bridges (PSCBs) as observational information to perform Bayesian inference on the state variables associated with creep, structural rigidity, dead loads, shrinkage and prestress. The creep development is modeled as a stochastic process, and the structural rigidity is modeled as a stochastic field using the Karhunen–Loève transform. By incorporating the stochastic process/field into the inference frame, detailed information on structural states can be extracted. Considering the high dimension of the state variables, their posterior distributions are derived by the Hamiltonian Markov chain Monte Carlo (HMCMC) algorithm. As an illustrative example, two sets of deflection measurement of a case bridge are used to update the state variables in a sequential manner. Bayesian inference can calibrate the state variables, while the uncertainties associated with the state variables can be reduced. A K-means analysis can reveal the typical modes in the joint posterior distribution of the state variables, corresponding to the typical failure modes in the attributive analysis of the excessive deflection. The updated state variables are used in the probabilistic condition assessment associated with the deflection evolution.

Self-Debonding of Adhesive Thin Films on Convex Cylindrical Surfaces and Spherical Surfaces

Abstract The emerging skin-integrated devices have been embedded with various functions, whose ideal implementation typically relies on intact bonding to curved substrates. However, the predeformation, which originates from the attachment of a thin film to a curved substrate, attempts to peel the film (i.e., self-debonding). It calls for strong enough interfacial adhesion in applications. On the other hand, too strong adhesion can destroy the surfaces of devices and substrates when the devices are peeled off after service. Therefore, seeking critical conditions becomes essential. Herein, we study the self-debonding of an adhesive thin film on a convex cylindrical surface. Taking Dugdale’s constant-stress law to describe the interfacial traction–separation relationship, we analytically unveil that the self-debonding behaviors are not solely determined by the interfacial energy. Instead, both the interfacial strength and critical interfacial separation are decisive. We thus obtain a phase diagram consisting of two critical conditions correspondingly. Similar results appear in the finite element analysis with the trapezoidal cohesive law, quantitatively showing the evolution of deflection and interfacial detachment force. Furthermore, we find that the circular film, symmetrically adhering to a spherical surface with small deflection, can still share similar self-debonding behavior. Our results provide guidance on how to stick a thin film on a convex cylindrical or spherical surface well with proper interfacial adhesion.

Fatigue Test on Heavy Haul Railway Tunnel Bottom Structure With Base Cavity

The presence of a base cavity will degrade the bearing capacity of tunnel bottom structures, and will also have a noteworthy impact on its fatigue performance. In order to study the fatigue performance and cumulative damage to tunnel bottom structure, a series of bending fatigue tests are conducted by reference to a heavy haul railway tunnel with a base cavity. Through the tests, fatigue evolution characteristics of tunnel bottom structure with cavity are obtained, then based on the expression of S-N curves, a non-linear fatigue cumulative damage model is therefore proposed, the deflection evolution and cumulative damage evolution can be divided into three stages, and characterized with an “s-shaped” curve. The tests results reveal that the damage to the tunnel bottom structure develops rapidly when a cavity exists in the base rock, fatigue occurs more easily, and the fatigue life of specimens decreases with the increase of the stress level and cavity width.

Displacement monitoring of crossbeams in an airport runway extension using digital image correlation

The structure of the Madeira Airport runway extension was built above the sea and is composed by a slab supported by frames at heights above 60 m. When landing in the E-W direction, aircraft touch this structure, which results in bending of the support beams.A vision system was installed under the runway in order to evaluate the deflection of the two support beams more directly involved with impact loads upon landing, but otherwise also involved in take-off or taxiing operations. Each system consists of a camera mounted on a beam, directed at the midspan of the following beam, whose displacement is set to be measured. The section captured by the camera has been prepared with a 2 m by 1 m speckle pattern target for displacement tracking using digital image correlation (DIC). A trigger mechanism was developed in order to save only the images obtained upon clear operational events. The camera acquires images continuously onto a circular buffer and compares them with a reference using DIC. When a displacement is detected, the images on the buffer, along with the frames taken in the next few seconds, are saved for posterior image processing.This system was successful at obtaining measurements for the monitored areas’ displacement fields and the evolution of deflection through time for each event. Significant values for strain are yet to be obtained, as they were, most likely, too small for the system’s resolution, for the events captured to this date.

Evolution Mechanism and Stability Analysis of Roof Deflection of Composite Structure Roadway Under Dynamic Load Disturbance

The lithology of the roof of the mining roadway is compound and the thickness of each layer varies considerably, and it is disturbed by dynamic load all the year round. The above factors has caused a huge difference in the stability of the roadway surrounding rock. Taking the 11,020 lower tunnel of a mine in Henan Province as the engineering geological background, using on-site investigation, formula derivation, numerical simulation and other methods, the composite roof roadway model group was established to study the deflection evolution characteristics of the surrounding rock under dynamic load disturbance, and summarize the plastic zone of the surrounding rock of the roadway Deformation and evolution of roof surrounding rock to evaluate the stability of surrounding rock with different roof structures. The research results show that the change of the roof surrounding rock structure will also lead to the change of the center deflection of the roadway roof. Therefore, the center deflection of the surrounding rock of various roof composite structures is different, and the deflection is the most direct indicator of the stability of the surrounding rock. The center deflection (\(\omega_{0}\)) of the soft rock type is the largest, the center deflection (\(\omega_{0}\))of the upper soft and the lower hard type, and the soft and hard type is larger, and the soft and hard progressive type, thin, hard and thick soft type (\(\omega_{0}\)) is the smallest, and the dynamic load The relationship between the magnitude of deflection before and after the disturbance is consistent. By constructing a composite roof roadway numerical model group, using the plastic failure zone of the roadway as the evaluation standard, the surrounding rock stability is evaluated and divided, and then the cross-point field measurement method is used to verify the stability of the surrounding rock on the roof of different composite structures. And the development of composite roof roadway surrounding rock deformation and failure mechanism and numerical simulation method has important theoretical significance and practical value for the analysis and control of composite roof roadway surrounding rock stability.

Experimental study on stiffness degradation of Crts Ⅱ ballastless track-bridge structural system under fatigue train load

In this paper, a 1:4 scale specimen of concrete box bridge with ballastless track was constructed. The deflection evolution and stiffness degradation of the Crts Ⅱ ballastless track-bridge structural system were studied by carrying out a multistage fatigue loading test with 1.8 × 107 cycles. The results showed that, first, no cracks were formed on the surface of structural system during the test, the dynamic and static deflection ratio of the mid-span section of the structure changed from 108.49% to 106.74%, and the dynamic deflection and static deflection ratio gradually decreased. The cumulative dynamic deflection ratio of the structure exhibited obvious characteristics of the “three-stages” of evolution of the structural fatigue mechanical properties. Second, the static stiffness of the structural mid-span section, which had the most significant change compared to that of the other sections, decreased by 23.82% after the fatigue test. The static stiffness of stage 2, which had the greatest number of cycles, decreased the most compared to that of the other stages. Third, the dynamic stiffness degradation rates of sections L/4, L/2 and 3L/4 of the structure were 18.99%, 19.25%, and 18.59%, respectively. The dynamic stiffness degradation of the structure exhibited the evolution law of “three stages”, and the dynamic stiffness of the structure decreased most significantly in the initial stage of the fatigue test compared to that during the other stages. Moreover, the theoretical results of the stiffness decreasing rate of the mid-span section of the structure were consistent with the experimental results, and the service life of the beam in the structural system was far beyond the design life under the fatigue train load.

A multi-area fatigue damage model of composite honeycomb sandwich panels under three-point bending load

The fatigue damage of composite sandwich panels is divided into two parts: the face sheet damage and the core damage. Both the two kinds of damage cause the performance degradation of panels, however only the core damage results in the ultimate failure. In this paper, a fatigue damage model of the face sheet and the core is proposed and three-point bending tests are carried out to obtain the deflection evolution curves. With the proposed model, the fatigue damage can be predicted accurately, which proves the validity of the fatigue damage model proposed in this paper.

Numerical modeling and experimental validation of fatigue damage in Cross-Ply CFRP composites under inhomogeneous stress states

Composite materials made of fiber-reinforced plastics (FRPs) used in practice-relevant components are subjected to varying static and cyclic loads during their service life. In general, the loads acting on geometrically complex components generate inhomogeneous stress states, which have different effects on damage initiation and propagation. This contribution focuses on the numerical modeling of the fatigue damage evolution under inhomogeneous stress states using a bending test as an example. Firstly, a Finite-Element (FE) based Fatigue Damage Model (FDM) is extended for predicting the fatigue damage evolution under inhomogeneous stress states. To validate the numerical analysis, a suitable bending device is developed to perform experimental tests. In order to generate a complex and inhomogeneous stress state, the specimens are firmly clamped on both sides. Secondly, experimental investigations and detailed FE simulations of the bending tests are performed at different global stress ratios. Based on the number of load cycles, the deflection evolution of the bending specimens is obtained numerically (employing the FDM) as well as experimentally. Finally, the comparison of simulation results with experiments demonstrates the predictive capability and applicability of the extended FDM as an engineering tool.

Prediction of Deflection Progression of RC Beams Strengthened with NSM FRP Composites

The deflection progression of Reinforced Concrete (RC) beams under cyclic loads gives a reliable indication of the accumulation of fatigue damages. Excessive increase in deflection raises a red flag for an immediate need for rehabilitation. This paper presents an analytical model for predicting the deflection evolution of RC beams strengthened with Near Surface Mounted (NSM) Fiber Reinforced Polymer (FRP) reinforcement. The model was validated based on experimental and numerical analyses.

Investigation on the behavior of a laser propagating through a random environment induced by wind.

Wind is an important factor in environment disturbance, and the inhomogeneous distribution of wind velocity leads to random airflow, which severely affects beam propagation. In this paper, numerical and experimental studies have been performed to investigate the behavior of a laser propagating through a random environment induced by wind, and the main focus is the beam deflection evolution under the effect of the wind velocity. The experiment is performed with the wind tunnel, and the beam deviates from the center during propagation, a process in which the average beam deflection presents an increasing trend for the larger wind velocity and the airflow interval. The simulation model of beam propagation through this kind of environment is proposed, and the numerical simulation agrees with the experimental results. With the model, the average beam deflection results are extended into the high-speed region, and the comparison between the airflow and turbulence environment is also presented. The results can find potential applications in optical propagation and communication between two moving platforms with high speed.

Analytical solution for a viscoelastic plate on a Pasternak foundation

This work contributed an analytical quasistatic solution to the problem of an infinite viscoelastic plate supported on a Pasternak foundation and subjected to axisymmetric normal loading. The derivation was based on defining a set of iterative functions, each containing information on the plate’s relaxation modulus and on the time-variation of the loading. By writing the sought solution as a linear combination of these functions it was shown how to decompose the original viscoelastic problem into a set of independent elastic plate problems for which analytical solutions exist. Thus, the plate’s deflection evolution at any point of interest was provided in closed-form, without resorting to integral transform techniques. The formulation was applied and subsequently validated for several test cases, demonstrating that a very small set of elastic solutions is needed for generating a highly accurate viscoelastic result. Overall, the proposed solution is deemed well suited for engineering calculations, as a computational kernel for backcalculation, and for benchmarking numerical solutions.

A Numerical Study on the Thermo-mechanical Response of a Composite Beam Exposed to Fire

This study presents an analytical framework for estimating the thermo-mechanical behavior of a composite beam exposed to fire. The framework involves: a fire simulation from which the evolution of temperature on the structure surface is obtained; data transfer by an interface model, whereby the surface temperature is assigned to the finite element model of the structure for thermo-mechanical analysis; and nonlinear thermo-mechanical analysis for predicting the structural response under high temperatures. We use a plastic-damage model for calculating the response of concrete slabs, and propose a method to determine the stiffness degradation parameter of the plastic-damage model by a nonlinear regression of concrete cylinder test data. To validate simulation results, structural fire experiments have been performed on a real-scale steel–concrete composite beam using the fire load prescribed by ASTM E119 standard fire curve. The calculated evolution of deflection at the center of the beam shows good agreement with experimental results. The local test results as well as the effective plastic strain distribution and section rotation of the composite beam at elevated temperatures are also investigated.

Bending Performance of Lightweight Aggregate Concrete-filled Steel Tube Composite Beam

A composite beam, which consists of a Lightweight Aggregate Concrete Filled Steel Tube (LACFST), and a reinforced concrete slab deck, was investigated. Bending tests were performed to study its behaviour. Based on the test results and the assumptions therein, calculation methods proposed and design suggestions were proved by finite element analysis. The results shows that the composite beam had good ductility and high bearing capacity. The design bearing capacity can be calculated using a force balance method. The flexural stiffness, at the serviceability-level, can be found by superposition of the slab deck and LACFST beam stiffness. A three-line M-δ model was proposed for the lightweight aggregate concrete steel tube composite beam moment–deflection evolution. After validation by finite element analysis, the neutral axis was suggested as lying between the top of the steel tube and the bottom of the concrete deck when the composite beam failed.

Damage characteristics analysis of GFRP-Balsa sandwich beams under Four-point fatigue bending

Four-point bending static and fatigue experiments were performed on composite sandwich beams with glass fiber reinforced polymer (GFRP) face sheets and Balsa wood cores. Specimens with various span-to-depth ratios were prepared using a vacuum-assisted resin transfer molding process. The results showed that the sandwich beams under both static and fatigue tests failed due to core shear and debonding. The S–N curves of sandwich beams were determined using an exponential empirical model. The study showed that to sustain at least one million cycles, the service load should be limited to 60% of the ultimate load. The deflection evolution of the sandwich beams were found to occur in three stages, namely, transient fall, stable evolution, and rapid failure. Furthermore, a fatigue damage model closely related to the possible detection of damage initiation and progression was proposed. The model was proved to be appropriate for describing the fatigue response of GFRP-Balsa sandwich beams.

Simulation of fire resistance behaviour of pultruded GFRP beams – Part I: Models description and kinematic issues

This two-part paper presents a numerical study about the fire resistance behaviour of pultruded GFRP profiles with square tubular cross-section subjected to bending and the ISO 834 time-temperature curve. The first paper deals with the development of numerical and analytical models and the discussion of relevant kinematic issues, including the evolution of beam deflection and position of neutral axis with the fire exposure time. The second part [1] reports an in-depth investigation on the side of static issues, which include the evolution of stress distributions and failure initiation with the fire exposure time. In the present paper, three–dimensional finite element models were developed to simulate fire resistance tests previously conducted by the authors on GFRP beams, in which different degradation curves were considered for compressive, tensile and shear moduli, based on experimental data. In these numerical simulations, both effects of varying the assignment of material properties (depending on the position of neutral axis) and of considering different thermal expansion coefficients were taken into account, and some conclusions were drawn on their influence on mid-span deflection evolutions. Since no failure criterion was implemented, both models were not able to reproduce the failure of the beams, but the overall tendency of the numerical results was consistent with the experimental data. Alongside the numerical study, analytical models based on Timoshenko beam theory were also developed and allowed obtaining accurate predictions of the mid-span deflection evolution of the GFRP beams; the analytical results were in close agreement with the numerical ones and also with the experimental data.

Comparative fire behavior of geopolymer and epoxy resin bonded fiber sheet strengthened RC beams

This study presents results from fire resistance experiments on one RC control beam and seven fiber sheet strengthened RC beams, using geopolymer and epoxy resin as adhesive agents. Thermal response and deflection evolution of these beams with fire exposure time were monitored. The effectiveness of carbon fiber reinforced geopolymer (CFRG) strengthening system and carbon fiber reinforced polymer (CFRP) strengthening system at high temperatures is compared. Post-fire test observations and measured response parameters clearly show that the CFRG strengthening system remains fully effective at high temperatures, and thus CFRG strengthened beams experience lower deflections for longer duration (about 2 h) of fire exposure than corresponding CFRP strengthened beam with similar load levels. However, CFRG strengthened beams do not exhibit higher fire resistance than CFRP strengthened beam as anticipated. To explain this unexpected trend in results, detailed analysis, as well as numerous material level exploratory tests were conducted. The different failure mechanisms and additional contribution from cable action so as to enhance fire behavior of CFRP and CFRG strengthened beams were analyzed. Further test results and analysis clearly show that the early falling-off of fire insulation and fracturing of longitudinal CFRG system is the main cause for lower fire resistance in CFRG strengthened beams. When a layer of primer is applied between geopolymers and the insulation, the early falling-off of fire insulation can be prevented, and thus the fire resistance of CFRG strengthened beams can be enhanced (above 3 h).

Wear-caused deflection evolution of a slide rail, considering linear and non-linear wear models

The research presented in this paper details an experimental-numerical approach for the quantitative correlation between wear and end-point deflection in a slide rail. Focusing the attention on slide rail utilized in white-goods applications, the aim is to evaluate the number of cycles the slide rail can operate, under different load conditions, before it should be replaced due to unacceptable end-point deflection. In this paper, two formulations are utilized to describe the wear: Archard model for the linear wear and Lemaitre damage model for the nonlinear wear. The linear wear gradually reduces the surface of the slide rail whereas the nonlinear one accounts for the surface element deletion (i.e. due to pitting). To determine the constants to use in the wear models, simple tension test and sliding wear test, by utilizing a designed and developed experiment machine, have been carried out. A full slide rail model simulation has been implemented in ABAQUS including both linear and non-linear wear models and the results have been compared with those of the real rails under different load condition, provided by the rail manufacturer. The comparison between numerically estimated and real rail results proved the reliability of the developed numerical model, limiting the error in a ±10% range. The proposed approach allows predicting the displacement vs cycle curves, parametrized for different loads and, based on a chosen failure criterion, to predict the lifetime of the rail.

Structural Performance of Polymer Fiber Reinforced Engineered Cementitious Composites Subjected to Static and Fatigue Flexural Loading

This paper presents the influence of silica sand, local crushed sand and different supplementary cementing materials (SCMs) to Portland cement (C) ratio (SCM/C) on the flexural fatigue performance of engineered cementitious composites (ECCs). ECC is a micromechanically-based designed high-performance polymer fiber reinforced concrete with high ductility which exhibits strain-hardening and micro-cracking behavior in tension and flexure. The relative high cost remains an obstacle for wider commercial use of ECC. The replacement of cement by SCMs, and the use of local sand aggregates can lower cost and enhance greenness of the ECC. The main variables of this study were: type and size of aggregates (local crushed or standard silica sand), type of SCMs (fly ash “FA” or slag), SCM/cement ratio of 1.2 or 2.2, three fatigue stress levels and number of fatigue cycles up to 1 million. The study showed that ECC mixtures produced with crushed sand (with high volume of fly ash and slag) exhibited strain hardening behavior (under static loading) with deformation capacities comparable with those made with silica sand. Class F-fly ash combined with crushed sand was the best choice (compared to class CI fly ash and slag) in order to enhance the ECC ductility with slag–ECC mixtures producing lowest deflection capacity. FA–ECC mixtures with silica sand developed more damage under fatigue loading due to higher deflection evolution than FA–ECC mixtures with crushed sand.