Estimation Of Deflection Research Articles

Influence of Temperature Pulse on a Nickel Microbeams under Couple Stress Theory

In this paper, the vibration of microbeams due to a temperature pulse has been investigated. The thermoelastic coupled equations for microbeam resonator have been derived via the modified theory of couple stress in connection with the generalized thermoelasticity with relaxation time. The analytical expressions for studied fields due to modified couple stress for the microbeam have been obtained by applying the Laplace transform method. In addition, some comparisons have been displayed in graphs to estimate the effects of different parameters such as the couple stress parameter and pulse of temperature on the considered fields. Numerical conclusions demonstrate that the estimation of deflection expected by the new theory is lower than that of the classical one. Comparisons are made with the results of different models in the absence and presence of couple stress theory. Particular cases of interest are also derived.

An adaptation of the super-Gaussian wake model for yawed wind turbines

The wake of a yawed wind turbine tends to be deflected and does not follow the incoming wind direction. This phenomenon, often referred to as “wake deflection”, has recently received a lot of attention from the wind energy research community: it is possible to dynamically optimize a wind farm power production by yawing some turbines to deflect their wakes, thus minimizing wake losses over the whole wind farm. In the present work, an analytical model for estimating the deflection of a yawed wind turbine wake is proposed. This new model is based on a super-Gaussian shape assumption for the velocity profile, enabling the estimation of the wake deflection in both near and far wake regions. First, the super-Gaussian model will be briefly introduced. Then, the new wake deflection model will be presented, as well as an updated version of the well known Jimenez model. This revised model allows a proper comparison with the proposed super-Gaussian model, since it is based on a similar definition of the wake width. Finally, results will be compared with experimental data from the literature.

Estimation of diaphragm wall deflections for deep braced excavation in anisotropic clays using ensemble learning

This paper adopts the NGI-ADP soil model to carry out finite element analysis, based on which the effects of soft clay anisotropy on the diaphragm wall deflections in the braced excavation were evaluated. More than one thousand finite element cases were numerically analyzed, followed by extensive parametric studies. Surrogate models were developed via ensemble learning methods (ELMs), including the eXtreme Gradient Boosting (XGBoost), and Random Forest Regression (RFR) to predict the maximum lateral wall deformation (δhmax). Then the results of ELMs were compared with conventional soft computing methods such as Decision Tree Regression (DTR), Multilayer Perceptron Regression (MLPR), and Multivariate Adaptive Regression Splines (MARS). This study presents a cutting-edge application of ensemble learning in geotechnical engineering and a reasonable methodology that allows engineers to determine the wall deflection in a fast, alternative way.

Analysis of flexural concrete beams prestressed with basalt composite bars. Analytical-experimental approach

This present work describes the complex analysis of flexural concrete members prestressed with basalt fiber reinforced polymer (BFRP) bars considering consecutive phases of the loading applied. The aim of this research was to propose analytical approach for the prediction of effective prestress force that directly influence the serviceability limit state of prestressed concrete members, in particular to deflections. Proposed method considering prestress losses for deflection estimation is based on the concept of prestressed concrete laws within particular assumptions. The method is based on strain and curvature analysis, effective moment of inertia including decompression effect and early aging effects of both the concrete and BFRP. The instantaneous and time-dependent prestress losses, cross-sectional stress-strain, deflection and cracking behavior of concrete members reinforced with BFRP bars are described as an interrelated process. This complex approach allows to avoid disappearing of prestressing effect, such as camber or strain of decompression, as a base point and the principle of serviceability analysis of prestressed concrete members. Also, an experimental program was expanded with the purpose to evaluate the influence of prestress level for flexural stiffness of the real scale concrete beams prestressed with BFRP bars.

Estimation of Deflections in Cantilever and Fixed Castellated Beams with Hexagonal, Square and Circular Openings

Estimation of Deflections in Cantilever and Fixed Castellated Beams with Hexagonal, Square and Circular Openings

An analysis of railway track behaviour based on distributed optical fibre acoustic sensing

Trackside monitoring of railways provides useful data for understanding the condition and mechanical behaviour of railway track, prior research has shown that railway track performance varies significantly along its length, primarily owing to changing support conditions. Understanding the changing performance along track offers the potential for improved track design and maintenance. Different technologies are used to investigate this. For example, inertial sensors, or high-speed filming with digital image correlation (DIC) for track deflection, and traditional strain gauges for loads. The latter usually rely on in-situ calibration. These techniques are suitable for measurements at discrete locations along the track length but are not suited to measuring performance variability even along a few hundred meters of a railway line. This paper investigates the use of a recently developed sensing system known as distributed acoustic sensor (DAS) that uses optical fibres. This method has the potential to be used over very long lengths of track; offers high sample rates; and has a gauge length and spatial resolution suitable for investigating the load-deflection behaviour of the track. This study presents DAS optical fibre strain measurements from a study site and presents novel methods for determining the rail deflection and the load per sleeper end. The DAS results are compared with point location measurements using a traditional strain gauge and deflections determined using imaging and DIC. The DAS system offers reliable distributed strain measurement that convert to estimates of track deflection and load with the potential for continuous spatial and temporal coverage over significant lengths of track.

Response Characteristics of a Steel Fiber-Reinforced Porosity-Free Concrete Beam Under an Impact Load

The utilization of ultra-high-strength concrete offers a weight reduction of concrete structures and improvements in disaster protection performance. Recently, porosity-free concrete (PFC) having the world’s highest compressive strength of 400 MPa has been developed, and its basic mechanical properties were determined; however, its impact-resistant capacity is yet to be examined. In this study, investigation of the impact resistance behavior of PFC is performed using a weight dropping impact test on a fiber-reinforced PFC beam. Steel fiber-reinforced PFC is used for preventing brittle failure, and the full plastic moment of the PFC beam cross-section is determined based on material test results. Also, the estimation of maximum response deflection is attempted by a simple plastic analysis. It was demonstrated that the response deflection could be reduced by 30–50% by increasing the steel fiber mixing rate in the PFC beam from 1 to 2%. The proposed estimation method revealed that the response deflection of the PFC beam could be estimated with an accuracy of approximately 80% considering the calculated full plastic moment when the plastic hinge is clearly formed. In the future, to establish a design procedure for the impact-resistant capacity of protective structures from steel fiber-reinforced PFC, it is necessary to conduct experimental and numerical research focusing on ultimate strength, including statistical processing.

Output-only damage diagnosis for plan-symmetric buildings with asymmetric damage using modal flexibility-based deflections

Effective methods for vibration-based damage diagnosis in building structures are based on the estimation of structural deflections from identified modal flexibility (MF) matrices. However, most of the existing methods and previous studies that use MF-based deflections were developed by considering the case of buildings that can be modeled as planar structures (e.g. plan-symmetric buildings) both in the baseline and possibly damaged states. In an attempt to fill this research gap, a deflection-based method for output-only damage diagnosis in building structures tested under ambient vibrations is proposed in this paper. The method is applicable for simple rectangular plan-symmetric “box type” 3D building structures which may experience asymmetric damage, and it can be used for detecting, localizing and quantifying the damage. One of the main differences between the proposed and the existing methods is related to the inspection loads adopted to estimate the MF-based deflections. The inspection loads of the proposed method are more complex than the uniform translational loads adopted in the existing methods. Such proposed loads in fact can be assembled only after having estimated the position of the center of stiffness for each story of the structure. According to the proposed approach, the locations of the centers of stiffness are extracted from the experimentally-derived modal flexibility matrices, before performing the damage diagnosis process. The effectiveness and validity of the proposed method was demonstrated both through numerical analyses and by executing experimental ambient vibration tests on a frame building. The results of the proposed method were also compared with the existing approach which was developed for planar structures. This comparison (made both through numerical and experimental analyses) demonstrated that only the proposed approach can be used to perform a correct damage diagnosis process in plan-symmetric buildings which may experience asymmetric damage, especially when considering the damage quantification problem.

Debonding evolution in nonlinear FRP-retrofitted RC beams with cohesive interface

A novel semi-analytical formulation of the governing equations of an FRP retrofitted reinforced concrete beam under bending, based on the concept of moment-curvature, is presented and it is applied to compute the complete nonlinear load-deflection curve, FRP-concrete interfacial shear stress, the FRP laminate strain and the debonding load of statically determinate RC beams retrofitted by an adhesively bonded FRP laminate. The beam may be subjected to any loading, including uniformly distributed or discrete point load(s). The governing equations satisfy the equilibrium and strain compatibility requirements of the beam but slip at the FRP-concrete interface is permitted. A novel procedure for constructing the full nonlinear moment-curvature relationship of beams undergoing interfacial slip is presented in detail, but it is shown that practically a trilinear relationship is satisfactory for obtaining an accurate estimate of the beam deflection and stresses. The robustness and accuracy of the method are demonstrated by analyzing several beams tested by other researchers under uniformly distributed load or four-point bending, with remarkably close agreement between the experimental and corresponding computed values.

Material Configurational Forces applied to mixed-mode fatigue crack propagation and life prediction in elastic-plastic material

Within the framework of material configurational mechanics, an innovative fatigue model based on configurational force is proposed to predict the mixed-mode fatigue crack propagation in elastic-plastic material. This fatigue mode can provide the estimation of crack initiation, crack deflection, and residual fatigue lifetime simultaneously. The configurational-force fatigue model has the following basic stipulations: (a) the onset of crack growth occurs when the resultant of configurational forces reaches a critical value; (b) the crack growth takes place along the direction of resultant configurational force vector; and (c) the growth rate of mixed-mode fatigue crack is correlated to the equivalent range of material configurational forces. In order to validate the accuracy of the newly proposed fatigue model, a series of experiments are constructed by the compact tension shear specimen. The mixed-mode fatigue crack growth path and rate are obtained under different mixed-mode loading conditions. In addition, numerical implementation of configurational-force fatigue model is performed in elastic-plastic material. The results show that the mixed-model fatigue crack deflections predicted by the configurational-force fatigue model are in good agreement with experimental observations. Meanwhile the fatigue crack growth rate in elastic-plastic material has the power law relation with the equivalent range of material configurational forces, which is regardless of mixed-mode loading. It is demonstrated that the configurational-force fatigue model is able to provide a more convenient and accurate procedure to predict the mixed mode elastic-plastic fatigue crack propagation and lifetime.

Optimal Sliding Mode Control Method for Active Suspension Control

A non-linear quarter car vehicle model is used in this study, for developing an active suspension control algorithm. The control method used is optimal sliding mode control, along with feedback linearization technique for compensating the nonlinear aspects of the plant. In addition to the work in recent literature that applies these control methods, estimation of the static suspension deflection; i.e. vehicle sprung mass is performed. Through simulation results, it is shown that correct information of vehicle sprung mass, compared to taking it as a constant parameter in control design, improves the performance of the controller. This in turn, reduces the sprung mass acceleration level, and enhances ride comfort.

Deflection estimation of glued laminated timber beams reinforced with CFRP fibre composites

Deflection estimation of glued laminated timber beams reinforced with CFRP fibre composites

Приближение функций частными суммами ряда Фурье по многочленам, ортогональным на произвольных сетках

for arbitrary continuous function f(t) on the segment [−1,1] we construct discrete Fourier sums Sn,N(f,t) on a system of polynomials forming an orthonormal system on non-uniform grids $${T_N} = \left\{{{t_j}} \right\}\matrix{{N - 1} \cr {j = 0} \cr}$$ of N points from segment [−1,1] with weight Δtj=tj+1−tj. Approximation properties of the constructed partial sums Sn,N(f,t) of order n ≤ N−1 are investigated. A two-sided pointwise estimate is obtained for the Lebesgue function Ln,N(t) of considered discrete Fourier sums for $$n = O\left({\delta \matrix{{- 1/5} \cr N \cr}} \right),{\delta _N} = {\max _0} \le j \le N - 1\Delta {t_j}$$. The question of the convergence of Sn,N(f,t) to f(t) is also investigated. In particular, we obtain the deflection estimation of a partial sum Sn,N(f,t) from f(t) for $$n = O\left({\delta \matrix{{- 1/5} \cr N \cr}} \right)$$, which depends on n and the position of a point t ∊ [−1,1].

Analysis and design of two layered flexible pavement systems: A new mechanistic approach

Analysis of two layered flexible pavements is considered as a significant aspect for design of low volume roads, which typically consist of a thick granular base course directly laid over subgrade with or without a thin asphalt-wearing course. Permanent deformation or rutting has been observed to be the major distress mode in thin surfaced or unsurfaced low volume roads. In the present study, a new formulation has been proposed to determine the surface and interface deflections for both single and standard axle dual wheel assembly for a two layered pavement system. The present formulation has been developed based on mechanistic approach and the solutions obtained from 3-dimensional finite element program, using ABAQUS taking into account the influence of rectangular tire imprint, modulus of granular base course, pavement thickness and ratio of modulus of pavement and subgrade. The effect of Poisson’s ratio of granular base and subgrade is observed to be very insignificant. For the estimation of surface and interface deflections, deflection factors have been generated in the form of non-dimensional charts as a function of ratio of modulus of pavement and subgrade, and ratio of pavement thickness and tire width.

Deflection Monitoring of Bi-Dimensional Structures by Fiber Bragg Gratings Strain Sensors

In this paper, we report about the deflection estimation of bi-dimensional structure by using fiber Bragg gratings (FBGs) as strain sensors embedded in the structure and an algorithm based on the classical beam theory with small deformation assumption. The proposed technique allows a real-time indirect structural monitoring solving the existing difficulties in measuring the deflection directly and can be applied to small as well large structure, and it is crucial in high-energy physics, where particle detectors have to measure the position of the incoming radiation with a resolution of few tens of micrometers. The obtained results have been compared with mechanical comparator direct deflection measurements showing good agreement, showing a resolution of few tens of micronmeters over a surface of the order of about 1 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The dynamic range of deflection monitoring is dependent on the panel dimension: in the hypothesis of 1-m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> panel, the deflection limit is around 15 cm since FBG can measure very high strain (greater than 10000 μm/m).

Feasibility of using continuous, stiff materials for reinforcing freshwater ice covers

Winter roads are economical and effective means of providing reliable transportation links to remote regions. Operators establishing ice crossings over rivers and lakes have been facing increased pressure to deliver higher volumes of goods, larger loads, in challenging climatic conditions. A question arose from industry: “is there a way to safely provide additional bearing capacity in ice covers and assist with extending operating seasons, possibly through reinforcing the ice?” This study investigated this operational challenge by developing a model to simulate ice reinforcement theories using ANSYS computer modeling techniques. ANSYS 18.0 was utilized to successfully model reinforced ice covers and estimate the ice deflection under a centrally concentrated load. ANSYS computer models allow us to learn complex behaviours of materials and provide a more accurate estimation of deflection compared to the analytical method, which provides a closed-form solution to a given problem. The results show that the reinforcing material is able to stiffen the ice cover which enables a larger surface area to carry the load; a higher percentage of the reinforcement by volume further reduces ice deflection. The test results also indicate that the reinforcing material must be considerably stiffer than the ice so that the load can be more efficiently transferred from the ice to the reinforcing material. The results highlight a successful modelling of reinforced ice covers and discuss the feasibility of installing the reinforcing material, through an example using wood as a possible reinforcing material because it is readily available on site and meets a number of pre-determined criteria. While the creation of an ice reinforcement modeling tool was a success, further research is needed to verify the feasibility of using a variety of materials as reinforcement to increase the safe bearing capacity of ice covers as well as evaluate different applications and orientations of the reinforcement to achieve the best outcome. All of this bearing in mind that the reinforcement must be able to be safely installed in situ within the ice cover. Moreover, a collection of actual ice deflections in the field is recommended to further assist in calibrating the ANSYS model. The simulations serve as an initial step in evaluating different reinforcement materials and methodologies. Subsequent research will need to evaluate the modelling in controlled, full-scale field applications prior to providing a tested solution for commercial use.

Modelling of the vertical deflection of ferroelectric bending tongues loaded at their free end

In this work, a model to describe the vertical deflection of ferroelectric bending tongues with a load at their free end is proposed. The model is based on the ferroelectric switching criterion developed by Hwang et al. [“Ferroelectric/ferroelastic interactions and a polarization switching model,” Acta Metall. Mater. 43, 2073–2084 (1995)] and the Euler-Bernoulli beam theory. It notably takes into account the geometry of the bending tongue, the mechanical and piezoelectric material properties, the applied electrical field, the crystallographic state of the ferroelectric thin film and its built-in strain. Hwang’s model is improved by incorporating strain saturation at high field, as expected for the butterfly loop. This allows accurate estimates of the vertical deflection for ferroelectric bending tongue based applications.

Deflection Calculation and Dynamic Detection of Non-Uniform Beam via Multi-Point Strain Measurement for Freight Trains

In railway freight transport, the vertical deflection of the load-carrying beam on well-hole car accounts for most clearance intrusions at the bottom when running on curves. This paper proposed a deflection calculation and detection method via in-transit strain measurement at multiple beam locations. First, the theoretical mechanical model between the deflection curve and support strains is built, by defining the variable function of bending moment and second moment of area. Quadratic integration constants are calculated employing the symmetric boundary conditions in angle and deflection. Then, the proposed analytical model is validated by the numerical simulation and on-site experiment. Beam deflections by proposed method deviate from simulation within 4.96%, while that deviation rises to 8.11% in loading experiment due to loading difference. In application, in-transit strain data are collected at the two support bottoms. Dynamic and synthetic deflection of load-carrying beams on different line curves is analyzed by theoretical analysis. The maximum deflection reaches 26.1 mm in dynamic and 65.5 mm in synthetic when the freight train runs on a 405-m radius line curve at the speed of 17.2 km/h. In safety evaluation, maximum rigid transformer displacement is calculated by identified load and measured suspension stiffness coefficient. Considering beam deflection and suspension displacement, the maximum vertical movement of the transformer is 110.4 mm, which does not exceed the allowable distance, 250 mm. Research outcomes demonstrate the effectiveness and reliability of the proposed method, which enables the real-time deflection detection and safety evaluation in freight train transport, as well as estimation of the maximum deflection in forthcoming transport.

Footing settlement formula based on multi-variable regression analyses

The formulas offered so far on the settlement of raft footings provide only a rough estimate of the actual settlement. One of the best ways to make an accurate estimation is to conduct 3-dimensional finite element analyses. However, the required procedure for these analyses is comparatively cumbersome and expensive and needs a bit more expertise. In order to address this issue, in this study, a raft footing settlement formula was developed based on ninety finite element model configurations. The formula was derived using multi-parameter exponential regression analyses. The settlement formula incorporates the dimensions and the elastic modulus of a rectangular raft, vertical uniform pressure and soil moduli and Poisson\'s ratios up to 5 layers. In addition to this, an equation was offered for the estimation of average deflection of the raft. The proposed formula was checked against 3 well-documented case studies. The formula that is derived from 3D finite element analyses is useful in optimising the raft properties.

A Modeling Method for Abrupt Change Shafts in Gearboxes and Experiment Verification

The modeling method of the shaft with abrupt change of section is essential in gearbox design. This study reviewed the proposed piece-wise beam model for abrupt change shaft, which is dedicated to estimate shaft deflection. The proposed model is an equivalent model, which is established by comparing and analysing the distribution of the flexural rigidity of the shaft model using solid element. Based on the proposed model a design tool is developed for creating the piece-wise beam model with high efficiency and convenience. As verification of the piece-wise beam model, a test bench with abrupt change shaft is designed and constructed. The shaft deflection with static load has been measured. Experiment analysis has been made by comparing the results between experiments and simulation, which is obtained using solid model, the traditional beam model and the proposed piece-wise beam model. Result shows that the piece-wise beam model is more accurate than the traditional beam model in shaft deflection estimation. The experiment result reveals the correctness and effectiveness of the piece-wise beam model and the design tool.