Initial Deflection Research Articles

Time-Dependent Behavior of Full-Scale Recycled Aggregate Concrete Beams under Long-Term Loading.

Sixteen full-scale recycled aggregate concrete (RAC) beams were cast and tested to study their time-dependent behavior under long-term loading. The test parameters include the replacement rate of the recycled coarse aggregates (RCAs), the replacement rate of the recycled fine aggregates (RFAs), the concrete strength, and the stress ratio. The influence of the above variables on the deflection and stiffness is discussed. The results show that the RCAs will increase the deflection of the specimen at a low stress ratio; at a high stress ratio, the beams will experience nonlinear creep, and the deflection of the specimen will be affected by the RCAs and the stress ratio. The RFAs have a substantial influence on the time-dependent behavior of the specimen, and the deflection of the specimen with 100% replacement of recycled aggregates can increase by 30%; the strength of the concrete does not have a substantial influence on the time-dependent behavior of the specimen; and the stress ratio has an influence on the initial deflection of the specimen. A deflection calculation formula is established based on the stress–strain relationship of the beam under long-term loading and the characteristics of the RAC. The calculation results are in good agreement with the test results.

Experimental investigation on the long-term behaviour of prefabricated timber-concrete composite beams with steel plate connections

This paper presents the results of long-term experiments performed on three timber-concrete composite (TCC) beams. An innovative fabricated steel plate connection system, which consists of screws and steel plates embedded in concrete slabs, was adopted in the TCC beam specimens. The adopted shear connection can provide dry-type connection for TCC beams. Steel plates were embedded in concrete slabs while the concrete slab was constructed in factories. The timber beam and concrete slab can be assembled together using screws at the construction site. In this experimental programme, the beam specimens were subjected to constant loading for 613 days in indoor uncontrolled environments. The influence of long-term loading levels and the number of shear connections on the long-term performance of TCC beams was investigated and discussed. The mid-span deflection, timber strain, and interface relative slip at the positions of both connections and beam-ends were recorded throughout the long-term tests. It was found the long-term deflection of the TCC beam increased by approximately 60% while the long-term loads were doubled. Under the influence of the variable temperature and humidity, the TCC specimens with 8 shear connections showed slighter fluctuations compared with the TCC beam with 6 shear connections. In the 613-day observation period, the maximum deflection increment recorded was 6.56 mm for the specimen with eight shear connections and 20% loading level. A rheological model consisting of two Kelvin bodies was employed to fit the curves of creep coefficients. The final deflections predicted of all specimens at the end of 50-year service life were 2.1~2.7 times the initial deflections caused by the applied loads. All beam specimens showed relative small increments in mid-span deflection, strain and relative slip over time without any degradations, demonstrating the excellent long-term performance of TCC beams using the innovative steel plate connection system, which is also easily fabricated.

Concrete cracking and deflection analysis of RC beams strengthened with prestressed FRP reinforcements under external load action

Fibre reinforced polymer (FRP) reinforcements (laminates, sheets, strips, rods) are considered for retrofitting of RC structures worldwide. Such reinforcements are light, easy to install, corrosion resistant, satisfying aesthetical and design requirements. In order to use full potential of the FRP it should be pretensioned, this way reducing crack widths and deflections. In most cases in practice strengthening will be carried out for structures exposed to external load with initial cracks and deflection. However, there is the lack of experimental and theoretical research of such phenomena when RC structure is strengthened with prestressed FRP reinforcements under external load action. Therefore, here will be presented experimental program for the full analysis of this phenomena. 14 identical RC beams were casted and tested at the courtesy of Vilnius Gediminas Technical University (VGTU): 2 control RC beams, 6 beams strengthened with prestressed carbon fibre reinforced polymer (CFRP) laminates without external load action, 6 beams – under external load action. Different prestressing levels were used in both cases: 17 ÷ 56% from the nominal load bearing capacity of FRP. Based on the results theoretical models for calculation are being presented for consideration.

Effect of locomotion on the auditory steady state response of head-fixed mice

Objectives Electroencephalographic (EEG) examinations of the auditory steady-state response (ASSR) can non-invasively probe cortical function to generate the gamma-band (40 Hz) oscillation, which is increasingly applied to the neurophysiological studies on the rodent models of psychiatric disorders. Though, it has been well established that the brain activities are significantly modulated by the behavioural state (such as locomotion), how the ASSR is affected remains unclear. Methods We investigated the effect of locomotion by recording local field potential (LFP) evoked by 40-Hz click-train from multiple brain areas: auditory cortex (AC), medial geniculate body (MGB), hippocampus (HP) and prefrontal cortex (PFC), in head-fixed mice free to run on a treadmill. Comparisons were conducted on the LFPs during spontaneous movement and stationary conditions. Results We found that in both the auditory (AC and MGB) and non-auditory areas (HP and PFC), locomotion reduced the initial negative deflection of LFP (early response during 0–100 ms from stimulus onset), and had no significant effect on the ASSR phase-locking to the late stimulus (100–500 ms). Conclusions Our results suggest that different neural mechanisms contribute to the early response and ASSR, and the ASSR is a more robust biomarker to investigate the pathogenesis of neuropsychiatric disorders.

Vibration of the Biomass Boiler Tube Excited with Impact of the Cleaning Device

In boilers with biomass fuel, a significant problem is caused due to the slag layer formed from the unburned particles during combustion. In the paper, a tube cleaning method from slag is proposed. The method is based on the impact effect of the end of the tube with the aim to produce vibration for slag elimination. The tube is modeled as a clamped-free nonlinear oscillatory system. The initial impact of the tube causes vibrations. The mathematical model of the system is a nonlinear partial differential equation with zero initial deflection. To obtain the ordinary differential equations, the Galerkin method is applied. By discretizing the equation into a finite degree of freedom system, using the undamped linear mode shapes of the straight beam as basic functions, the reduced order model, consisting of ordinary differential equations in time, is obtained. The ordinary time equations are analytically solved by adopting the Krylov–Bogoliubov procedure. Special cases of nonlinear differential equations are investigated. In the paper, the influence of the nonlinear parameters and initial conditions on the vibration properties of the tube is obtained. We use the procedure developed in the paper and the analytical results for computation of the impact parameters of the cleaning device.

Piezo-micro-ultrasound-transducers for air-coupled arrays: Modeling and experiments in the linear and non-linear regimes

The paper is focused on the multi-physics modeling, via the finite element method (FEM), of a 4 × 4 air-coupled array of Piezoelectric Micromachined Ultrasonic Transducers (PMUTs), and on its mechanical and acoustic validation by means of the comparison, in the time domain, with experimental results. A two-stage numerical procedure is employed, in order to evaluate the complete performance of the device, by means of two FEM models. In the first stage, the electro-mechanical-acoustic (EMA) problem is solved for the stand-alone transducer, taking into account the fabrication induced residual stresses and the multiple couplings between different physics. The numerical results are compared with the experimental ones in terms of initial deflection and time histories of pressure, in the linear and non-linear regime: the proposed model correctly captures the reported phenomena and perfectly matches the experimental trends. The second stage is devoted to the simulation of the 4 × 4 PMUTs array performance, belonging to the silicon die. The vibrating plates are modeled as equivalent rigid pistons. The acceleration histories, computed in the first stage, are imposed on the pistons, while a rigid baffle condition is enforced on the remaining part of the die surface. The model is adopted to predict the pressure field for different patterns of the array’s activation.

Finite-element analysis of plate stability under conditions of nonlinear creep

Resolving equations are obtained for the finite element analysis of the stability of plates and shells with allowance for nonlinear creep. The issue of plate stability under creep process is investigated by the example of a round plate rigidly clamped along the contour with an initial deflection under the action of radial compressive forces. It has been established that for plates made of a material that obeys the nonlinear Maxwell-Gurevich law, there is a long critical load p ∞. When the load is less than the long critical (p < p∞), the deflection growth rate decays, i.e. buckling does not occur, at p = p∞ the deflection increases at a constant speed, and at p > p ∞, the rate of growth of the deflection increases.

Influence of aggregate interference on the crack propagation of asphalt concrete by the configurational force fracture criterion

In this study, the influence of aggregate interference on the crack propagation of asphalt concrete by the configurational force fracture criterion has been investigated. Since the presence of aggregates inside the asphalt concrete generally changes the nearby stress distribution and exerts a significant impact on the behavior of composite crack growth, the crack passing through single aggregate and asymmetric double aggregate are simulated based on the configurational force fracture criterion using the extended finite element method (XFEM). It was observed that under pure tensile load, the crack will propagate away from the aggregate; but when the crack has an initial deflection angle β, the crack will propagate towards the aggregate, until the crack “pierces” the second aggregate. In terms of the crack tip configurational force, the aggregate has an interference effect on the crack propagation, where the crack tip configurational force decreases with an increase in the aggregate particle size. Moreover, the interference of aggregate on the crack propagation path has a certain limit. It was also found that under the interference of asymmetric double-aggregate; larger the particle size range of the aggregate, easier is the formation of overhead structure inside the material, which eventually results in local instability. This instability drastically affects the crack resistance of the asphalt mixture.

Impacts of Residual Stress on Micro Vibratory Platform Used for Inertial Sensor Calibration.

A micro vibratory platform driven by converse piezoelectric effects is a promising in-situ recalibration platform to eliminate the influence of bias and scale factor drift caused by long-term storage of micro-electro–mechanical system (MEMS) inertial sensors. The calibration accuracy is critically determined by the stable and repeatable vibration of platform, and it is unavoidably impacted by the residual stress of micro structures and lead zirconate titanate (PZT) hysteresis. The abnormal phenomenon of the observed displacement response in experiments was investigated analytically using the stiffness model of beams and hysteresis model of piezoelectric material. Rather than the hysteresis, the initial deflection formed by the residual stress of the beam was identified as the main cause of the response error around the zero position. This conclusion provides guidelines to improve the performance and control of micro vibratory platforms.

Cold bending of vertical glass plates: Wind loads and geometrical instabilities

The study investigates the mechanical response of glass shells cold bent into hyperparaboloid shapes used in building technology. Focus is addressed on two subjects: the application of the cold bending procedure to vertically oriented rather than horizontal plates, which allows to minimize the disturbance produced by the initial deflection due to self-weight, and the effect of wind load on curved glass panels installed in glazing façades.The particular case of a vertical monolithic glass plate (2000 × 2000 × 10 mm) loaded symmetrically on two diagonally opposite corners is studied experimentally and numerically, developing a finite element model, and the results compared each other. Both experiments and numerical analyses show that a mechanical disturbance, introduced e.g., on the centre of the plate, promotes a change in the deformation mode during the bending process. Geometrical instabilities which impair the optical quality of the glass, and trigger a serviceability limit state failure, are evidenced.A parametric analysis is conducted to investigate the influence of the size and the aspect ratio of the glass plate on the cold forming procedure. The examined response parameters include the geometrical distortion of the glass plate, involving the possible occurrence of optical distortion and the maximum tensile stress in the plate.In the second part of the study, the effect of wind load on curved glass shells is numerically evaluated. The results point out the possible trigger of a limit equilibrium stability, with a “snap-through” transition from an equilibrium state to another non-adjacent equilibrium configuration which can result in a sudden break of the glass plate. This phenomenon is affected from the size of the glass plate and the curvature imposed to the plate during cold bending. The proposed methodology could represent a convenient tool to assist practitioners in selecting the appropriate thickness of façade glass panels.

Numerical study on upheaval buckling for surface laid subsea pipelines with topographic step imperfection

Upheaval buckling may occur for subsea pipelines laid on the seabed with topographic step imperfection under high temperature. In order to predict the post buckling behaviour of upheaval buckling, a finite element model of ABAQUS is proposed to simulate upheaval buckling for surface laid subsea pipelines with step imperfection. Firstly, a new method to introduce a step imperfection from an originally flat seabed is presented. Then, the finite element model of ABAQUS proposed in this paper is verified through the analytical results. The results obtained by FEA and analytical method have a good agreement. The influence of temperature difference, model length and step height on configuration and post buckling behaviour is investigated in detail. Our results show that rigid seabed assumption is reasonable in this study. The model length of the pipeline must be larger than the feed-in length. Otherwise, displacement amplitude, maximum stress and axial thermal expansion will be underestimated. For larger step height, displacement amplitude and maximum stress are larger at lower temperature difference due to the initial deflection induced by step imperfection of seabed, however, they become smaller at high enough temperature difference. The influence of step height and thickness of the pipe on the critical buckling force can be fitted well by a simple formula. The critical buckling force is barely affected by the axial friction coefficient between pipe and seabed.

Direct measurements and numerical predictions of welding-induced initial deformations in a full-scale steel stiffened plate structure

Abstract As a sequel to another paper of the authors on welding-induced residual stresses [1], this paper aimed to obtain a direct measurement database of welding-induced initial deformations in a full-scale steel stiffened plate structure and also to study the applicability of computational models to predict them. A full-scale steel stiffened plate structure in association with bottom plate panels of an as-built 1,900 TEU containership was fabricated by exactly the same technology of welding as used in today's shipbuilding industry. The 3D scanner was employed to measure welding-induced initial deformations of the structure. Computational models using the three-dimensional thermo-elastic-plastic finite element method were developed to predict the plate initial deflections. A comparison between direct measurements and numerical predictions was made. Details of direct measurement databases are documented as they are useful to validate the computational models formulated by other researchers.

Post-buckling analysis of imperfect multi-scale hybrid nanocomposite beams rested on a nonlinear stiff substrate

Present paper undergoes with the analysis of the post-buckling behaviors of multi-scale hybrid nanocomposite beam-type structures manufactured from both macro- and nanoscale reinforcing elements, namely carbon fibers and carbon nanotubes (CNTs), respectively, in addition to the host polymeric matrix. The equivalent material properties of the hybrid nanocomposite will be gathered utilizing a two-step micromechanical scheme while the influences of the CNTs’ agglomeration phenomenon are covered. Continued by using the concept of the virtual work’s principle, the nonlinear governing equation of the motion will be derived on the basis of the combination of the von Karman hypothesis with the well-known Euler–Bernoulli beam theory while the beam is rested on a three-parameter nonlinear foundation. It is noteworthy that the impact of the existence of an initial deflection in the continuous system is included in the present study, too. At the end of the manuscript, the obtained governing equation will be solved analytically within the framework of the Galerkin’s method once both simply supported–simply supported (S–S) and clamped–clamped (C–C) boundary conditions are considered. It is shown that the stability response of the NC structure can be deeply influenced tailoring the agglomeration parameters.

An experimental and numerical investigation on ultimate strength of stiffened plates with opening and perforation corrosion

Stiffened plates with openings exist in ship structures such as longitudinal girders and side shell platforms etc. Different from intact structures, the ultimate strengths for such kind of structures have not been extensively studied yet. In this paper, experiments have been designed and carried out to investigate the ultimate strengths and collapse behavior of stiffened plates with openings, and attached structures are introduced with simplified square tubes, and corrosion caused degradations are introduced and simplified as perforations. Three experimental models are employed to study the effects of perforation distribution. Additionally, numerical studies have been performed with Nonlinear Finite Element Analysis (NFEA) and results match well with the experimental results, based on the measured initial deflections by laser scanning technique. Collapse shapes have also been compared and analyzed, and influences of different types of initial deflections and boundary conditions on ultimate strength have been investigated. The results shown in this paper can be helpful for understanding the mechanism of structural collapse, and provide reference for the ultimate strength experimental designs of such structures.

Large-amplitude membrane flutter in inviscid flow

We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex sheet wakes in two-dimensional inviscid fluid flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free to move in the transverse direction, the membranes flutter periodically at intermediate values of mass density. As mass density increases, the motions are increasingly aperiodic, and the amplitudes increase and spatial and temporal frequencies decrease. As mass density decreases from the periodic regime, the amplitudes decrease and spatial and temporal frequencies increase until the motions become difficult to resolve numerically. With both edges free to move in the transverse direction, the membranes flutter similarly to the fixed–free case, but also translate vertically with steady, periodic or aperiodic trajectories, and with non-zero slopes that lead to small angles of attack with respect to the oncoming flow.

Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: A semi-analytical approach

abstract In the present paper, for the first time, an attempt has been made to obtain the solution for bending and stress under the thermal environment using Galerkin Vlasov's method. A non-polynomial based higher-order shear deformation theory with inverse tangent hyperbolic shape function is used to define the displacement field. The formulation is performed for the author's recently developed sandwich plate using a new modified sigmoid function-based functionally graded material (S-FGM) plate of different symmetric and non-symmetric configurations. Using a one-dimensional steady-state heat conduction equation, a new temperature distribution through the thickness based on modified sigmoid law is proposed. Three different types of porosity are considered viz. even, uneven but symmetric and uneven but non-symmetric. A new uneven non-symmetric porosity model is used in which micro-voids are varied in accordance with material property variation in the thickness direction in order to capture the accurate distribution of voids on the plate. The principle of virtual work is employed to derive equilibrium equations. An exact solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions. From the present study on static analysis, it is deduced that more refined and accurate results for plate in thermal environment, it is necessary to include the thermal effect on the stiffness of the plate in addition to the initial deflection of the plate. The effect of boundary conditions on stress and deflection distribution along the surface of the porous plate is studied, and it is observed that the distribution is prominently affected by the type of symmetric or asymmetric boundary conditions. The considerable increase in deflection and stress can be seen for even porosity distribution (P-1) in comparison to uneven symmetric (P-2) or uneven non-symmetric (P-3) porosity distribution. In addition, the maximum transverse shear stresses are offset more from the center of the sandwich plate with an increase in temperature differences with a maximum offset at ΔT = 300 K and minimum offset at ΔT = 0 K. Different examples are considered to check the accuracy and validation of the present formulation. The calculated outcomes and interpretations can be useful as a validation study for the imminent investigation of sandwich S-FGM plates having porosities in the thermal environment.

NONLINEAR LAGER DEFORMATION ANALYSIS OF SINGLE ARC BELLOWS DIAPHRAGM

The single arc bellows diaphragm is regarded as the combined structure of a circular plate with initial deflection by the method of simulated shell. Based on nonlinear large deflection bending theory, the nonlinear large deformation of a single circular diaphragm is analyzed. Taking the maximum deflection of the circular part of the diaphragm as a perturbation parameter and using modified iteration method of theory of plates and shells, the nonlinear large deformation of a single circular arc bellows diaphragm with one end fixed and another end free is solved. Under boundary conditions and continuity conditions, quadratic nonlinearity analytical solutions with higher accuracy are obtained. According to the vector height of the arc and the wavelength of the arc in a single circular arc bellows diaphragm, the characteristic curve of the maximum deflection of the arc is drawn. The characteristic curve is analyzed, the deflection of the diaphragm nonlinearly increases with the increase of the vector height of the single arc diaphragm, and the deflection of the diaphragm nonlinearly increases with the increase of the arc length of the single arc bellows diaphragm.

An extended sequential limit analysis based on moving coordinates for pressurized spherical cap membranes with large shape change

Sequential limit analysis (SLA) is an effective and normally used method to calculate the plastic limit load of structures with large deformation. However, attribute to the assumption of neglecting the changing behavior of shape and plane stress direction, the conventional SLA method would be inaccurate in the plastic response prediction for the large-shape-change structures, especially for the pressurized spherical cap. This research develops a novel analytical model for the pressurized spherical cap based on the advanced SLA method, which features introducing the moving coordinate system and considering of the changing behavior of shape and plane stress direction into the conventional method. With the proposed method, the effects of geometry and material parameters on the plastic limit load are analyzed. Compared with the validating FE simulation results of ABAQUS software, the newly extended SLA method performances a more precise prediction of the load deflection response and plastic limit load than the normal one. Due to the limit yield degree and bending moment, the accuracy of the new model will increase with the increase of yield strength and radius. The larger the initial deflection of the pressurized spherical cap is, the smaller the relative error between the analysis results of advanced SLA and FE method is. Moreover, this newly proposed SLA remains effective and accurate within a wide range of the initial thickness-curvature radius ratio, especially for low elasticity modulus materials.

Strain gradient based static stability analysis of composite crystalline shell structures having porosities

This paper studies nonlinear stability behavior of a nanocrystalline silicon curved nanoshell considering strain gradient size-dependency. Nanocrystallines are composite materials with an interface phase and randomly distributed nano-size grains and pores. Imperfectness of the curved nanoshell has been defined based on an initial deflection. The formulation of nanocrystalline nanoshell has been established by thin shell theory and an analytical approach has been used in order to solve the buckling problem. For accurately describing the size effects related to nano-grains or nano-pores, their surface energies have been included. Nonlinear stability curves of the nanoshell are affected by the size of nano-grain, curvature radius and nano-pore volume fraction. It is found that increasing the nano-pore volume fraction results in lower buckling loads.

Устойчивость стенок подкрановых балок с усталостными трещинами в зоне сжатого пояса

The paper describes a method for assessing the bearing capacity of the crane beam walls with fatigue cracks. There has been developed and implemented an algorithm for evaluating the stress-strain and limit state of the beam with a crack in the wall under a compressed belt. There has been established the dependence of the stress-strain and limit states of the beam wall on the value of the initial relative beam bending and the crack length in the section under the action of the bending moment and transverse force. The author presents the results of numerical studies of the effect of cracks on the bearing capacity of the beam wall. The influence of the amplitude of the initial beam wall deflection on the critical stress parameters is revealed. The dependence of the values of critical stress parameters on the relative crack length is considered.