Deflection Time Histories Research Articles

Integrated finite element and artificial neural network methods for constructing asphalt concrete dynamic modulus master curve using deflection time-history data

Dynamic modulus |E*| is one of the essential material properties input in the American Association of State Highway and Transportation Officials (AASHTO) Mechanistic-Empirical Pavement Design Guide (MEPDG). Asphalt concrete (AC) dynamic modulus master curve is used to determine the modulus of asphalt concrete over a wide range of temperature and frequency. However, the standard laboratory test procedures for establishing asphalt concrete |E*| and plotting the AC |E*| master curve are time consuming and require considerable resources. Therefore, this study aims to predict AC |E*| master curve by using data from a falling weight deflectometer (FWD) deflection time-history. Prior to developing the model, a simple performance testing (SPT) dynamic modulus test was conducted in the laboratory on five core specimens to obtain the dynamic modulus data at several test temperatures and load frequencies. Results of SPT dynamic modulus show that the |E*| of all specimens is influenced by both loading rate and test temperature. The specimens are stiffer at low temperature and high frequency, and the |E*| values are the lowest at the highest temperature and lowest frequency. Artificial neural network (ANN) models are designed using the FWD deflection-time history data obtained by the finite element method (FEM) to predict the AC |E*| master curve. This study uses two types of ANN models, namely multilayer feed-forward neural network (MLFN) and radial basis function network (RBFN). ANN results show that both MLFN and RBFN models have a promising potential in the construction of AC |E*| master curve. A comparison of the two types of ANNs revealed that RBFN has a lower percentage of error, and is therefore more accurate than MLFN.

Experimental investigation of slender RC columns under horizontal static and impact loads

This paper reports an experimental investigation on the behaviour of slender reinforced concrete (RC) columns under horizontal static or impact loading. Fourteen square RC columns were tested under horizontal impact loading by using a modern horizontal impact facility. These specimens were subjected to the same design impact velocity of 0.8 m/s. The effects of three main parameters, namely the specimen slenderness ratio, the longitudinal reinforcement ratio, and the axial compression ratio, were considered. Based on the impact test results, the descriptions of failure mode, crack pattern, time histories of impact force, deflection, and strain are illustrated. On the other hand, tests on three additional RC columns with different cross-section dimensions subjected to horizontal static loading were undertaken for comparison purpose. In the comparisons of the load–displacement relationships for static and impact load cases, the significant divergence can be observed owing to the existence of the inertial force initiated in the dynamic responses. After the completion of the impact test, six impact-damaged specimens were tested under static loading to evaluate their residual resistance and the corresponding behaviour. It is found that the ultimate capacities of damaged specimens could reduce by 7%–14% compared with those of undamaged ones.

Dynamic behavior of particulate metal matrix nanocomposite plates under low velocity impact

The main purpose of this work is to investigate low velocity impact behavior of metal matrix nanocomposite plates reinforced with silicon carbide nanoscale particles. First, a micromechanical model is proposed to predict the effective mechanical properties of metal matrix nanocomposites. Two features of the nanocomposite microstructure affecting the elastic properties, including agglomerated state of silicon carbide nanoparticles and size factor, are taken into account in the micromechanical simulation. Then, finite element method is used to analyze the time histories of contact force and center deflection of silicon carbide nanoparticle-reinforced metal matrix nanocomposite plates. Several detailed parametric studies are accomplished to explore the influence of volume fraction, diameter and dispersion type of silicon carbide nanoparticles, spherical impactor velocity and diameter, plate dimensions, as well as different boundary conditions on the dynamic response of metal matrix nanocomposite plates. The presented approach accuracy is verified with the available open literature results displaying a clear agreement. The results indicate that adding the silicon carbide nanoparticles into the metal matrix materials leads to a reduction in plate center deflection and an increase in contact force between the plate and projectile. Moreover, it is found that the nanoparticle agglomeration dramatically decreases the contact force and increases the center deflection of metal matrix nanocomposite plates.

Impact and vibration response of multi-layered graphene sheets under different striker based on the analytical model and molecular dynamics

An impact behavior of striker on double-layered (DLGS) and multi-layered (MLGS) graphene sheet is investigated based on three degrees of freedom spring-mass model and the molecular dynamics (MD) simulations. The van der Waals (vdW) interaction between two layers of a DLGS is incorporated in the analytical model. An analytical model is able to predict the time history of deflection and vibration of the graphene sheets (GSs) and MD simulation cooperates various values of a dimension, chirality, boundary condition, number of layered and also striker parameters such as mass, velocity, and geometry. The analytical method is verified by MD simulations. The results from the spring-mass model demonstrated good agreement with MD simulation for a square and rectangular DLGS. The analytical model also accounts the relative motion between two layered of GS that is due to the local indentation in upper GS as can be seen in MD simulation. The maximum deflection and vibration after impact by the sphere, cone, sharp cone, and block strikers are investigated by MD simulations.

Performance of circular CFDST members with external stainless steel tube under transverse impact loading

Abstract This paper presents an experimental and numerical study on the impact performance of circular concrete-filled double skin steel tubular (CFDST) members with external stainless steel tube. Austenitic 304 stainless steel was used for all the test specimens. Taguchi approach was employed for the parametric design of the experimental program. The testing parameters were the impact height, hollowness ratio and axial load level. 18 specimens were tested under transverse impact loading to obtain the failure patterns, the time histories of impact force and mid-span deflection, as well as the strain developments in the stainless steel tube. Finite element (FE) models were then established and verified against the test results, in which the strain rate effects of the stainless steel, the carbon steel and the infilled concrete were considered. The validated FE model was then employed to investigate the whole dynamic response of CFDST members with outer stainless steel tube subjected to impact. The impact resistance of the stainless composite member was also compared with that of the CFDST member with an external carbon steel tube.

Mechanical behavior of SFRC beams subjected to both impact and fire loadings

To explore the mechanical behavior of SFRC beams subjected to both impact and fire loadings, 4 beams were tested with high-performance drop-weight test system, four point bending test machine and assembled electric furnace. The beams were firstly subjected to impact loadings and then exposed to fire with a constant load. During the test process, the crack patterns of beams were observed while the time histories of mid-span deflections and rebar strain were recorded. Then, the fire resistance of these beams was discussed. Based on the experiment, three-dimensional macroscopic finite element numerical model considering the effects of strain rate and high temperature was established. The impact loading process was simulated firstly; and then taking simulation results as the initial state, SFRC beams subjected to both fire and constant loading were simulated with a sequentially coupled thermal-stress analysis method. Moreover, considering the heterogeneity of concrete’s internal structure, a meso-scale simulation was also conducted with the procedures similar to that in macroscopic simulation. Good agreement between both the macro-/meso-scale simulation results and the test results illustrates the rationality and effectiveness of the present numerical analysis methods. The advantages of mesoscopic model were indicated through the comparison of macro-/meso-scopic results. It has been found that when the impact energy is low, the local concrete is cracked but a small overall deformation is remained. Nevertheless, this degrades the fire resistance of SFRC beams to some ex-tent. When the steel fiber dosage increases, resulting in an increasing shear strength of concrete matrix, the coexistence phenomenon of bending and shear cracks of beams under the impact load is changed to bending cracks as a dominant. Moreover, when subjected to elevated temperatures with a constant load, the distribution of cracks on the impact-damaged SFRC beams is relatively concentrated and a brittle failure occurs.

An experimental study on the mitigation effects of fine water mist on confined-blast loading and dynamic response of steel plates

The blast loading from an explosion of a condensed explosive in a confined space is quite different from that in an open environment. Due to the confinement effect, a confined-blast load usually causes more severe damage. The detonation products from a fuel-rich explosive, such as Trinitrotoluene (TNT), can react with the surrounding air under specific conditions and release additional energy, resulting in a significant increase of reflected shockwaves and quasi-static pressure in a confined space. Mitigation of the confined-blast loading is an effective way to protect structures from destruction. In this paper, a detailed experimental investigation of the influence of water mist on both the mitigation of blast load and dynamic response of the structure is presented. Six cases of experimental tests, with different charge masses of 80, 120 and 160 g of TNT explosive, with and without the presence of water mist, are performed in a confined chamber, with the shock pressure and deflection-time history curves of blast-loaded steel plates being recorded, as well as quasi-static pressure and temperature of the contained gas. By analysing the experimental data, it is found that the water mist decreases the reflected blast wave and quasi-static pressure by restraining the combustion effect and subsequent energy release of detonation products. As a consequence, both the first peak deflection and the residual deformation of the blast-loaded steel plates decrease greatly. Furthermore, based on a non-dimensional analysis of the experimental results for plates with different thickness subjected to different loading conditions, a new empirical relationship between non-dimensional deflection of the plate and a non-dimensional load parameter (for fully confined blast loading) was obtained. By employing this new empirical relation, the mitigation effect of fine water mist on confined blast load was determined quantitatively. The use of water mist is a very good alternative to mitigate the damage of structures subjected to a confined-blast load in the design of anti-blast structures.

Response of ultra-high performance cementitious composites filled steel tube (UHPCC-FST) subjected to low-velocity impact

Abstract This paper presents a combined experimental and numerical study on the transverse impact behavior of ultra-high performance cementitious composites filled steel tube (UHPCC-FST). UHPCC-FSTs were firstly fabricated by preparing the UHPCC with the cube compressive strength of 141.5 MPa. Then three specimens were tested in a drop-hammer impact device, and the impact force- and deflection-time histories of specimens under different release heights (5.0, 8.0 and 11.0 m) of the drop hammer were obtained and discussed. Furthermore, by using the commercial finite element (FE) program Hypermesh/LS-DYNA, a FE model was established to predict the impact behavior of UHPCC-FST. K&C constitutive model for concrete was adopted, and the corresponding model parameters for UHPCC were calibrated based on a series of test data (static compressive and direct tensile tests, dynamic compressive and tensile tests, triaxial compressive test, fly plate impact test), which were then validated by the present and existing drop hammer tests.

Multiscale analysis of the low-velocity impact behavior of ceramic nanoparticle-reinforced metal matrix nanocomposite beams by micromechanics and finite element approaches

An efficient multiscale analysis is proposed to investigate the dynamic behavior of metal matrix nanocomposite beams reinforced by SiC nanoparticles under low-velocity impact loads. First, an analytical micromechanics model is developed to obtain the effective elastic properties of ceramic nanoparticle-reinforced metal matrix nanocomposite, and then the finite element method is used to predict the dynamic response of beams made of this nanocomposite material. Two important microstructural features, including size effect and agglomeration of nanoscale particles, are incorporated into the micromechanical analysis. The present simulation results for the elastic modulus and low-velocity impact response show good agreement with previously published results. The effects of volume percent, diameter and dispersion type of ceramic nanoparticles, geometrical features and boundary conditions of nanostructure, velocity and size of projectile on the contact force, and center deflection time histories of metal matrix nanocomposite beams are extensively examined. Analysis shows that homogenously distributed SiC nanoparticles into the metal matrix nanocomposites can obviously increase the nanostructure/projectile contact force and decrease both the beam center deflection and impact duration which is due to the enhancement of elastic properties. However, the ceramic nanoparticle agglomeration has an effect on the decrease of contact force and the increase of both the center deflection and impact duration. Also, it is concluded that decreasing nanoparticle size can increase the contact force and decrease the beam center deflection.

Application of Falling Weight Deflectometer (FWD) Data and Energy Ratio (ER) Approach for Cracking Performance Evaluation of Asphalt Pavements

This study primarily focuses on evaluating the falling weight deflectometer (FWD) time history data for use in relative cracking assessment of asphalt pavements. Eight field project sections with a similar pavement structure were selected for evaluation; they include sections with and without the evidence of cracks. FWD tests were conducted for all selected field sections at a similar temperature to obtain load–deflection time history data. The results of the FWD-dissipated energy were further compared with the results of the energy ratio (ER), which is a well-known performance-based fracture property previously introduced for the cracking performance evaluation of asphalt mixtures. Pavement structures with the existence of cracks showed significantly greater FWD-dissipated energy and maximum deflection indicating a relatively higher rate of deterioration and/or damage for the pavement systems. Additionally, a proportional relationship identified between rate of change in normalized ER and FWD-dissipated energy confirmed that the FWD time history data was able to effectively differentiate pavement structures with and without the existence of cracks. Comparative results between the FWD-dissipated energy and the ER further support the validity of application of FWD-dissipated energy and the maximum deflection as a reliable material and/or pavement structural response indicator that can be used for cracking performance evaluation of asphalt pavements.

Who Says Backcalculation Is Only about Layer Moduli?

In this study, an existing finite layer algorithm for dynamic analysis of pavement structure was enhanced to incorporate the nonlinear behavior of unbound pavement materials. The nonlinear (stress-dependent) modulus was approximated in the vertical direction, which is similar to the approach used with multi-layered elastic and viscoelastic analysis methods for incorporating material nonlinearity. First, the enhanced finite layer algorithm was used to backcalculate the layer thickness, unit weight, Poisson’s ratio, and damping ratio in addition to the linear (viscoelastic and elastic) modulus of all layers. Then, the parameters backcalculated from the linear analysis were used to estimate the seed values for the subsequent nonlinear analysis in which the stress-dependent moduli of the unbound layers were backcalculated. Deflection data from two field sections (with thick and thin asphalt concrete layer) were used for demonstration. The results showed excellent agreement between the measured and backcalculated deflection time histories. In addition, it was found that the use of backcalculated parameters for the thickness, unit weight, Poisson’s ratio, and damping resulted in lower errors for both the linear and nonlinear analyses. Furthermore, the results of the backcalculation indicated that the material nonlinearity was more pronounced for the thin pavement, in which case the backcalculation error may be reduced further by incorporating the stress-dependent modulus.

Eccentric low-velocity impact on fiber-metal laminates under in-plane loading using unified zigzag theory

This paper investigates the eccentric low-velocity impact of Fiber metal laminates (FMLs) subjected to spherical projectile using a unified Zig-Zag plate theory. The presented zig-zag plate theory enforces transverse shear stress continuity through the thickness and can be reduced to conventional plate theories using appropriate shape function. The governing equations and suitable boundary conditions are obtained using the principle of minimum total potenital energy. Runge-Kutta method is employed to solve initial value problem resulted by the method of Ritz. The present model is validated by comparison and good agreement between its results and those of reports in open literature. Influence of various specifications of impact phenomenon such as laminate thickness, projectile radius, projectile velocity, in-plane load and eccentricity parameter is examined on deflection and contact force time history. The obtained results indicate that continuity of transverse shear stress is required to achieve accurate contact force even for moderately thin FMLs.

An Indirect Method for Monitoring Dynamic Deflection of Beam-Like Structures Based on Strain Responses

An indirect method for monitoring dynamic deflection of beam-like structures using strain responses measured by long-gauge fiber Bragg grating (FBG) sensors is proposed in this paper. Firstly, a theoretical derivation shows that structural deflection is in direct and linear relationship to long-gauge strain. Meanwhile, the method is suitable for structures with different boundary conditions and irrelevant to external loads. Secondly, the influence of boundary conditions, load type and sensor gauge length on the method is investigated by numerical simulation. Finally, an experiment of a simply supported beam subjected to dynamic loads was designed to verify the method. Experimental results show that both deflection time-history of arbitrary points of structures and deflection distribution along structures at a certain time can be obtained with high-precision. Therefore, the method presented can be a new alternative for the deflection evaluation and maintenance of engineering structures.

Fire resistance of steel fiber reinforced concrete beams after low-velocity impact loading

Engineering structures in the city environment surrounded with combustible materials are prone to be in the danger of combined effects of blast-induced impact loading and fire. Four steel-fiber reinforced concrete (SFRC) beams were tested after pre-impact loading (impact velocity = 5.4 m/s) to explore their fire-resistance. The beams were first subjected to impact loadings and then exposed to fire with a constant load. The failure patterns of beams were observed, and the time histories of mid-span deflections, temperature field as well as rebar strains were recorded. Moreover, the fire resistance of these beams were discussed. A three-dimensional finite element numerical model considering the effects of strain rate and high temperature were established. In the simulations, a two-step analysis method was utilized. In the first-step, the impact loading process was simulated. While, in the second-step, and the failure behavior of the SFRC beams subjected to both fire and constant mechanical loading was modeled with a sequentially coupled thermal-stress analysis method, in which the simulation results obtained in the first-step were taken as the initial state. Good agreement between the simulation results and the test results illustrates the validation of the simulation method. It is found that the failure patterns of SFRC under the low-velocity impact load is altered from shear type to bending type with the increase of steel fiber dosage. When the impact energy is relative lower, though weakened by the pre-impact, the beam still work in an elastic stage and shows good fire resistance. Moreover, limited to the low-energy impact conditions, the influence of steel fiber content on the thermal and mechanical behaviors of damaged beam can be ignored.

Cantilever Beam Natural Frequencies in Centrifugal Inertia Field

Abstract In the advanced mechanical science the well known fact is that the gravity influences on the natural frequencies and modes even for the vertical structures and pillars. But, the condition that should be fulfilled in order for the gravity to be taken into account is connected with the ration between the gravity value and the geometrical cross section inertia. The gravity is related to the earth acceleration but for moving structures there exist many other acceleration exaggerated forces and such are forces caused by the centrifugal accelerations. Large rotating structures, as wind power generators, chopper wings, large antennas and radars, unfolding space structures and many others are such examples. It is expected, that acceleration based forces influence on the structure modal and frequency properties, which is a subject of the present investigations. In the paper, rotating beams are subject to investigations and modal and frequency analysis is carried out. Analytical dependences for the natural resonances are derived and their dependences on the angular velocity and centrifugal accelerations are derived. Several examples of large rotating beams with different orientations of the rotating shaft are presented. Numerical experiments are conducted. Time histories of the beam tip deflections, that depict the beam oscillations are presented.

Time depended deformation and buckling of viscoelastic thick plates by a fully discretized finite strip method using Third order shear deformation theory

Abstract Time depended deformation and critical buckling load of viscoelastic thick plates were studied using finite strip method with the trigonometric functions in longitudinal direction and the polynomial functions in transverse direction. The plates were considered to be thick and the third order shear deformation theory was used to consider the effect of shear stresses in thickness. The mechanical properties of the material were considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. Time history of maximum deflection of viscoelastic plates subjected to transverse loading and unloading on plates was calculated using a fully discretized formulation. In addition, the critical in–plane load of plates was calculated by a nonlinear procedure in different times of loading. Moreover, the effect of thickness and the interaction of biaxial in–plane loading on critical load of plate were studied.

Domain-boundary element method for elastodynamics of functionally graded Timoshenko beams

A new domain-boundary element method is developed for elastodynamic analysis of functionally graded Timoshenko beams. Three governing partial differential equations of motion are derived by considering through-the-thickness variations of the physical properties. Weighted-residual forms are imposed utilizing the static fundamental solutions. These forms are then reduced to three integral equations containing domain integrals with time derivatives of unknown functions. Through domain discretization and shape function approximation, integral equations are converted to a system of ordinary differential equations in time. Forced dynamic response is revealed by solving the system of equations via Houbolt method. Comparison of dynamic responses generated for homogeneous beams to those calculated through an analytical solution and finite difference method verify the developed procedures. Further parametric analyses are performed for functionally graded Timoshenko beams under step, harmonic, and impulsive loadings. The numerical results presented illustrate the influence of material inhomogeneity on time histories of deflection and stress. Domain-boundary element method is demonstrated to be an effective technique for elastodynamic analysis of functionally graded structures.

Numerical simulations of nuclear power plant containment subjected to aircraft impact

Since the September 11 attacks, the protective performance of the nuclear power plant (NPP) containment against the impact of large commercial aircraft has been drawing much attention in the field of nuclear security. This paper addresses the numerical simulations of NPP containment subjected to aircraft impact. Firstly, the fine FE models of the Chinese Ling Ao NPP prestressed containment and A320 aircraft are established, and calibrated by the prototype impact test of GE-J79 engine and the modified Riera function, respectively. Then, based on the verified FE models, the entire impact process of the aircraft collision with the containment is reproduced by the missile-target interaction method, which is preferable by comparing with the loading-time history method in analyzing the dynamic responses of the containment. Furthermore, the parametric study is performed to investigate the influences of impact condition (position, angle and velocity) and structural configuration (wall thickness, reinforcement ratio and prestressing force) on the deflection-time history of the NPP containment in the impact central zone. Finally, an explicit formula for predicting the maximum impact deflection of the containment against the aircraft collision is proposed, which is helpful for the engineers in designing the NPP containment.

Dynamics of two impacting beams with clearance nonlinearity

Analytical solutions describing the transient dynamics of two Euler-Bernoulli beams with tips separated by clearance, are obtained. The tips of the beams impact when one of the beams is harmonically excited. Expressions of transient dynamics are presented as a superposition of particular solutions that satisfy to inhomogeneous boundary conditions, and eigenfunctions series with time dependent coefficients and homogeneous boundary conditions. The transition from impact phase to out-of-contact phase and vice versa is implemented using conditions that switch, involving construction of expressions for shear forces and relative position of beam tips. After each transition from one phase to another, the functions describing the time dependent coefficients in the eigenfunctions series are updated. This update involves the solution of ordinary differential equations with initial conditions corresponding to the end of the previous phase. The system of impacting beams reveals complex dynamics, including chaotic behaviour. Transient dynamics surfaces, time histories of beams deflections, impact forces, coefficients of restitution and phase planes are presented.

A new stability and sensitivity design and diagnosis approach

In the stability and sensitivity design and diagnosis approaches, there are various methodologies available. Bond graph modeling by lumping technique is one of the universal methodologies in methodical analysis used by many researchers in all over the world. The accuracy of the method is validated in different arenas. Bond graphs are a concise, pictorial representation of the energy storage, dissipation and exchange mechanisms of interacting dynamic systems, subsystems and components. This paper proposes a bond graph modeling for distributed parameter systems using lumping techniques. Therefore, a steel frame structure was modeled to analyze employing bond graph modeling of distributed system using lumping technique. In the analytical part, the effectiveness of bond graphs to model this system is demonstrated. The dynamic responses of the system were computed and compared with those computed from the finite element analysis. The calculated maximum deflection time histories were found to be comparable. The sensitivity and the stability of the steel frame structure was also studied in different aspects. Thus, the proposed methodology, with its simplicity, can be used for stability and sensitivity analyses as alternative to finite element method for steel structures. The major value brought in the practical design is the simplicity of the proposed method for steel structures.