Final Deflection Research Articles

Experimental Study of Sandwich Panels Subjected to Foam Projectile Impact

Similar blast loading characteristics can be obtained using impact of aluminium foam projectiles, which enables blast tests to be mimicked in a laboratory scale and in a safer environment. The purpose of this study is to determine the back-face deflection history of aluminium sandwich panels experimentally by aids of a laser displacement meter when panels are subjected to the impact of metal foam projectiles. This information was usually determined using finite element analysis (FEA) due to the difficulty in the experiment. The projectiles are cylindrical ALPORAS aluminium foam with diameter of 37 mm, length of 50 mm and nominal relative density of 10%. The sandwich panels consist of two 1 mm aluminium face-sheets and an aluminium honeycomb as the core. There are five different core configurations with a brand name of HEXCEL. The projectiles are fired towards the centre of the sandwich panels at different velocities using a gas gun. During the tests, a laser optical displacement measuring device is used to record the history of the back-face deflection experimentally. The deflection of the back-face is found to reach the maximum before coming to rest at a smaller value. The final back-face deflections of the sandwich panels show exponential relationship with the projectile impulse. The final deflections are compared with the deflection of monolithic plates with equal mass. The sandwich panels deflect less than the monolithic plate with an equal mass up to a critical value but continue to increase significantly afterwards. Care should be taken when using sandwich panels as protective structures against foam projectiles as beyond this point, the monolithic plates outperform the sandwich panels in absorbing the impact load.

Appropriate Coupling Solvers for the Numerical Simulation of Rolled Homogeneous Armor Plate Response Subjected to Blast Loading

Rolled homogeneous armor (RHA) plate subjected to blast loading is a complex problem involving the nonlinear fluid-structure interaction. The numerical techniques using the spatial discretization scheme that has been provided as a solver in the AUTODYN computer code will be used in this study in order to predict the RHA response subjected to explosive (TNT) blast loading. The final deflection will be used as a reference in order to identify the suitable solver for both materials RHA and TNT; then the plastic deformation will be chosen in the simulation process. Instead of using the same solver for RHA and TNT domains, the optimization of solver can be achieved if it is only used in an appropriate domain, or in other words, a different domain will be using different solver. The solvers, which were available in AUTODYN, were used in the analysis of impact and explosion or fluid-structure interaction. Therefore, in this paper, we will determine the suitable solver for both materials (TNT and RHA plate), and the appropriate interaction coupling solver will be obtained. Defining TNT and RHA plates using the Arbitrary Lagrangian Eulerian solver has found the best coupling solver for this case study when compared with existing experimental data. This coupling solver will be used for future analysis in simulating blast-loading phenomena.

The dynamic performance of simply-supported rigid-plastic circular steel plates subjected to localised blast loading

Near-field explosive charges, such as buried land mines, produce localised blast loadings which can potentially cause damage to property and/or loss of life in both military and civil structures. As the localised short duration blast pulse affects most severely a small area of a plated structure, boundary effects are not as significant as they are when a quasi-static or global blast loading is applied and full plate action may not be utilised.Many common structural forms are composed of individual plated elements and thus the investigation of localised blast loading effects on plates is a prerequisite to understanding the integral behaviour. Typically, plates are made of ductile materials such as steel, which exhibit considerable post-yield deformation capacity when subjected to such extreme dynamic loads. Analytical study of the dynamic plastic response of rigid-plastic plated structures is the aim of the present study.A circular plate is studied in the present work and a general form of a localised blast loading function with a spatial variation having a central radial zone with constant pressure and exponentially decaying profile outside the zone is assumed. Assuming that steel exhibits perfectly plastic behaviour and ignoring membrane action, transverse shear and rotatory inertia effects, the static plastic collapse pressure is initially found and the analysis is extended to take into account the inertial effects arising from dynamic loading. Results for the permanent transverse displacements are found for rectangular and linearly and exponentially decaying pulse loads.For high loads and/or loads of short duration, it was found that the permanent transverse displacement can be found by replacing the applied pulse load by means of an impulsive velocity without great loss of accuracy. Good correlation with numerical simulations obtained from ABAQUS/Explicit is achieved (within 15% accuracy) for plate geometries falling within the identified limits where membrane and shear effects are negligible.The predicted final transverse displacements are found to be dependent on the loading pulse shape, but the pulse-shape effects are eliminated by using the correlation parameters (effective impulse and pressure) advocated by Youngdahl (1971) [52] to give a single pulse shape-independent curve for the final plate deflection as a function of the effective pressure and effective impulse.

On pulse pressure loading of plates with holes

Abstract This paper reports the application of an energy solution to a complex problem involving large inelastic deformation in thin, clamped ductile square plates with either square or circular holes under the action of transverse pulse pressure loading. The work is part of a collaborative project to study blast loading of steel plates with penetrations as used for deck plating or bulkheads that may be required to resist loading far in excess of their design limit due to the effects of an accidental explosion. A novel differential pressure loading device was used to impart dynamic loading to 1/8 scaled 0.5 m, 1.1 mm thick, clamped mild steel square plates with a central aperture up to 4% of the plate area. This data was used to validate the energy approach that considers both plastic hinge formation and extensional effects. Accounting for strain rate, scaling and dynamic effects in the tests gave more than acceptable results when compared with final deflections in the tested plates. It is concluded that the energy approach together with small-scale test validation paves the way for a versatile robust design methodology which can be used to advantage for screening purposes and/or early stage conceptual design studies.

Model tests on interaction between soil and geosynthetics subjected to localized subsidence in landfills

In a landfill, excessive tensile strains or failure of the liner system due to localized subsidence underneath the geosynthetic liner, is a concern in design and operation of the landfill. The localized subsidence can be commonly withstood by reinforcements such as geogrids. A total of nine model tests were carried out to study the influence of soil arching in overburden sandy soil on the geosynthetics and the interaction between the soil and the geosynthetics. The localized subsidence was modeled by a strip trapdoor under the geosynthetic reinforcements. The reinforcement includes several layers of polyvinylchlorid (PVC) membrane or both PVC membrane and a compacted clay layer. Test results show that the vertical soil pressure acting on the geosynthetics within the subsidence zone is strongly related to the deflection of the geosynthetics. The soil pressure acting on the deflected geosynthetics will decrease to a minimum value with respect to its deflection if the final deflection is large enough, and this minimum value is almost independent of the overburden height. Otherwise, the deflection of geosynthetics cannot result in a full degree of soil arching, and the soil pressure within the subsidence zone increases with the increase of overburden height. Deflections and strains of the geosynthetics obviously decrease with the increase of their tensile stiffness. The presence of a compacted clay layer buffer can therefore reduce both deflections and strains of the geosynthetics. Finally, a composite liner structure is recommended for landfills to withstand the localized subsidences.

Influence of Rheological Behaviour on Load-Carrying Capacity of Timber-Concrete Composite Beams Under Long Term Loading

Wood and concrete are materials with different time dependent behaviour and both have different reactions to thermal and humidity changes of environment. In timber-concrete composite beams it results in generation of inelastic strains and redistribution of stress in cross-section.To determine load carrying capacity of composite wood-concrete element is possible according to Additions B of EN 1995-1-1, Design of Timber Structures. But this calculation technique does not consider the influence of rheological properties of composite materials as shrinkage, eventually bulking of materials, the influence of composite on creep coefficient and the influence of environmental changes. In this paper, the analytical calculation model of long term behavior of the timber-concrete composite beams is presented, which considers the most significant rheological phenomena such as: viscous-elastic creep of concrete and wood, mechano-sorptive creep of wood, creep of shear connection, concrete shrinkage and strains due to thermal and relative humidity changes of environment. This model is applicable for simple beams with linear material properties and allows determining the final deflection in the middle span and stressing distribution in the middle cross- section of the composite beams affected by long term loading. Applying the presented calculation model and results of experimental tests, the analysis of rheological behavior influence on long term load carrying capacity of timber-concrete beams is described as well.

Implantable Defibrillator Electrograms and Origin of Left Ventricular Impulses: An Analysis of Regionalization Ability and Visual Spatial Resolution

The implantable cardioverter-defibrillator (ICD) electrogram (EG) is a documentation of ventricular tachycardia. We prospectively analyzed EGs from ICD electrodes located at the right ventricle apex to establish (1) ability to regionalize origin of left ventricle (LV) impulses, and (2) spatial resolution to distinguish between paced sites. LV electro-anatomic maps were generated in 15 patients. ICD-EGs were recorded during pacing from 22 ± 10 LV sites. Voltage of far-field EG deflections (initial, peak, final) and time intervals between far-field and bipolar EGs were measured. Blinded visual analysis was used for spatial resolution. Initial deflections were more negative and initial/peak ratios were larger for lateral versus septal and superior versus inferior sites. Time intervals were shorter for apical versus basal and septal versus lateral sites. Best predictive cutoff values were voltage of initial deflection <-1.24 mV, and initial/peak ratio >0.45 for a lateral site, voltage of final deflection <-0.30 for an inferior site, and time interval <80 milliseconds for an apical site. In a subsequent group of 9 patients, these values predicted correctly paced site location in 54-75% and tachycardia exit site in 60-100%. Recognition of paced sites as different by EG inspection was 91% accurate. Sensitivity increased with distance (0.96 if ≥ 2 cm vs 0.84 if < 2 cm, P < 0.001) and with presence of low-voltage tissue between sites (0.94 vs 0.88, P < 0.001). Standard ICD-EG analysis can help regionalize LV sites of impulse formation. It can accurately distinguish between 2 sites of impulse formation if they are ≥2 cm apart.

Large plastic deflection of fully clamped beam subjected to impact load

By taking into account plastic dissipation by the axial (membrane) force induced by large deflection, a modifying factor is introduced into the bending‐only formulation (valid for small deflection) to construct the equations of motion for the large deflection where both bending moment and axial force are of importance. A complete theoretical solution is undertaken to trace the entire response history (including the transient phase) of a fully clamped beam subjected to impact load and a favourable succinct solution is obtained. In comparison with the small deflection solution, the axial force induced by large deflection is found to substantially decrease the final deflection of structures. This solution provides reliable prediction for deflections up to some 10 times the beam thickness.

Effect of Pier Vertical Deformations on Deflections of Main Girders for High Pier and Long-Span Continuous Rigid-Frame Bridges

In some long-span prestressed concrete box girder bridges, excessive deflections of main girders are often observed. These unacceptable deflections have detrimental influence on the serviceability and safety of the structures. To better understand and estimate short term and long term deflections for prestressed concrete box girder bridges, pier vertical deformation and its effect on deflections of main girders of Jinghe Bridg is investigated in this paper. Piers in Jinghe Bridge are tall and the difference in height between piers up to 22 m. Analysis indicates that although the short term deformations of piers are small, the long term deformations of piers can be 3 times as large as that of short-term ones. The maximum short-term downward deflection of Jinghe Bridge caused by pier deformation for main girders is 7.7 mm and the maximum long-term downward deflection is 33.3 mm. These values are relatively small compared with the span length of the bridge. But when the deflection of the main girder itself is also included, the final total deflection of the main girder may exceed the design code limit.

Timber beams subjected to long - term loading

Timber beams subjected to long - term loadingWood is a significant structural material, which is often used for timber bearing structures. Elements of timber structures must especially satisfy safety requirements, which are expressed by the ultimate limit states in the established standards. The structure must also satisfy the serviceability limit states. Local and global deformations make it impossible for the structure to serve the purpose it was designed for. It is important to take the deflections and their possible increase into account in the design to provide a structure which can be used during the whole period of service. Based on earlier examinations, it is known that a timber element over the course of long-term loading shows creep behavior. The structure of wood is able to adapt to the conditions of the surrounding environment. The properties of wood are especially affected by the relative humidity of the air and then by the type, intensity and duration of the loading. The most important factors affecting the serviceability of timber structures are volume changes caused by humidity and additional deflections caused by the effects of long-term loading. These phenomena emphasize the importance of serviceability limit states for timber structures. The paper deals with a long-term experimental investigation of timber girders that are currently often used. The aim was to obtain the deflection curves and mark the time dependence and the final deflections. The paper will also define the approximations for simulating the time-dependent deflections and obtain the creep coefficients for calculating the final deflections of the girders investigated.

Dynamic plastic response of clamped stiffened plates with large deflection

Study on the dynamic response, and especially the nonlinear dynamic response of stiffened plates is complicated by their discontinuity and inhomogeneity. The finite element method (FEM) and the finite strip method are usually adopted in their analysis. Although many useful conclusions have been obtained, the computational cost is enormous. Based on some assumptions, the dynamic plastic response of clamped stiffened plates with large deflections was theoretically investigated herein by a singly symmetric beam model. Firstly, the deflection conditions that a plastic string must satisfy were obtained by the linearized moment-axial force interaction curve for singly symmetric cross sections and the associated plastic flow rule. Secondly, the possible motion mechanisms of the beam under different load intensity were analysed in detail. For structures with plastic deformations, a simplified method was then given that the arbitrary impact load can be replaced equivalently by a rectangular pulse. Finally, to confirm the validity of the proposed method, the dynamic plastic response of a one-way stiffened plate with four fully clamped edges was calculated. The theoretical results were in good agreement with those of FEM. It indicates that the present calculation model is easy and feasible, and the equivalent substitution of load almost has no influence on the final deflection.

Dynamic rigid-plastic deformation of arbitrarily shaped plates

A rigid, perfectly-plastic model of solids is applied to study the dynamic behavior of simply supported or clamped, arbitrarily shaped plates on visco-elastic foundation. The role of membrane forces and transverse shear forces in the yield condition and the influence of geometry changes are neglected. The plate is subjected to explosive loads uniformly distributed over the surface. Several mechanisms of dynamic deformation of the plate are considered. For each mechanism, equations of the dynamic behavior are obtained. Operating conditions of these mechanisms are analyzed. Analytical expressions for the limit and high loads and for the maximum final deflections are obtained. Detailed analyses are given for an astroid-shaped plate, for a plate with a contour consisting of two arcs and for a plate with an internal free hole or a rigid insert.

Response of Beams to Shock Loading: Inelastic Range

Four classical support conditions are investigated for beams with distributed loading, which has a temporal form of rectangular pulse. First, a simple calculation is presented, using algebraic equations of momentum and energy conservation to derive approximate deflection results. Then, exact relationships, derived from work by others and describing a total of five regimes of motion, are quoted and discussed. These relations were developed using a popular, rigid-plastic material model. On the other hand, there is an elastic–perfectly plastic material model, which represents a more realistic description of material properties. When solutions are obtained by means of a numerical simulation, employing the better material model, it is found that the simpler solutions developed here provide more accurate results of final deflections.

THE MECHANISM OF JET VECTORING USING SYNTHETIC JET ACTUATORS

The control mechanism of jet vectoring using synthetic jet actuators is investigated. The final deflection angle of the primary jet is a result of the primary jet controlled by synthetic jets at three different regions. The lower static pressure near the primary jet exit induced by the synthetic jet, the entrainment and absorption of the primary jet fluid by the synthetic jet during the blowing and the suction stroke, the coupling and interaction between the vortices of synthetic jet and the shear layer of the primary jet are the main control mechanisms for the synthetic jet actuator vectoring a primary jet. The main factors influencing jet vectoring are analyzed and summarized, and a preparatory model for jet vectoring using synthetic jet actuator is presented.

Wavelength-dependent waveform characteristics of tectal evoked potentials in rainbow trout

Wavelength-dependent properties of tectal evoked potentials (TEPs) in rainbow trout, Oncorhynchus mykiss (Walbaum, 1792), were examined. It was found that TEP waveforms show distinct variation as a function of wavelength. In addition, the data suggest that the On and Off channels of the tectum each possess different wavelength-dependent characteristics. Middle wavelength stimulation typically evoked a waveform similar to that reported for another anamniote vertebrate, the toad (genus Bufo Laurenti, 1768). For the On and Off responses, this waveform comprised two negative deflections, N1 and N2, which were interrupted by a positive deflection, P2. The N2 deflection was followed by a final positive deflection, P3. Principal component analysis revealed that the N2–P3 complex of the On response was significantly more pronounced at longer wavelengths. In contrast, the N2–P3 complex was most pronounced at middle wavelengths for the Off response. The N1 deflection was relatively invariant with respect to wavelength. Should colour-opponent tectal units provide a significant contribution to the TEP, it is probable that its waveform characteristics provide signs of underlying neural processes which facilitate colour discrimination.

Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member. I: One Hinge along Member

The ultimate load of a typical steel frame is dependent on the geometrically nonlinear and material yielding effects. The complexity for considering material yielding by the plastic hinge approach is the unknown location of the plastic hinge, which can occur at the ends or any position along the element length. For the latter case, a member is divided into many elements in order to approximate the location of a plastic hinge. This process is tedious, inconvenient to use, and involves extensive computer time. Further, the strength check for sectional capacity using the LRFD code requires an assumption of the \iK factor or the effective length ratio, which further complicates a computer analysis for the ultimate load of a steel frame. To describe the formation of a plastic hinge along an element in a member at the ultimate limit state, a single element capable of modeling the P–δ. effect as well as the formation of the plastic hinge is needed. This paper adopts a simple concept of superimposition of triangular deflected shapes due to the formation of plastic hinge to the fifth order deflection shape for elastic deflection to yield the final deflection of the element, the plastic pointwise equilibrium polynomial (PPEP) element. Equilibrium of moment and shear at midspan of an element is maintained for accurate modeling of the P–δ effect in the tangent and secant stiffness. The robustness, accuracy and reliability of the developed element are demonstrated in a number of worked examples.

Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member. II: Three Hinges along Member

The ultimate load of a typical steel frame is dependent on the geometrically nonlinear and material yielding effects. The complexity for considering material yielding by the plastic hinge approach is the unknown location of the plastic hinge, which can occur at the ends or any position along the element length. For the latter case, a member is divided into many elements in order to approximate the location of a plastic hinge. This process is tedious, inconvenient to use, and involves extensive computer time. Further, the strength check for sectional capacity using the LRFD code requires an assumption of the \iK factor or the effective length ratio, which further complicates a computer analysis for the ultimate load of a steel frame. To describe the formation of a plastic hinge along an element in a member at the ultimate limit state, a single element capable of modeling the P–δ. effect as well as the formation of the plastic hinge is needed. This paper adopts a simple concept of superimposition of triangular deflected shapes due to the formation of plastic hinge to the fifth order deflection shape for elastic deflection to yield the final deflection of the element, the plastic pointwise equilibrium polynomial (PPEP) element. Equilibrium of moment and shear at midspan of an element is maintained for accurate modeling of the P–δ effect in the tangent and secant stiffness. The robustness, accuracy and reliability of the developed element are demonstrated in a number of worked examples.

Single objective reliability-based optimization of prestressed concrete beams

A general approach to the single objective reliability-based optimum (SORBO) design of prestressed concrete beams (PCB) is presented in this paper. The proposed approach incorporates all behavior and side constraints specified by the American Concrete Institute (ACI) code for prestressed concrete. Loading, material properties, prestressing force and the models used to predict structural performance at various stages––initial, final and ultimate stages––are all treated as random variables. Several limit states are considered, including permissible tensile and compressive stresses at both initial and final stages, prestressing losses, ultimate shear strength, ultimate flexural strength, cracking moment, crack width, and the immediate deflection and the final long term deflection. A general SORBO methodology is developed and solved by integrating PCB design and reliability analysis computer programs with an automated design optimization package using the feasible direction method. The single objective function represented by the overall cost of the PCB in terms of concrete, prestressing steel, mild steel, and formwork––is minimized subjected to 11 reliability constraints and four geometrical constraints. The design variables consist of six geometrical dimensions that shape the PCB cross section and one that represents the amount of prestressing steel. Numerical examples are presented to illustrate the application of the proposed approach to the SORBO of PCB. The results consist of, but not limited to, the initial and final prestressing forces, prestressing losses, immediate and final deflections, and upper and lower bounds on the parabolic tendon profile.

Effect of Cooling Condition on Deformation of Continuously Cast Stainless Steel 304

This work investigated the effect of the cooling condition on the deformation that was found for continuously cast stainless steel 304 slabs. The transient heat-transfer finite element analysis under various cooling conditions yielded temperature distributions within the slab, which were then used for subsequent calculations of the deformed shape. The asymmetric cooling condition in a cooling pit induced non-uniform and asymmetric thermal gradients with elapsed time. The non-zero final deflection and the reversal of curvature for the slab during cooling were attributed to the combined effect of asymmetric temperature profile and inelastic material property. Parametric studies revealed that a slab material of a low thermal conductivity or yield strength resulted in an increase for final deflection. The present analysis explained the physical cause of the deformation reasonably well.

Dynamic plastic behavior of a free–free beam striking the mid-span of a clamped beam with shear and membrane effects considered

Recently Yu et al. (Int. J. Solids Struct. 38 (2001) 261) made a study on the dynamic behavior of a flying free–free beam striking the tip of a cantilever beam using the rigid, perfectly plastic (r-p-p) material model. Later, also based on the r-p-p material model Yang and Yu (Mech. Struct. Mach. 29 (2001) 391) analyzed another impact problem of a free rotating hinge beam striking a cantilever beam. Both of these studies ignored the finite deflection effects on the plastic behavior of the colliding beams. However if the free–free beam strikes a clamped beam, the influence of finite-deflections, or, geometric changes, must be retained in the governing equation if the maximum permanent transverse displacement of the clamped beam exceeds the corresponding beam thickness. The problem becomes more interesting since the deformation mechanisms of the beam system and the partitioning of energy dissipation in the beams are significantly different from those predicted by ignoring the influence of membrane forces. Accordingly the failure modes of the structure are different. In the present paper, a theoretical model based on the r-p-p material idealization is proposed to simulate the dynamic behavior when the mid-point of a translating free–free beam impinging on the mid-span of a clamped beam with the beam axes perpendicular to each other. The plastic behavior of the beam system is explored with shear sliding and finite deflection effects taken into account. The final deflection, the dissipation of energy within the two beams after impact and the influence of the structural and material parameters are discussed. It is shown that membrane force plays an important role during the response process, especially when the deflection is of the same order as the thickness of the clamped beam.