Rigid Cantilever Research Articles

Field and numerical assessment of geofoam inclusion behind a rigid cantilever wall

The concept of compressible inclusion was introduced over two decades ago and earlier studies revealed that providing geofoam compressible inclusion between a retaining structure and backfill significantly reduces lateral pressure. Most studies are either 1-g model or numerical tests, and field tests are necessary to better understand and confirm previous research findings. In the present study, parametric tests are performed on a 6 m high concrete cantilever to check the effectiveness of inclusion on a rigid-yielding wall. The wall is instrumented to measure earth pressure, wall deflection, and geofoam compression during the backfilling. Field tests are performed with EPS15_500 (i.e., geofoam density of 15 kg/m3 and 500 mm thickness), EPS15_1000, EPS20_500, and the results are compared with the control test without inclusion. A developed numerical model is validated with the field results to determine the pressure variation for different cases. EPS15_1000 shows maximum reduction in lateral pressure, wall deflection, and geofoam compression, and can be a suitable compressible inclusion for the wall under investigation. The compressive strains generated in EPS, irrespective of EPS density and thickness, exceed the design strains suggested by previous studies. Majority of strains occurred due to compaction which was not considered by earlier studies.

Influence of rope fastening on the spectrum of its natural transverse vibrations

According to the previously developed method, which takes into account the bending stiffness of steel ropes during their transverse oscillation, the ropes of the pedestrian bridge ‘Lovers’ in the city of Tyumen were investigated. The obtained values of tension forces and bending stiffness were within the expected range. The high variation of bending stiffness values forced to pay attention to the accuracy of the initial values of rope lengths, which were obtained from the photograph. To measure the rope lengths, a method of nodal harmonic registration was proposed, but the results obtained by this method were higher than the values obtained from the photograph. The evaluation of measurement errors did not explain this overestimation, which led to the necessity to revise the solution of the differential equation of transverse oscillations. It turned out that previously only its partial solution was considered, assuming a hinged rope attachment, whereas it is cantilevered and has a bending reaction. Taking this feature into account by introducing an additional boundary condition allowed to improve the calculation model and explain the overestimation of the rope length in the method of nodal harmonics.Taking into account the nature of the rope attachment allowed us to introduce a generalised parameter s, which takes zero value for rigid cantilever attachment, and is equal to one for articulated attachment. Then the stiffness weakening inside the anchorage will be manifested by the growth of the parameter s and can be detected by the results of the oscillation spectrum registration.

Modelling of Mode I delamination using a stress intensity factor enhanced cohesive zone model

Cohesive zone modelling is a common approach to capture delamination in composite laminate structures. Recent experimental advancements now enable the direct measurement of Mode I traction-separation responses (TSRs) from a single specimen using the composite rigid double cantilever beam (cRDCB), overcoming a major obstacle in using cohesive zone modelling to model delamination. However, TSRs measured experimentally with the cRDCB specimen capture damage response as well as the stiffness contribution of the adjacent laminae, which can introduce significant artificial compliance into numerical models when modelling delamination separately from intralaminar behaviour. A two-stage analysis procedure utilizing a crack tip compensation function is presented to enhance the TSRs measured with the cRDCB specimen to accurately model Mode I delamination. The analysis procedure is demonstrated to improve the accuracy of delamination prediction within the statistical variation of published experimental data. Furthermore, the transferability of TSRs measured with cRDCB specimens is explored using available experimental DCB data. It is shown that the onset of damage and early damage behaviours measured with the cRDCB specimen appear to be transferable between geometries, whilst large-scale damage mechanics remain geometry dependent.

Predictive model of back-wall overpressure behind a cantilever wall

To reduce the hazards posed by blast shock waves, important potential targets are usually shielded by cantilever walls. The main factor that indicates whether there is damage is the back-wall overpressure, and of concern here is predicting the back-wall overpressure behind a rigid cantilever wall. This was measured in full-scale blast experiments using 20 kg of trinitrotoluene (TNT) located on the ground, and the experimental data reveal how the cantilever wall mitigates the shock wave. A 3D numerical model was established to determine how the wall size influences the diffraction of the shock wave and the peaks and attenuation of the back-wall overpressure. Based on the numerical results and dimensional analysis, a model is proposed that provides an effective means of predicting the back-wall overpressure rapidly from the TNT equivalent, the standoff distance, and the height of the wall.

On the Cover: A Composite Rigid Double Cantilever Beam Specimen for Assessing the Traction–Separation Response of Mode I Delamination in Composite Laminates

On the Cover: A Composite Rigid Double Cantilever Beam Specimen for Assessing the Traction–Separation Response of Mode I Delamination in Composite Laminates

A Composite Rigid Double Cantilever Beam Specimen for Assessing the Traction–Separation Response of Mode I Delamination in Composite Laminates

A Composite Rigid Double Cantilever Beam Specimen for Assessing the Traction–Separation Response of Mode I Delamination in Composite Laminates

Prediction of bonded asymmetric metallic cross-tension and single lap shear joints using finite element model with material-level adhesive properties and cohesive zone method

Predictive finite element (FE) models of adhesive joints are needed to enable the design and evaluation of adhesively joined structures, particularly large-scale structures that may be costly to assess experimentally. Although models calibrated to coupon-level tests have provided an important first-step, models based on material-level characterization are needed to enable joint assessment in complex modes of loading. In the present study, a structural epoxy adhesive was characterized using rigid double cantilever (Mode I) and bonded shear (Mode II) specimens to provide material-level input properties. Three single-lap shear (SLJ) and seven cross-tension (CT) specimen configurations were fabricated with aluminum and steel sheet materials. The specimens included symmetrical (the same adherend material and thickness) and asymmetrical (dissimilar adherend material or unequal thickness) configurations, with three loading angles (0°, 45°, 90°) for the CT specimens. Finite element models of the SLJ and CT specimens were developed using Cohesive Zone Modeling for the adhesive, with properties determined from the Mode I and Mode II characterization tests. The FE models of the SLJ and CT test specimens predicted the peak load within an average difference of 2%–19%. The joint strength varied between different test configurations, owing to adherend deformation, load eccentricity and mixed-mode loading. Importantly, the model parameters were not calibrated to the SLJ and CT tests. The FE models were able to predict joint response for varying test specimen geometry, adherend thickness, adherend material, and modes of loading.

Reliability evaluation for cantilevered retaining walls considering uncertainty of mainshock-aftershock sequences

A method for the probabilistic analysis and reliability evaluation of retaining walls is presented in this paper. This paper examines the stochastic dynamic response of the rigid cantilever retaining wall subjected to mainshock-aftershock sequences. A variable generation strategy for minimizing the lowest generalized F-discrepancy is used to facilitate the simulation of stochastic seismic sequences. The correlation between the main shock and the aftershock is established through a copula function. The direct probability integral method (DPIM) is used to estimate the reliability of the retaining wall when the wall is subjected to stochastic seismic sequences. The results show that the dynamic reliability of different physical quantities at different safety thresholds can be obtained by the above methods without assuming the probability distribution of the response. This study also demonstrates that aftershocks can degrade the structural reliability to varying degrees, with the degradation intensifying in proportion to the increase in design requirements.

Two-Phase Smoothed Particle Hydrodynamics Modelling of Hydrodynamic-Aerodynamic and Wave-Structure Interaction

A two-phase (air and water) smoothed particle hydrodynamics (SPH) method is employed to study the hydrodynamic-aerodynamic and wave interaction with fixed and floating structures in a wave basin. The method is first verified for a classical two-phase dam-breaking. A mirror-open boundary is implemented at the top and left sides of a two-phase wave basin with a piston to generate a second-order regular wave. It is observed that, compared to the single-phase simulation, the two-phase one obtains a smoother water surface and prevents the non-physical water splash when interacting with the sloped dissipative beach. This wave basin is also used to investigate wave-structure problems such as wave interaction with a rigid cantilever beam fixed to the basin bottom and downstream of the wave-maker mechanism and the dynamics of a single floating box and two floating boxes in the waves. A typical wave-structure interaction period is captured and described using pressure contours and velocity vectors at three selected instants for the wave-rigid cantilever beam case. With the increase of the structure’s height, the wave height after the structure decreases, but no evident variation is found when changing its thickness. Besides the hydrodynamics interaction, a periodical collision is observed between the two floating boxes on the wave surface.

Coriolis Force Sliding Mode Control Method for the Rotary Motion of the Central Rigid Body-Flexible Cantilever Beam System in TBM

Beam slab structure is often encountered in a complex tunnel boring machine. Beam slab structure is subject to dynamic load, which is easy to cause fatigue damage and affect its service life. Therefore, it is necessary to control the vibration of this kind of beam slab structure. In this study, the central rigid body-flexible beam model is established for the rotating beam and plate rotating around the y-axis. Based on the Hamilton variational principle, the dynamic equation of the central rigid body-flexible beam system is established, and the dynamic model of the central rigid body-flexible beam system considering the influence of Coriolis force and centrifugal force is given. The vibration control of the central rigid body-flexible beam system is studied. The vibration mode of the rotating Euler Bernoulli beam is determined by using the elastic wave and vibration mode theory. The influence of the rotating motion on the beam vibration is analyzed, and the variable structure control law is designed to suppress the beam vibration. Numerical simulation results show that the control method can effectively suppress the first-order and second-order vibration of the beam and verify the effectiveness of the control strategy.

A comparison of pad metallization in miniaturized microfabricated silicon microcantilever-based wafer probes for low contact force low skate on-wafer measurements

Miniaturized, microfabricated microelectromechanical systems-based wafer probes are used here to evaluate different contact pad metallization at low tip forces (<mN) and low skate on the on-wafer pads. The target application is low force RF probes for on-wafer measurements which cause minimal damage to both probes and pads. Low force enables the use of softer, more conductive metallisation. We have studied four different thin film contact pad metals based on their thin film electrical resistivity and micro-hardness: gold, nickel, molybdenum, and chromium. The contact pads sizes were micrometre (1.9 × 1.9 µm2) and sub-micrometre (0.6 × 0.6 µm2). The contact resistance of Au–Au, Ni–Au, Mo–Au, and Cr–Au was measured as a function of tip deflection. The tip force (loading) of the contacts was evaluated from the deflection of the cantilever. It was observed that an overtravel of 300 nm resulting in a contact force of ∼400 µN was sufficient to achieve a contact resistance <1 Ω for a sub-micrometre gold contact pad. Our results are compared with an analytical model of contact resistance in loaded metal-metal contacts—a reasonable fit was found. A larger contact resistance was observed for the other metals—but their hardness may be advantageous when probing other materials. Using a combination of a rigid silicon cantilever (>1000 Nm−1) and small contact pads enabled us to show that it is the length of the pad (in contact with the surface) which determines the contact resistivity rather than the total contact pad area.

ВЛАСНІ ЗГИННІ КОЛИВАННЯ БАЛКИ ЗІ СПЕЦІАЛЬНИМ ЗАКОНОМ ЗМІНИ ШИРИНИ

Purpose. The aim of the work is to construct a closed analytical solution of the problem of natural vibrations of the beam, the width of which varies according to the law exp (αx2). Methodology. The approach is based on the provisions of symmetric analysis of differential equations with variable coefficients. This approach allows you to find a way to obtain an analytical solution of the corresponding differential equation and, ultimately, the boundary value problem. Findings. The main result is the construction of the algorithm and obtaining the solution of the differential equation of the IV order, which describes the transverse bending vibrations of the beam with a special law of change of width (the thickness of the beam is a constant value). Two examples of the analysis of oscillations of such beam in case of its bilateral rigid fastening and cantilever fastening are resulted. For these cases, the frequency equations are obtained, the natural frequencies and amplitude coefficients are found, which are necessary for the construction of natural forms of oscillations. Originality.The approach presented in this paper is based on the idea of symmetries of differential equations and is characterized by a sim- plified analysis of the solution of the problem of bending oscillations of the beam with a special law of width. The method proposed for solving the boundary value problem is convenient and simple, because the results are found without the use of numerical research methods. Practical value.Examples of the exact analysis of fluctuations which allow to assert about real possibility of expansion of an existing number of configurations of a beam, both on width, and on ways of fastening are resulted. Such beams can, for example, be used as prototype samples for resonant tests of materials for fatigue strength. Сonclusions. The given algorithm for constructing the solution of the problem on eigenvalues for a beam with the given special law of change of width is universal and can be extended to other constructions of beams. Since in this case the question arises only about the choice of the approximation function, which allows to use the method of symmetries and obtain an exact solution of the corresponding differential equation of the IV order, which in turn describes the transverse oscillations of the beams.

Numerical Investigation of Wave Energy Absorbed by the Edinburgh Nodding Duck Device in Front of a Vertical Wall

Abstract An open-source computational fluid dynamics (CFD) package, openfoam, is extended and applied to study the power takeoff (PTO) efficiency absorbed by an Edinburgh nodding duck wave energy converter (WEC) device installed in front of a vertical wall. The duck WEC device is axis-fixed by a rigid cantilever beam extended from the vertical wall. After numerical validations and convergent verifications, the characteristics of the duck WEC device for power takeoff with various distances between the rotation center of the duck WEC device and the vertical wall are examined. The present numerical investigation illustrates that the absorbing efficiency by the duck WEC device is insensitive to the distance when subjected to incident waves of higher frequencies, while sensitive when subjected to incident waves of lower frequencies. Furthermore, for incident waves of lower frequencies, when the distance is approximately 0.58 times of the wavelength, a lower absorbing efficiency is achieved. While a higher absorbing efficiency is achieved, when the distance is approximately 0.32 times of the wavelength. Besides, the wave-induced force and torque impacting on the vertical wall are checked. It is found that both the force and torque significantly decrease when the distance is approximately 0.32 times of the wavelength, owing to the installation of the duck WEC device in front of the vertical wall.

Safety Assessment of Rigid Frame Cantilever Construction Based on Matter-Element and Extension

In order to effectively evaluate the safety status of the cantilever construction of a large-span rigid frame bridge, this paper takes a four-span rigid frame bridge as the engineering background, selects the failure probability of the cantilever construction, the natural environment, the cantilever construction operation, and the management level as the evaluation factors and divides the possibility level into Five levels, an extension model is established to evaluate the cantilever construction of the bridge. This paper first uses fuzzy comprehensive evaluation to quantify the natural environment and cantilever construction technology, then calculates the failure probability of the bridge cantilever construction based on Monte Carlo theory, and finally scores according to the management level of the management system. Invite relevant experts to obtain the weight set of each evaluation factor through the 1-9 scale method, and use the goodness evaluation method in the matter-element extension method for evaluation. The results show that the safety assessment result of the cantilever construction of the bridge is a medium risk, which provides a reliable basis for predicting and avoiding risks. Based on the matter-element extension method, the rigid frame cantilever construction safety assessment takes into account the uncertainty and ambiguity of failure, and more objectively reflects the safety status of the cantilever construction during the construction period. The calculation results of different safety evaluation models are compared with the results of this paper, which verifies the feasibility and effectiveness of the matter-element extension theory applied to the safety evaluation of cantilever construction.

Influence of thickness on the flow field generated by an oscillating cantilever beam

The aerodynamic performance of oscillating piezoelectric fans has been the focus of many research studies due to their potential as active cooling mechanisms for thermal management applications. These studies have typically focused on commercially available fans with flexible beams that are made to oscillate by tuning the alternating input voltages to the beam’s resonant frequency. Geometric variables such as fan height and length have previously been investigated; however, fan thickness has remained a fixed geometric constraint ( $${\mathcal {O}}\sim 0.1$$ mm) to allow feasible resonant frequencies to be achieved. This study investigates the influence of beam thickness on the flow field generated by an oscillating beam. The beam in this study is a rigid cantilever that is mechanically oscillated at a fixed amplitude and frequency thereby obviating the requirement to operate at resonance. Thicknesses of 1 and 3.7 mm are considered. A custom-designed particle-image velocity (PIV) facility was used to capture the induced phase-locked and time-averaged flow fields in two planes. The beams were noted to produce markedly different wakes within the oscillation plane. The 1-mm beam induced two distinct diverging jets—consistent with much of the literature on piezoelectric fans. In comparison, the 3.7-mm beam created two strong lateral wake regions with minimal fluid disturbance downstream of the beam tip. Out-of-plane measurements, as well as numerical models, revealed that fluid separation from the 3.7-mm beam is inhibited due to the more dominant influence of viscous friction on the larger, upper and lower surfaces of the rigid structure. The numerical analysis also revealed the significant influence of shed, counter-rotating vortex pairs on the pressure fields around the beam structures during the subsequent half-stroke. The results of this work may inform the design of oscillating fans for use in thermal management applications, as well as contribute to the literature on the complex phenomenon of flapping wing flight.

Stress distribution in column-plate foundations of Monument of Christ The King erected in Świebodzin

The paper presents results of numerical simulations of the stress distribution and deformations within of foundations of huge monument of Christ The King erected in Świebodzin (Poland) in 2010. It is 3 meters taller than the better known statue of Christ the Redeemer in Rio de Janeiro, standing at 30.1 meters tall without its pedestal. Foundations were built as a system of reinforced concrete columns and slabs which can be classified as a spatial column-slab system. Actual mechanical parameters of the substrate and of the artificial mound made of field stones, sand, gravel and clay were adopted in calculations. The numerical simulations of structural members of foundation and determination of the stress distribution are presented in the article. Monument itself was not included into the model. Instead of it the rigid cantilever was introduced to which resultant forces were applied. Three different stages were distinguished: the initial state after foundation and mound accomplishment, the initial state plus the dead load and the initial state plus the dead load and the wind load. It was assumed that the wind load was taken into account in a quasi-static formulation by applying the equivalent horizontal force and the torque. Stresses and displacements for these three stages were determined by Finite Element Method using Simulia ABAQUS system. It was disclosed what was a contribution of particular parts of foundations in sustaining loads in considered load cases. The state of exertion of structural members of foundations and the soil itself was assessed. It was showed that the column-slab foundations and soils of the mound play important role in taking loads of the statue, spreading them and safe transferring to the undisturbed level of natural soils. According to the numerical simulations results the columns of foundation take as much as 64% of the vertical load (in the most unfavourable load conditions). At the same time soils of the mound take through the side surface of piles about 20 % of the vertical load.

Characterization of Mode I and Mode II traction–separation laws for cohesive separation of uncured thermoset tows

As part of an effort to predict wrinkling of carbon-fiber tows during automated fiber placement, the cohesive zone traction–separation relations for two carbon fiber epoxy prepreg tows are quantified for Mode I and Mode II loading using a rigid double cantilever beam (RDCB) specimen. An explicit expression for normal traction versus normal separation ($$\upsigma \hbox { vs }\updelta _\mathrm{n}$$) and tangential traction versus tangential separation $$(\tau \hbox { vs }\updelta _\mathrm{t})$$ are derived using static equilibrium equations for an RDCB considering a compressive zone ahead of the process zone. The traction–separation relationships are in term of quantities that can be measured using a full field measurement technique (StereoDIC). The baseline traction–separation relationships in this work are obtained using conditions representative of those experienced by an uncured tow undergoing automated fiber placement (AFP) onto a substrate of a similar material with layup temperature $$\hbox {T} = 40\,{^{\circ }}\hbox {C}$$, pressure p = 1 MPa and contact time t = 1 s. The RDCB specimen is loaded in displacement control at a constant load line displacement rate of 0.3 mm/min. Speckle images for StereoDIC are captured using stereo vision systems equipped for capturing images of the RDCB specimen with a field of view of $$100\hbox { mm }\times 75\hbox { mm}$$. Analysis of the data obtained for Mode I and Mode II loading shows that the Mode I energy release rate $${\varvec{\mathscr {{G}}}}_\mathrm{I }= 120\hbox { J}/\hbox {m}^{2}$$ and Mode II energy release rate $${\varvec{\mathscr {{G}}}}_\mathrm{{II}} = 255\hbox { J}/\hbox {m}^{2}$$, with the maximum normal traction $${\varvec{\upsigma }}_\mathrm{\mathrm{max}} = 0.50\hbox { MPa}$$ and the maximum shear traction $${\varvec{\tau }}_\mathrm{\mathrm{max}} = 0.35\hbox { MPa}$$.

Bio-adhesion evaluation of a chitosan-based bone bio-adhesive

Conventional treatment of complex fractures includes the use of plates and nails, which may compromise the affected limb's functionality. Previous studies have demonstrated promising results through chemical, mechanical, and cytotoxicity tests of a chitosan-based adhesive—proposed as a new method to bond high energy fractures—in dry environments with adequate adhesion, malleability, and biocompatibility. In this study, we focused on performing an evaluation of bio-adhesives’ mechanical properties and bone-adhesive joint using two chitosan-based formulations (with and without a cross-linking agent). The texture profile analysis determined adhesive properties, such as cohesiveness, adhesiveness, hardness, and resilience at different cure times. Bone-adhesive joint was evaluated according to the tensile bond strength test and shear bond strength test. Fracture toughness and cohesive strength were calculated through a rigid double cantilever beam test at mode I failure. Bone-adhesive joints were tested in two environments: dry and submersed in water at 37 °C for 1, 6, and 24 h (curing time), an approximation of surgery conditions. The experimental results showed an incremental of adhesiveness and hardness of the cross-linked adhesive during the first 15 min, which was determined as the usage time to spread on the bone fracture. The joint interaction between the adhesive and bone surfaces was studied; chitosan-based formulations showed an adhesive joint failure under dry conditions in most of the cases. However, this behavior changed under aqueous conditions, presenting cohesive failures. Under aqueous conditions, cross-linked bone-adhesive presented an augmented tensile bond strength up to 0.024 ± 0.0036 MPa, a shear bond strength up to 0.031 ± 0.0069 MPa, and fracture toughness of 2.38 ± 0.54 J/m2 was observed with a cure time of 24 h. Finally, the presence of the cross-linking agent in the cross-linked bio-adhesive reduced the sensitivity of the adhesive to water; a promising finding that should be explored in future studies.

Investigación del colapso de un muro de mampostería de ladrillo no reforzada bajo fuerzas de vientos moderadas

Several methodologies used for the collapse assessment of an unreinforced brick masonry wall subject to out-of-plane bending due to moderate wind loads in Medellin, Colombia are presented. Models include a rigid cantilever model of masonry elements, deformable cantilever and frame models of intermediate concrete columns and beams with and without masonry contribution to the wind resistance, and a finite element model with all concrete frame elements, masonry units and panel openings modeled explicitly. Wind demands are estimated using spatial interpolation of actual wind velocity measurements near the site. Results are presented in terms of peak deflections at the wall top, as well as peak force and stress demand-to-capacity ratios on concrete frames and masonry elements, respectively. Wind pressure distribution, P-Delta effects, interaction and relative contribution to the out-of-plane bending resistance of concrete framing and masonry elements with either one- or two-way action are shown to be the main parameters affecting results, in addition to model selection. Despite significant differences between models, recommended parameters and assumptions lead in all cases to the correct determination of the wall's imminent collapse under the estimated wind demands.

Оценка механических характеристик кристаллов соляных пород на основе математической модели процесса наноиндентирования на зондовом силовом микроскопе Dimension Icon

Зондовый силовой микроскоп (ЗСМ) Dimension Icon применяется как для оценки рельефа поверхности исследуемого образца, так и для получения силового отклика образца при взаимодействии кантилевера (индентора специальной формы, расположенного на конце упругой консоли) с поверхностью образца. При этом, в отличие от других приборов, например NanoTest-600, где в результате индентирования исследователь получает величину твердости и эффективного модуля упругости с помощью программного обеспечения, «зашитого» в данный прибор, ЗСМ позволяет получить только кривую отклонения индентора в зависимости от перемещения основания кантилевера. Зная коэффициент жесткости на изгиб упругой консоли, исследователь может самостоятельно определить кривую «усилие-перемещение» индентора на этапе нагрузки и разгрузки. Далее возникает задача интерпретации полученной кривой: каким образом можно оценить механические характеристики материала на ее основе? Ответ на этот вопрос зависит, в частности, от характера механического поведения материала. Для диапазона глубин индентирования, превышающих головную сферическую часть зонда кантилевера, при предположении упруго-идеально-пластической модели материала рассмотрена двумерная осесимметричная задача индентирования образца на этапе нагрузки и разгрузки. Численное моделирование осуществлено в пакете ANSYS в рамках контактной задачи в предположении абсолютно жесткого наконечника кантилевера. Путем обработки результатов вычислительного эксперимента предложена методика оценки предела текучести и модуля упругости поверхностных слоев образца. На основе данных ранее проведенных экспериментов получены конкретные значения механических характеристик для кристаллов соляных пород.