Out Of Plane Displacements Research Articles

The deformation response of ultra-thin polymer films on steel sheet in a tensile straining test: the role of slip bands emerging at the polymer/metal interface

Abstract Forming of pre-coated sheet metal becomes of increasing importance in various fields of industrial application. In the recent years, ultra-thin plasma-polymer films have emerged as promising candidates as pre-treatments for steel sheet. Not much, however, is known about the forming behaviour of ultra-thin polymer coatings on ductile substrates, while an extensive literature exists for the reverse case, metal films on polymer, or brittle films on deformable substrates in general. For these cases, advanced models exist, mostly based on the so-called shear lag approximation. The heterogenous, highly localized strain and stress distribution, typical of ductile substrates, as well as out of plane displacements at the interface are disregarded, but cannot be neglected at the high strain levels of interest for elastic polymer films. This paper will focus on the role of slip bands on cracking of ultra-thin polymer films.

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

A Type of EMAT for Simultaneous Detection of Two Components of Rayleigh Wave

A new design of electromagnetic acoustic transducer (EMAT) is proposed for simultaneous measurement of in-plane and out of plane displacement components of Rayleigh wave. The EMAT consists of nine magnets and two meander-line-coils (MLCs). There almost only exists vertical or horizontal magnetic field at some specific positions in the magnetic field generated by the EMAT. By adjusting the interval between adjacent conductors and the position of conductors, the conductors in one coil are almost only in the vertical magnetic field and the conductors in the other coil are almost only in the horizontal magnetic field. Therefore, the two coils in this EMAT will almost only react with in-plane and out of plane displacements respectively. With this EMAT, repeated positioning or large area is not required during the measurement process. In addition, this EMAT can measure the two displacement components simultaneously without calculation. Meanwhile, this EMAT is much more sensitive to the ultrasonic waves for the magnetic field generated by the EMAT is enhanced. The measurement results of this EMAT are consistent with those of conventional EMATs, which indicates that the measurement results are accurate and reliable.

Analysis of Bi-stable Hexagonal Composite Laminate Under Thermal Load

This paper concerns the non-linear morphing behavior of composite laminate for creating asymmetric bi-stability in the symmetric geometry. The hexagonal and compound trapezoidal-hexagonal geometry are the proposed solution to create asymmetric bi-stability as new geometries. By creating asymmetric bi-stability, the strain energy of the two stable states will be different. This difference prevents continuous actuating between stable states and helps to obtain effectively control in the morphing process. The effects of laminate stacking sequence, temperature, and geometry on the strain energy and out of plane displacements of the two stable states are investigated. The non-linear finite element method is used for simulation, and the numerical results are validated with the experiments. Using hexagonal geometry allows the creation of tessellated surfaces consisting of the bi-stable and mono-stable sections that can be deformed in different directions and can be used in the adaptive structures such as reflector antenna or control surfaces.

Effect of central circular cut-out and low velocity impact damage on shear buckling and post-buckling of composite laminated plates

The effect of circular cut-out and low velocity impact damage on shear buckling and post-buckling performances of composite plates was investigated experimentally and numerically. Numerical solution for the buckling problem was obtained using an approximate Ritz method. Experiments were carried out for shear loaded pristine and damaged specimens, with a comparison of out of plane displacements, strain field, failure modes and mechanisms. For the two different thicknesses tested namely thin and thick laminates, experimental results showed a decrease of 25% and 27% in the post-buckling load for impact damage and center circular cut-out, respectively for the thin laminate. Whereas no significant reduction was detected for the thick laminate. A good correlation between numerical and experimental results were shown in the results.

In-situ Full Field Out of Plane Displacement and Strain Measurements at the Micro-Scale in Single Reinforcement Composites under Transverse Load

Micromechanics damage models applied to composites predict stresses and strains in the matrix and fibers as a function of the microstructure, constituting phases mechanical properties and load histories. Material parameters, like interface properties, are identified through inverse methods based on macroscopic stress-strain curves. Predictions are also benchmarked against macroscopic measurements. This situation does not capture local phenomena and hinders the robustness of the indentification/validation process. The purpose of this work is to provide full displacement and strain fields at the scale of a single fibre embedded into a matrix to allow the modelling community to either develop and identify micromechanics damage models or to benchmark their own predictions. Such data is critically lacking in the community. To that end, we have investigated three single fibers having radically different bonding strength with epoxy in addition to a bundle of about a hundred carbon fibers that were used as reinforcements of standard “dogbone” epoxy specimens. A laser scanning confocal microscope (LSCM) is used for micro digital image correlation (μDIC) during in-situ quasi-static tests of single-reinforcement dogbone specimens. For all specimens, damage initiated with fiber debonding at the free surface along the tensile direction. The crack then propagates around the interface while slightly growing along the fiber. The interfacial crack is shown to grow faster for couples with weak interfacial bonding. Strong fiber / matrix bonding is shown to stop Mode II transverse interfacial debonding which significantly delays specimen failure. Analysis of the LSCM micrographs with μDIC is used to provide measurements of displacements, strains, and measure depth during each test. The importance of out of plane displacements in interfacial debonding is highlighted. Out of plane displacement is shown to play a role in interfacial crack opening and growth and ought to be considered when studying or modeling damage in FRCs. μDIC is shown to be a promising technique to provide a better understanding of the damage mechanisms at the fiber or bundle scales and to determine interfacial toughness of a specific fibre / matrix couple in order to perform accurate damage modeling in FRCs. Displacement, strain, and confidence field results for each pixel from each experiment and at each time step are also provided in an extensive data package for detailed comparison with simulation results.

A Study on Steel Plate Shear Wall

The main objective of this research study was to evaluate the parameters of stiffened and unstiffened steel plate shear wall under seismic loads. The scope of effort included simulating five unstiffened steel plate shear wall with varying thickness, three singly stiffened steel plate shear wall, and three doubly stiffened steel plate shear wall. The validation and simulation was done using software package ANSYS v16 using loads derived from ETABS. Overall, Unstiffened steel plate shear walls produced high in-plane and out of plane displacements which decreased with increase in thickness of plate; than singly stiffened followed by doubly stiffened steel plate shear walls. With introduction of stiffener in steel plate shear wall, the in-plane displacement values reduced by about 1%, and about 3% when doubly stiffened on the other hand the out of plane came down by 50% when stiffened singly and also when doubly stiffened. It was noteworthy that stiffener does not play any significant effect on any parameter except for out of plane displacement.

Experimental and numerical investigation of high velocity soft impact loading on aircraft materials

Bird strike on aircraft remains a serious threat to flight safety. Experimental investigations employing real birds are associated with high cost and low reproducibility. Therefore, physical substitute materials are often used instead of real birds. This study investigates the soft impact loading on aluminium and laminated glass targets from ballistic gelatine and rubber projectiles. The two targets simulate strike on the aircrafts' fuselage and windshield respectively. The full field out of plane displacements of the targets were recorded for velocities 110 to 170 ms−1 using digital image correlation during gas gun experiments. A simulation model based on Smoothed Particle Hydrodynamics was developed and validated against the experimental data from all four projectile-target material combinations. It was shown that for the same momentum, a rubber projectile exerts a higher pressure on a target as compared to gelatine, even though the out of plane displacements and in-plane strains are similar. This led to fractures in the impacted laminated glass when rubber was used. The study offers new experimental data as well as efficient design modelling tools to mitigate damage imposed during bird strike. The models provide a way towards enabling the optimisation of real, large scale aircraft structures and components.

Evaluation of out-of-plane deformation of masonry infill walls due to in-plane loading by digital image correlation

Cyclic in-plane tests were performed on 1:2 scaled, single-storey, single-bay models of weak reinforced concrete frames with masonry infill. Deformations of masonry walls were evaluated using digital image correlation, which enabled quantitative and qualitative insights into out of plane displacements. Results imply that robustness of masonry infill units represents a major role in infill wall behavior and that the use of robust units could serve as an effective seismic strengthening method of RC frames. This was also implied by selected results of shake-table tests.

Full-Field Indentation Damage Measurement Using Digital Image Correlation.

A novel approach based on full-field indentation measurements to characterize and quantify the effect of contact in thin plates is presented. The proposed method has been employed to evaluate the indentation damage generated in the presence of bending deformation, resulting from the contact between a thin plate and a rigid sphere. For this purpose, the 3D Digital Image Correlation (3D-DIC) technique has been adopted to quantify the out of plane displacements at the back face of the plate. Tests were conducted using aluminum thin plates and a rigid bearing sphere to evaluate the influence of the thickness and the material behavior during contact. Information provided by the 3D-DIC technique has been employed to perform an indirect measurement of the contact area during the loading and unloading path of the test. A symmetrical distribution in the contact damage region due to the symmetry of the indenter was always observed. In the case of aluminum plates, the presence of a high level of plasticity caused shearing deformation as the load increased. Results show the full-field contact damage area for different plates’ thicknesses at different loads. The contact damage region was bigger when the thickness of the specimen increased, and therefore, bending deformation was reduced. With the proposed approach, the elastic recovery at the contact location was quantified during the unloading, as well as the remaining permanent indentation damage after releasing the load. Results show the information obtained by full-field measurements at the contact location during the test, which implies a substantial improvement compared with pointwise techniques.

Análise numérica do comportamento de painéis pré-moldados de fechamento e suas ligações em edificações de pequena altura: estudo de caso

The civil construction has intensified efforts in the search and implementation of strategies for the modernization of the sector, in which the rationalization of constructive processes has a crucial role. The most notable trends are related to employment of systems, wholly or partly pre-fabricated, able to maximize the potential of rationalization of enforcement proceedings. In this context, this study aims to analyze some important problems arising from the use of precast panels of closing in small height buildings or until 3 floors, application that has becoming very common in the country. The elements of analysis are panel-structure connections for gravity and bracing, vertical and lateral load, and thermal effects. Numerical analyzes are developed using the ANSYS computer program for the modeling of the problem. The physical nonlinear behavior of materials involved is considered in the simulations. The analyses show that thermal effects are critical at panels and connections considered. The presence of variable temperature results in out of plane displacements as well as increasing stress in the connections of concrete panels, particularly in the case of welded joints. Keywords: precast panel, building, numerical analysis.

Spatial distributions of magnetostriction, displacements and noise generation of model transformer cores

Recently, the relevance of audible noise of power transformers tends to increase due to the growing environmental awareness. For sound assessment, two standardised methods reveal the global noise of the whole system, as resulting from the interaction of core, windings, oil and tank. But for a deeper understanding of noise generation, it would be advantageous to investigate also the individual roles of the single above components in closer ways. This paper summarizes attempts to study the first component, i.e. the soft magnetic core, by means of model cores. For the first time, we analysed local distributions of all three strain, displacement and audible noise, keeping in mind that these quantities depend on many parameters like material, stacking, clamping, induction, rotational magnetization, or additional DC-bias, in complex ways. In-plane strain proved to be dominated by magnetostriction, with maximum intensities in corners and T-joints. The interpretation of in-plane displacements proves to be complicated by the unknown resting point of the whole system. However, the results reflect contributions of both magnetostriction and magneto-static forces. Out-of plane displacements proved to be dominated by effects of magneto-static forces, in particular at overlaps of corners and T-joints, due to imperfect clamping. Regional measurements of audible noise were performed in the near-field mode by means of automatic scanning by microphone over free core regions within a noise-isolating scanning chamber. As to be expected, the results showed strongly inhomogeneous distributions with maxima at T-joints and corners. As a conclusion, model core results have very restricted relevance for full sized cores in quantitative ways. But they favour an understanding for crucial mechanisms and for core regions that play dominating roles.

Variational models for prestrained plates with Monge-Ampère constraint

We derive a new variational model in the description of prestrained elastic thin films. The model consists of minimizing a biharmonic energy of the out-of plane displacements $v\in W^{2,2}(\Omega, \mathbb{R})$, satisfying the Monge-Ampèere constraint: $$ \det\nabla^2v = f . $$ Here, $f=-\mbox{curl}^T\mbox{curl} (S_g)_{2\times 2}$ is the linearized Gauss curvature of the incompatibility (prestrain) family of Riemannian metrics $G^h= \mbox{Id}_3 + 2 h^\gamma S_g+ h.o.t.$, imposed on the referential configurations of the thin films with midplate $\Omega$ and small thickness $h$. We further discuss multiplicity properties of the minimizers of this model in some special cases.

Numerical simulation of RC infill walls under cyclic loading and calibration with widely used hysteretic models and experiments

Addition of reinforced concrete (RC) infill walls into the structural system has been a commonly preferred strengthening technique within the last decades for seismic rehabilitation of RC frames. As a consequence, generating a representative numerical model of an RC infill wall has become an important issue. As the initial step of this study, measured structural responses of two selected well-known large-scale RC infill wall experiments subjected to displacement controlled cyclic loading are taken into account. Later, by calibrating the numerical model prepared in Perform-3D computer program utilizing fiber cross-sections, a practical and a compatible analytical model is obtained and proposed herein. Structural systems of the experiments are mathematically modeled by elements consisting of vertical and horizontal fiber layers to represent the bending/axial behavior and to control the out of plane displacements, respectively. Nonlinear behavior of the reinforcing steel is represented by a tri-linear backbone curve without strength degradation, while a multi-linear hysteretic behavior considering the strength loss is utilized for the structural concrete. Furthermore, those recently conducted experiments are simulated by a couple of widely used hysteretic models for comparative purposes, which are preferred in most cases by the researchers during the analytical investigation of RC structures, so that their adequacy for reflecting the nonlinear behavior of infill walls are also studied. It is shown with comparisons for the experimentally measured and the analytically derived results that the calibrated mathematical model proposed herein is more compatible with the measured values than the widely used hysteretic rules for capturing the behavior of these types of frames retrofitted by RC infill walls under reversed cyclic loading. Although numerical simulations are carried out for a limited number of tests and it is assumed that sufficient amount of anchoring dowels is provided at the interface of the existing frame and the RC infill, the proposed calibrated model conforms to both experiments’ measured responses by means of seismic behavior for not only the undamaged single bay frames converted to the RC infill wall, but also pre-damaged multi-bay strengthened structures, which include structural deficiencies like low concrete strength, inadequate stiffness and insufficient confinement.

Multiple phase estimation in digital holographic interferometry using product cubic phase function

Digital holographic interferometry (DHI) involves multi-directional illumination of an object to measure the in-plane and out-of plane displacements simultaneously. This results in multiple interference phases which have to be reliably estimated. The paper proposes a method where the interference field is represented as sum of multicomponent quadratic phase signal. Subsequently, product cubic phase function (PCPF) is used to estimate the quadratic coefficients. Using these coefficients multiple interference phases are estimated. The applicability of this method in DHI is demonstrated with simulation results.

Composed columns from cold-formed steel Z-profiles: Experiments and code-based predictions of the overall compression capacity

Built-up cold-formed steel members are tested in compression. The main objective behind the experiments is to determine the overall compression capacity of double-Z columns, which are often used in the Belgian engineering practice. Eight full-scale tests on 4.45m long columns are performed and out-of plane displacements and strains at six locations per member are recorded. The effect of initial imperfections is evaluated based on the measured longitudinal strains at mid-height. An attempt to relate the obtained ultimate capacity to prediction methods, based on the European standard for steel structures [1,2], is presented. The assumptions made in the analytical prediction and the gaps within the cited standard are explained and discussed. Certain aspects of the behaviour of such members cannot be represented in an Eurocode-base prediction, due to the restricted scope of [1,2]. A reference is made to North American Specification for the design of cold-formed steel structural members [3] as well, where a slightly better design methodology is available. Amendments to EN 1993-1-3:2006 are proposed and a design approach, based on the direct strength method is presented.

The employment of 0/90 unsymmetric samples for the characterisation of the thermo-oxidation behaviour of composite materials at high temperatures

The present paper explores the possibility to employ 0/90 unsymmetric plates as a tool for characterising the thermo-oxidation behaviour and the environmental ageing of composite materials at high temperature. The continuous monitoring of the out of plane displacements and the curvatures of such samples can be used for the identification of the thermo-oxidation induced irreversible chemical strain/stress build up and material property changes. A model has been developed to take into account the effects of thermo-oxidation on the time-dependent plate curvatures. Simulations show that 0/90 unsymmetric plates are very sensitive to thermo-oxidation induced changes, thus effective for capturing the searched thermo-oxidation effects. The predictions of the present model may serve for parametric studies and design of tests.

Synthetic jets based on micro magneto mechanical systems for aerodynamic flow control

A magneto-mechanical micro-actuator providing an axisymmetric synthetic microjet for active flow control was designed, fabricated and characterized. The micro-actuator consists of an enclosed cavity with a small orifice in one face and a high flexible elastomeric (PDMS) membrane in the opposite one. The membrane vibration is achieved using a magnetic actuation chosen for its capacity for providing large out of plane displacements and forces necessary for the performances aimed for. The paper presents first numerical simulations of the flow performed during the design process in order to identify a general jet formation criterion and optimize the device's performances. The fabrication process of this micro-magneto-mechanical system (MMMS) is then briefly described. The full size of the device, including packaging and actuation, does not exceed 1 cm3. The evaluation of the performances of the synthetic jet with 600 µm orifice was performed. The results show that the optimum working point is in the frequency range 400–700 Hz which is in accordance with the frequency response of the magnet-membrane mechanical resonator. In this frequency range, the microjet reaches maximum speeds ranging from 25 m s−1 to 55 m s−1 for an electromagnetic power consumption of 500 mW. Finally the axial velocity transient and stream-wise behaviours in the near and far fields are reported and discussed.

연성 금속의 파괴과정에서 발생하는 소성영역의 현장 측정

A plastic zone size is regarded as a measure of material resistance, and also it determines the fracture behavior. The importance of estimating or measuring the plastic zone size cannot be too emphasized. In this article, SDSP(Stereo Digital Speckle Photography) is examined as a new techniques to measure the plastic zone developed in a ductile metal. This technique is simple, vibration free and non-contact, and measures simultaneously in-plane displacements as well as out-of plane displacements like the side necking. Experimental results for a CT specimen are presented to demonstrate the accuracy in comparison with those obtained by recrystallization technique and finite element analysis.