Out Of Plane Displacement Research Articles

Third-order electro-elastic analysis of sandwich doubly curved piezoelectric micro shells

The present paper studies size dependent electro-elastic analysis of sandwich doubly curved piezoelectric micro shells. The structure is composed of a micro elastic core and two piezoelectric micro layers as sensor and actuator. The kinematic relations are developed based on third-order shear deformation theory proposed by Reddy. The principle of virtual work is used to derive governing equations in terms of primary displacements, rotation components, and electric potential. The sandwich doubly curved micro shell is resting on Pasternak’s foundation. After verification of numerical results, the analytical results are presented in terms of important parameters such as micro length scale parameter, applied electric potential, and some geometric parameters of the problem. The numerical results indicate that the in-plane deformation and out of plane displacement are decreased with increase of micro length scale parameter and decrease of applied electric potential.

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.

Lattice Boltzmann method applied to antiplane shear loading of a stationary crack

AbstractIn this work, the dynamic behavior of linear elastic solids under antiplane shear deformation is studied by the Lattice Boltzmann method (LBM). The governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. We use the approach developed by Guangwu as starting point to solve this problem numerically. The numerical performance of the lattice Boltzmann scheme is tested for a stationary crack which can be compared to an analytical solution. Furthermore the performance of the lattice Boltzmann simulations are compared to classical Finite Element Method (FEM) computations with regard to calculation time and accuracy. Finally the stability with respect to the relaxation parameter is studied.

Characterization of bi-stable pure and hybrid composite laminates – An experimental investigation of the static and dynamic responses

In this study, the static and dynamic responses of bi-stable hybrid composite laminates [0/AL/90]T and [02/AL/902]T were scrutinized, and their behavior was compared to bi-stable pure composite laminates including [0/90]T and [02/902]T. The work consisted of an analytical study that was validated experimentally. An analytical method based on Hamilton’s principle was developed to investigate the static and vibration characteristics of the laminates. Experimentally, curvatures and out-of plane-displacement, and snap-through load were measured using a quasi-static loading on a universal testing machine. Further experimental analysis was performed to characterize the damping viscous ratio, natural frequency, and critical base excitation that cause the snapping between the two different stable shapes. The results show that the hybridization of bi-stable pure composite laminates has the potential to increase the stable curvatures and enhance the static load-carrying capability up to five times when compared to a pure bi-stable composite laminate of the same thickness. It was also observed that the hybridization of bi-stable pure composite laminates may result in a dramatic change in the dynamic response. The natural frequencies of bi-stable hybrid composite laminates are increased in comparison with bi-stable pure composite laminates. The critical base excitation required for snapping has increased significantly for the hybrid composite laminate. The qualitative and quantitative comparisons between the analytical and experimental results were very promising and they agreed well.

The elasticity of the ½ a0 and a0 dislocation loop in α-Fe thin foil

Dislocation loops in irradiated ferritic steels have a Burgers vector of the type ½ a0 <111> or a0 <100>. When they are located in a thin foil such as the one used in transmission electron microscopy, the presence of the two free surfaces modify the elastic field by the action of the so-called ‘image forces’, which can in turn influence the loops. In this work, a general analytical method was deployed to calculate the image forces in an anisotropic bcc α-Fe thin foil containing a nanometric dislocation loop. We observe that image forces induce an out of plane displacement that doubles the bulging of the thin foil surfaces induced by the loop. The elastic field and energy induced by the image forces become remarkable when the depth of the dislocation loop is comparable to its size. Moreover, there is large difference in the response to image forces between the ½ a0 <111> and the a0 <100> loop, with a stronger one for the ½ a0 <111> loop, which relates to the anisotropy of the α-Fe.

Lattice Boltzmann simulation of antiplane shear loading of a stationary crack

In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61–69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu’s work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.

Influence of gaseous hydrogen on plastic strain in vicinity of fatigue crack tip in Armco pure iron

A multi-scale characterisation of the crack tip plasticity has been investigated in a fatigue crack propagation under gaseous hydrogen at gas pressure of 35 MPa in a commercially pure iron, Armco iron. The dislocation structure beneath a fracture surface was observed by a Transmission Electron Microscopy(TEM), and the cyclic and monotonic plastic zones were evaluated by an Out-of-Plane Displacement (OPD) measurement. By the TEM observation in a non-accelerated regime (ΔK = 11 MPa×m1/2), a dislocation cell structure was observed even in the brittle intergranular fracture in hydrogen. This result indicates a certain amount of plastic strain is introduced into the grains in front of an intergranular crack in hydrogen, and this may explain the mechanism of hydrogen-induced intergranular fatigue crack propagation. On the other hand, in an accelerated regime (ΔK = 18 and 20 MPa×m1/2), a distribution of scattered dislocation tangles without any cell or vein structure was observed in hydrogen. Besides, the inhibition of the cyclic plasticity near the crack path in hydrogen was confirmed by the OPD measurement. These results are clear evidences of hydrogen-induced localization of cyclic plasticity in the vicinity of a crack tip, which suggests a mechanism model of hydrogen-enhanced fatigue crack growth based on the plasticity localization.

Experimental verification of a quasi-trapped degenerate mode magnetic acoustic resonator

This paper presents an elastic resonator exhibiting modal degeneracy and quasi-energy trapping of the displacement field. Electromagnetic acoustic based coupling is employed to excite a pair of degenerate SH dominated modes in an aluminium plate. A circular mesa is machined symmetrically on the plate for the purpose of localising the displacement field. Numerical modelling of the modal properties are compared with experimental measurements. Mapping of the modeshapes using 3D laser vibrometry shows that displacement field to be highly localised to the region defining the mesa in agreement with the numerical model. The numerical model shows that significant out of plane displacement outside the mesa region is expected due to the propagating SV+P waves of the plate. It is expected that design modification will reduce the out of plane contributions thus improving the energy trapping. The high Q-factor of the degenerate trapped resonator has potential applications as a gyroscopic sensor or mass sensor.

Experimental and computational investigation of the blast response of Carbon-Epoxy weathered composite materials

Abstract An experimental study with corresponding numerical simulations was conducted to investigate the blast response of weathered Carbon-Epoxy composite plates. The dynamic behavior of the composite plates with and without prior exposure to an aggressive marine environment was explored using a shock tube apparatus coupled with a high speed photography system. In order to simulate prolonged exposure in an aggressive marine environment, specimens were submerged in an elevated temperature, 3.5% salt solution for 0, 30 and 60 days. The saline solution temperature was maintained at 65 °C to accelerate the aging process. Finite Element Modeling (FEM) for the blast loading experiments was performed using the Ls-Dyna code. Models have been developed for both the simply supported and fixed boundary condition cases. Tensile and four point bend tests were performed to characterize the quasi-static mechanical behavior of the composite material before and after prolonged exposure to aggressive marine environments. After 30 and 60 days of submergence, the tensile modulus decreased by 11% and 13%, the ultimate tensile strength decreased by 12% and 13%, and the ultimate flexural strength decreased by 22% and 22%, respectively. Dynamic blast loading experiments were performed on simply supported and fully clamped specimens, to determine the effects of the boundary conditions on the Carbon-Epoxy specimen response. The Weathered (30 and 60 days) and Non-Weathered (0 day) specimens displayed dramatically different behavior after being subjected to a blast load. For the simply supported case, Non-Weathered specimens displayed an average maximum out of plane displacement of 20 mm and recovered elastically. Weathered specimens, both 30 and 60 days exhibited similar initial transient behavior but failed catastrophically due to through thickness cracking at the point of maximum deflection. For the fixed boundary condition, the Non-Weathered specimens displayed an average maximum out of plane displacement of 5.57 mm, whereas the 30 day and 60 day weathered specimens displayed a maximum out of plane displacement of 6.89 mm and 6.96 mm, respectively. The corresponding numerical simulations matched well with the experimental data. However, for the fixed boundary case, the beam vibration of the simulation was off phase with the experimental results due to imperfect boundary conditions in the experiments.

Fast analysis of non-symmetric panels using semi-analytical techniques

Abstract A semi-analytical approach is presented for the analysis and optimization of laminated panels with non-symmetric lay-ups, and with the possibility of introducing requirements on the buckling load, the postbuckling response and the eigenfrequencies. The design strategy relies on the combined use of semi-analytical techniques for the structural analysis and genetic algorithms for the optimization. The structural analysis is performed with a highly efficient code based on thin plate theory, where the problem is formulated in terms of Airy stress function and out of plane displacement, expanded using trigonometric series. Eigenvalue analyses are performed to determine eigenfrequencies and buckling load, while an arc-length method is adopted for the postbuckling computation. The genetic algorithm is implemented with proper alphabet cardinalities to handle different steps for the angles of orientation, while specific mutation operators are used to guarantee good reliability of the optimization. To show the potentialities of the proposed optimization toolbox, two examples are presented regarding the design of balanced non-symmetric laminates subjected to linear and nonlinear constraints. The accuracy of the semi-analytical predictions is demonstrated by comparison with finite element results and benchmark cases taken from the literature.

P‐63: Effect of Glass Substrate Characteristics on Pattern Tolerance in Inverted Staggered Type TFT Array Fabrication

Deformation during a TFT fabrication process affects pattern tolerance because out of plane displacement may cause distortion of projected image of the pattern such as TFT, wiring, black matrix etc. The effect of glass properties on warpage caused during gate metal deposition and gate insulator deposition was investigated through numerical simulation. We found that thermal expansion coefficient of the glass substrate as well as Young's modulus should be taken into account to reduce the warpage.

Vibration response of laminated composite plate having weakly bonded layers

Free and forced vibration response of laminated composite and sandwich plate having weakly bonded layer is studied by using an efficient C0 continuous two dimensional finite element (FE) model. This FE model is based on higher order zigzag theory (HOZT) in which, in-plane displacements are obtained by superposing a global displacement field having cubical variation across thickness, on a zigzag displacement field having linear variation with a different slope in each layer. The out of plane displacement is assumed constant across the thickness of the plate. In the proposed model, transverse shear stresses are continuous at the layer interfaces and vanish at the top and bottom surfaces of the plate. At the same time, it is computationally as elegant as any single layer plate model since it requires the usual unknowns at the reference plane only. The inter-laminar imperfections are represented by in-plane displacement jumps at the layer interfaces and characterized by a linear spring layer model. In order to circumvent the problem of C1 continuity associated with the above plate theory at the time of FE implementation, first derivatives of the transverse displacement have been treated as independent variables. It is interesting to note that the plate model having all these refined features requires unknowns at the reference plane only. The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on HOZT for forced vibration problems. Numerical problems on free and forced vibration having different geometric and material properties of laminated composite and sandwich plates are solved. Some new problems have also been solved and new results have been presented which would be useful for future research.

Nature of the empty states and signature of the charge density wave instability and upper Peierls transition of TTF-TCNQ by temperature-dependent NEXAFS spectroscopy

The electronic structure of TTF-TCNQ was studied by near-edge X-ray absorption fine structure (NEXAFS) spectroscopy in order to detect a spectroscopic signature of the phase transitions, especially that occurring at 54 K, which is related to a Peierls gap opening on the TCNQ stacks. All unoccupied TCNQ orbitals predicted by first-principles calculations and, in particular the pair σ ∗ (π(ag ,b 3u)), located in the cyano groups, are clearly resolved in our experimental data. The latter orbital was observed for the first time in our NEXAFS spectra. The temperature dependence of NEXAFS peak intensities gives evidence of a subtle modification of the electronic structure when the charge density wave (CDW) fluctuations develop as the Peierls transition of the TCNQ stacks is approached from higher temperatures. These changes are explained on the basis of the charge transfer, the shape of the lower empty TCNQ molecular orbitals and the deformation of TCNQ during the pre-transitional CDW fluctuations. Finally the data suggest that the internal stack deformation consisting in a substantial out of plane displacement of the central ring with respect to the cyano-groups allows to gain Cα-Cα bonding energy which helps the stabilization of the Peierls transition on the TCNQ stack.

Phonons and electron‐phonon coupling in graphene‐h‐BN heterostructures

First principle calculations of the phonons of graphene‐h‐BN heterostructures are presented and compared to those of the constituents. It is shown that AA and AB′ stacking are not only energetically less favoured than AB but also dynamically unstable. Low energy flat phonon branches of h‐BN character with out of plane displacement have been identified and their coupling to electrons in graphene has been evaluated.

Effects of the transfer function evaluation on the impact force reconstruction with application to composite panels

The determination of a reliable transfer function for force reconstruction of impacts on composite panels is addressed in the paper. The reconstruction of the impact force history requires the knowledge of the transfer function which relates the response to the contact force. In this paper, a new method to determine the transfer function of a composite plate, instrumented with surface bonded piezoelectric sensors, is proposed. Impact tests are carried out and the data are used to evaluate the transfer function. The force reconstruction results, obtained by using the new transfer function, are compared with the results obtained with the classic approach. Significant improvements are observed in predicting the force history, particularly when large deflections are present; these are quantifiable as an out of plane displacement of the same order of magnitude as the thickness of the plate. The influence of increasing the impact velocity, with the related increase in the contact force, is also studied. The proposed method provides good results over a range of impact velocities. Multiple impacts were also investigated and the method could correctly reconstruct force histories of consecutive impacts.

C0 FE model based on HOZT for the analysis of laminated soft core skew sandwich plates: Bending and vibration

Bending and free vibration behaviour of laminated soft core skew sandwich plate with stiff laminate face sheets is investigated using a recently developed C0 finite element (FE) model based on higher order zigzag theory (HOZT) in this paper. The in-plane displacement fields are assumed as a combination of a linear zigzag function with different slopes at each layer and a cubically varying function over the entire thickness. The out of plane displacement is considered to be quadratic within the core and constant in the face sheets. The plate theory ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for accurate modelling of laminated skew sandwich plates. As very few element model based on this plate theory (HOZT) exist and they possess certain disadvantages, an attempt has been made to check the applicability of the refined element model. The nodal field variables are chosen in such a manner that there is no need to impose any penalty stiffness in the formulation. Refined C0 finite element model has been utilized to study some interesting problems on static and free vibration analysis of laminated skew sandwich plates.

Ultrasonic Guided Wave Tomography for Damage Detection in Harsh Environment

Guided wave tomography is an attractive tool for the detection and monitoring of the critical area in a structure. Using signal difference coefficient (SDC) as the tomographic feature, RAPID (Reconstruction Algorithm for the Probabilistic Inspection of Damage) is an effective and flexible tomography algorithm. In this algorithm, signal changes are exclusively attributed to the structural variation. However, external environment factors like water loading or oil loading also change signals significantly. The presence of anti-symmetric mode with a predominant out of plane displacement makes it very sensitive to these interferences and leads to false alarms. In this paper, Lamb wave is excited in the low-frequency domain, where only the fundamental modes A0 and S0 exist. The significant difference in group velocity between the two modes makes it possible to separate them in time domain. A new method is proposed to extract pure S0 mode signal as valid measurement data to improve the algorithm in addressing false alarm caused by water loading. The results of the experiment demonstrate that the improved algorithm has the capability of providing accurate identification of damage in the presence of water loading.

Design, Simulation and Optimization of Electrothermal Micro Actuator

This work presents the design and optimization of out of plane electrothermal MEMS actuators. The proposed concept is capable of generating large out of plane displacement at low driving power and a low actuation temperature. The performance of this actuator is evaluated and simulated in ANSYS. The out of plane displacement of 291µm at a temperature increase of 135°C from ambient has been achieved with the applied power of 2.7mW(0.7V). Moreover, a thermal time constant of 5.6ms and a frequency of 85Hz is accomplished for this actuator.

General dislocation image stress of anisotropic cubic thin film

A calculation method for accurately computing the displacement, image stress, and image energy induced by defects, such as cavities, precipitates, finite dislocation segments, and dislocation loops, in a free-standing anisotropic thin crystal film is presented. The anisotropic image stress is derived in the Fourier space from the standing Christoffel stress equilibrium equation for anisotropic materials, relying on the elastic parameters, the crystallographic orientation of the film and the considered defect. The image stress corresponds to the traction stress field, describing the stress field at the free surface. The latter is the stress induced by the same defects in an infinite medium evaluated at the location of the free surface. This method is applied to pure bcc Fe semi infinite single crystals and thin crystal films. The calculation results show that a stronger image stress induced in-plane and out-of plane displacement difference is produced with the anisotropic elasticity for bcc Fe, relative to the isotropic case, calculated by either Voigt or Reuss methods. It confirms that anisotropy has a strong influence on the image stress induced 3D displacement fields.

Measurement of piezoelectric transformer vibrations by digital holography

A method for the measurements of the out-of-plane displacement on the surface of vibrating object is presented herein. This method is based on frequency-shifted time-averaged digital holographic interferometry, employing the principle of phase shifting. This approach allows for significant noise reduction, which results in high sensitivity of measurements. This method makes it possible to measure vibrations with amplitudes in the nanometer range over the whole measured surface. This method was applied to the visualization of the out-of-plane vibration modes of piezoelectric transformers. The amplitude and modal shapes were measured with a very high resolution. Furthermore, aspects influencing the measurement errors are discussed and the measurement results by holographic method were compared with the well-established single-point laser interferometry measurement method.