Showing papers on "Displacement field published in 2021"

Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene

Abstract: Engineering moire superlattices by twisting layers in van der Waals (vdW) heterostructures has uncovered a wide array of quantum phenomena We constructed a vdW heterostructure that consists of three graphene layers stacked with alternating twist angles ±θ At the average twist angle θ ~ 156°, a theoretically predicted “magic angle” for the formation of flat electron bands, we observed displacement field–tunable superconductivity with a maximum critical temperature of 21 kelvin By tuning the doping level and displacement field, we found that superconducting regimes occur in conjunction with flavor polarization of moire bands and are bounded by a van Hove singularity (vHS) at high displacement fields Our findings display inconsistencies with a weak coupling description, suggesting that the observed moire superconductivity has an unconventional nature

Experimental study of displacement field of layered soils surrounding laterally loaded pile based on transparent soil

Abstract: In the pile-soil interaction system, the disturbed soil directly affects the safety of the laterally loaded pile. The soil displacement field helps to evaluate the range and degree of soil disturbance. This study presents a method of visualiziing the displacement field of the soil around the laterally loaded pile by using transparent soil technology, which overcomes the measurement obstacles caused by the non-transparency of the real soil. Glass sand and transparent pore solution were mixed to make a saturated transparent soil with two particle sizes (0.1 ~ 0.5 mm and 0.5 ~ 1 mm). Instead of real soil, transparent soil was used to observe the degree of disturbance in the process of interaction with laterally loaded piles. In addition, particle image velocimetry (PIV) was used to capture the displacement of transparent soil particles. The displacement of each particle was integrated into the displacement field by a MATLAB program. When a horizontal force was applied on the top of the pile, the particles in front of the pile were compressed, producing observable movement within a certain area. From the displacement vector diagram, it could be seen that the displacement area of the soil surface in front of the pile increases as the layer thickness of large particle soil increases. The vertical displacement of soil in front of the pile was compacted to form a wedge-shaped area under the horizontal load. The angle between the direction of soil motion and the horizontal plane was positively correlated with the thickness of the soil layer. Transparent soil and particle image velocimetry can help reveal the displacement trends of the soil around a laterally loaded pile. Based on this, an early warning can be provided when the displacement value and displacement angle of the soil around the laterally loaded pile exceeds the normal range.

On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates

Abstract: This paper presents a novel C0 higher-order layerwise finite element model for static and free vibration analysis of functionally graded materials (FGM) sandwich plates. The proposed layerwise model, which is developed for multilayer composite plates, supposes higher-order displacement field for the core and first-order displacement field for the face sheets maintaining a continuity of displacement at layer. Unlike the conventional layerwise models, the present one has an important feature that the number of variables is fixed and does not increase when increasing the number of layers. Thus, based on the suggested model, a computationally efficient C0 eight-node quadrilateral element is developed. Indeed, the new element is free of shear locking phenomenon without requiring any shear correction factors. Three common types of FGM plates, namely, (i) isotropic FGM plates; (ii) sandwich plates with FGM face sheets and homogeneous core and (iii) sandwich plates with homogeneous face sheets and FGM core, are considered in the present work. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equations of motion of the FGM sandwich plate are obtained via the classical Hamilton’s principle. Numerical results of present model are compared with 2D, quasi-3D, and 3D analytical solutions and other predicted by advanced finite element models reported in the literature. The results indicate that the developed finite element model is promising in terms of accuracy and fast rate of convergence for both thin and thick FGM sandwich plates. Finally, it can be concluded that the proposed model is accurate and efficient in predicting the bending and free vibration responses of FGM sandwich plates.

Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model

Abstract: In the present paper, a refined trigonometric higher-order shear deformation theory has been presented with the conjunction of nonlocal theory for the vibrational response of functionally graded (FG) porous nanoplate. The displacement field is chosen based on assumptions that the out of the plane displacement consists of bending and shear components whereas the transverse shear-strain has nonlinear variation along the thickness direction. The number of unknown variables is four, as against five in other renowned shear deformation theories. The governing equations have been derived using Hamilton's principle. A generalized porosity model has also been developed to accommodate both even and uneven type of distribution of porosity in the FG nanoplates. The closed-form solution of simply-supported FG porous nanoplates is obtained and the results are compared with the available reported results. In finite element solution, a C0 continuous isoparametric quadrilateral element has been used with various conventional and unconventional boundary conditions. The effects of various parameters like small-scale effect, aspect ratio, volume fraction index, porosity volume fraction, and thickness ratio have been investigated. The significant influence of small-scale effects and porosity inclusions have been observed in the reported results. It has been reported that both closed-form and finite element solutions with the present theory can make accurate predictions of the free vibration response.

Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets

Abstract: In this paper, the forced resonance vibration analysis of curved micro-size beams made of graphene nanoplatelets (GNPs) reinforced polymer composites is presented. The approximating of the effective material properties is on the basis of Halpin–Tsai model and a modified rule of mixture. The Timoshenko beam theory is applied to describe the displacement field for the microbeam. To incorporate small-size effects, the modified strain gradient theory, possessing three independent length scale coefficients, is employed. Hamilton principle is applied to formulate the size-dependent governing motion equations, which then is solved by Navier solution method. Ultimately, the influences of length scale coefficients, opening angle, weight fraction and the total number of layers in GNPs on composite curved microbeams corresponding to different GNPs distribution are discussed in detail through parametric studies. It is shown that, the resonance position is significantly affected by changing these parameters.

Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position

Abstract: This paper presents a high-order shear and normal deformation theory for the bending of FGM plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. Based on the novel shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. The accuracy of the present theory is verified by comparing the obtained results with other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending responses of the FGM plates are studied.

An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects

Abstract: This paper introduces the free vibrational response solution of a functionally graded (FG) “sandwich plate” resting on a viscoelastic foundation and subjected to a hygrothermal environment load using an accurate high-order shear deformation theory. In this study, three different types of FG “sandwich plate” geometries were investigated. Only four unknowns were considered in the displacement field, including an indeterminate integral, along with a sinusoidal shape function to represent transverse shear stresses. Hamilton’s principle was utilized to obtain the equation of motion by considering infinitesimal deformation theory combined with a generalized Hook’s law. The variables studied are the damping coefficient, aspect ratio, volume fraction density, moisture and temperature variation, and thickness. The results showed that the increase in damping coefficient $$({c}_{t})$$ as a property of the viscoelastic foundation would enhance the free-vibrational response of the plate. However, the degree of enhancement would be influenced by the hygrothermal environment.

Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation

Abstract: The present study is dealt with the applicability of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique on free vibration of functionally graded (FG) beam with uniformly distributed porosity along the thickness of the beam. The material properties such as Young’s modulus, mass density, and Poisson’s ratio are also considered to vary along the thickness of the FG beam as per the power-law exponent model. The porous FG beam is embedded in an elastic substrate; namely, the Kerr elastic foundation and the displacement field of the beam are governed by a refined higher-order shear deformation theory. The effectiveness of the Rayleigh–Ritz method is due to the use of the shifted Chebyshev polynomials as a shape function. The orthogonality of shifted Chebyshev polynomial makes the technique more computationally efficient and avoid ill-conditioning for the higher number of terms of the polynomial. Hinged–hinged, clamped–hinged, clamped–clamped, and clamped-free boundary conditions have been taken into account for the parametric study. Validation of the present model is examined by comparing it with the existing literature in special cases showing remarkable agreement. A pointwise convergence study is also carried out for shifted Chebyshev polynomial-based Rayleigh–Ritz method, and the effect of power-law exponent, porosity volume fraction index, and elastic foundation on natural frequencies is studied comprehensively.

Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory

Abstract: This paper presents a new nonlocal Hyperbolic Shear Deformation Beam Theory (HSDBT) for the free vibration of porous Functionally Graded (FG) nanobeams. A new displacement field containing integrals is proposed which involves only three variables. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect and its account for shear deformation by a hyperbolic variation of all displacements through the thickness without using the shear correction factor. It has been observed that during the manufacture of Functionally Graded Materials (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the free vibration analysis of FG beams taking into account the influence of these imperfections is established. Four different porosity types are considered for FG nanobeam. Material characteristics of the FG beam are supposed to vary continuously within thickness direction according to a power-law scheme which is modified to approximate material characteristics for considering the influence of porosities. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio, and the porosity types on the dynamic responses of the nanobeam are discussed.

Analytical algorithm for longitudinal deformation profile of a deep tunnel

Abstract: To investigate the longitudinal deformation profile (LDP) of a deep tunnel in non-hydrostatic condition, an analytical model is proposed in our study. In this model, the problem is considered as a superposition of two partial models, and the displacement field of the second partial model is the same as that of the concerned problem. Therefore, the problem can be solved by a model with simple boundary conditions. We obtain the solutions for the stress and displacement fields of an infinite body caused by arbitrary surface tractions on the boundary of the coming tunnel (zone inside the tunnel before excavation) by integrating the extended Kelvin solution over the boundary. The obtained stress solution is used to solve the specific surface tractions, which can satisfy the boundary conditions of the second partial model, on the boundary of the coming tunnel in an infinite body. Then, the specific surface tractions are substituted into the obtained displacement solution to solve the displacement on the wall and face of the tunnel. Therefore, the LDP can also be calculated. The proposed solution is verified by both numerical simulation and the LDP functions recommended by other researchers. The major advantage of our analytical model is that it can consider the effects of the axial and horizontal lateral pressure coefficients. It is revealed that the horizontal lateral pressure coefficient majorly affects the LDP behind the tunnel face, while the axial lateral pressure coefficient dominates the LDP ahead of the tunnel face. Furthermore, the deformation characteristics of the LDPs ahead of the face and the unexcavated core are investigated. The axial displacements of the excavation face can be used to predict the crown displacements ahead of the face.

Analytical solution of cross- and angle-ply nano plates with strain gradient theory for linear vibrations and buckling

Abstract: Vibrations and buckling of Kirchhoff nano plates are investigated using second-order strain gradient theory. The Navier displacement field has been considered for two different sets of boundary con...

High-Resolution 3-Dimensional Contact Deformation Tracking for FingerVision Sensor With Dense Random Color Pattern

Abstract: Recent studies on vision-based tactile sensing have shown promising results on the perception of contact information, which could improve the performance of dexterous manipulations. However, 3-dimensional contact deformation tracking at a higher resolution is desired and remains a challenge for vision-based tactile sensors with monocular configurations. In this work, a similar hardware structure to our previous FingerVision sensor is adopted. The dot markers are replaced with a novel random color pattern as the sensor's tracking target and a dense optical flow algorithm is used to track the deformation of its elastic contact interface. This results in a more accurate 2-dimensional deformation field estimation at a higher resolution in comparison with that obtained using sparse dot markers. Additionally, the denser and more accurate deformation field enables depth estimation with better fidelity. To achieve depth estimation purely from the optical flow field, Gaussian density feature extraction and processing framework are proposed. The resulting depth map can be used independently as a tactile sensing modality, or jointly with the accurate in-plane displacement field as a more complete deformation tracking of contact interfaces for vision-based tactile sensors.

Plasticity in Amorphous Solids Is Mediated by Topological Defects in the Displacement Field

Abstract: The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural ``defects'' or spatiotemporal correlations in the undeformed glass that may trigger plastic instability. In contrast, in this Letter we show that the topological defects that correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dislocation-like topological defects (DTDs) can be quantitatively characterized in terms of Burgers circuits (and the resulting Burgers vectors) that are constructed on the microscopic nonaffine displacement field. We demonstrate that (i) DTDs are the manifestation of incompatibility of deformation in glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the resulting average Burgers vector displays peaks in correspondence of major plastic events, including a spectacular nonlocal peak at the yielding transition, which results from self-organization into shear bands due to the attractive interaction between antiparallel DTDs; and (iii) application of Schmid's law to the DTDs leads to prediction of shear bands at 45\ifmmode^\circ\else\textdegree\fi{} for uniaxial deformations, as widely observed in experiments and simulations.

Random vibrations of stress-driven nonlocal beams with external damping

Abstract: Stochastic flexural vibrations of small-scale Bernoulli–Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding environment. Loadings are modeled by accounting for their random nature. Such a dynamic problem is characterized by a stochastic partial differential equation in space and time governing time-evolution of the relevant displacement field. Differential eigenanalyses are performed to evaluate modal time coordinates and mode shapes, providing a complete stochastic description of response solutions. Closed-form expressions of power spectral density, correlation function, stationary and non-stationary variances of displacement fields are analytically detected. Size-dependent dynamic behaviour is assessed in terms of stiffness, variance and power spectral density of displacements. The outcomes can be useful for design and optimization of structural components of modern small-scale devices, such as micro- and nano-electro-mechanical-systems.

A New DIC-Based Method to Identify the Crack Mechanism and Applications in Fracture Analysis of Red Sandstone Containing a Single Flaw

Abstract: As a representative non-interferometric optical technique, the digital image correlation (DIC) can provide full-field displacement and strain measurement for the deformed rocks. However, the standard DIC technique has a limitation in measuring the displacements at the discontinuity and cannot be directly used for identifying the crack mechanism. Thus, a new DIC-based method is proposed for automatically tracing the discontinuities and quantitatively identifying the crack mechanism, i.e. mode I, mode II, and mixed-mode I/II. The new method involves three steps, including displacement measurement from the standard DIC technique, displacement field reconstruction at the discontinuity with the modified subset splitting technique, and post-processing for crack identification and displacement jump measurement. The effectiveness and robustness of the modified subset splitting technique and post-processing method have been verified with the synthetic images and theoretical displacement fields of mode I crack and dislocation. Then, the proposed method is utilized to locate cracks and quantitatively identify the crack mechanism of the initiated cracks in red sandstone containing a single flaw under uniaxial compression. The crack development in the flawed red sandstone specimens is analyzed and the crack types are summarized, in which wing cracks are in mode I, while horsetail cracks and anti-wing cracks are identified as mixed-mode I/II crack. It is shown that the new method avoids some ambiguous identification of crack mechanism and present more objective results.