Showing papers on "Displacement field published in 2020"
TL;DR: Based on the similarity ratio theory, a physical model was built to investigate the failure mechanism of the anti-dip layered slope under excavation in this article, where the deformation characteristics of the slope at each stage were analyzed and compared with those of the surface slopes in the field.
Abstract: The failure mechanism of anti-dip layered slopes is essentially different from that of dip layered slopes. Therefore, it is important to investigate the failure mechanism of anti-dip slopes due to excavations. In this study, slope instability induced by mining excavation at the Changshanhao open-pit mine in Neimenggu province, China, was used as a case study. Based on the similarity ratio theory, a physical model was built to investigate the failure mechanism of the anti-dip layered slope under excavation. The physical model was monitored by various monitoring equipment including static strain data acquisition equipment, infrared thermal camera, and digital speckle displacement field measurement equipment. The evolution characteristics of the multi-physics fields including displacement field, strain field and temperature field of the physical model during the excavation were comprehensively obtained. According to the deformation characteristics of the anti-dip layered slope during excavation test, the failure mechanism can be divided into four stages: initial compression stage, crack generation stage, crack propagation stage and formation of sliding surface stage. The deformation characteristics of the slope at each stage were analyzed and compared with those of the anti-dip slope in the field. The comparison verified the rationality and accuracy of the physical model experiment, and provided a deeper understanding of the failure mechanism of anti-dip layered slope under excavation through the comprehensive monitoring data. The results of this work can be used as a reference for the follow-up reinforcement and treatment of similar anti-dip layered slopes.
145 citations
TL;DR: In this article, a quasi-3D hyperbolic shear deformation theory is proposed to analyze the statics and free vibration of functionally graded porous plates resting on elastic foundations, and the equations of motion are derived from the Hamilton principle.
Abstract: This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to
discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal
deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and
efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.
134 citations
TL;DR: The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor.
Abstract: This work presents an efficient and original high-order shear and normal deformation theory for the static and free vibration analysis of functionally graded plates. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. 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. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
100 citations
TL;DR: In this paper, a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions.
Abstract: In this study a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions. The key feature of this theoretical formulation is that, in addition to considering shear deformation effect, it has only three unknowns in the displacement field as in the case of the classical plate theory (CPT), contrary to five as in the first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Material characteristics of the sandwich plate faces are considered to vary within the thickness direction via an exponential law distribution as a function of the volume fractions of the constituents. Equations of motion are obtained by employing Hamilton\'s principle. Numerical results for buckling and free vibration analysis of exponentially graded sandwich plates under various boundary conditions are obtained and discussed. Verification studies confirmed that the present three -unknown shear deformation theory is comparable with higher-order shear deformation theories which contain a greater number of unknowns.
88 citations
TL;DR: In this article, the influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original high order shear theory.
Abstract: The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich
plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton\'s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT).
Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin\'s approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
87 citations
TL;DR: In this article, the buckling behavior of a single-layered graphene sheet (SLGS) embedded in visco-Pasternak s medium is studied using nonlocal four-unknown integral model.
Abstract: In the present work, the buckling behavior of a single-layered graphene sheet (SLGS) embedded in visco-Pasternak\' s medium is studied using nonlocal four-unknown integral model. This model has a displacement field with integral terms which includes the effect of transverse shear deformation without using shear correction factors. The visco-Pasternak\'s medium is introduced by considering the damping effect to the classical foundation model which modeled by the linear Winkler\'s coefficient and Pasternak\' s coefficients, damping parameter, and mode numbers on the buckling response of the SLGSs are studied and discussed.
78 citations
TL;DR: U-Mesh is presented: A data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm and shows that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly non- linear models in a compact form.
68 citations
TL;DR: In this paper, a van der Waals heterostructure consisting of three graphene layers stacked with alternating twisting angles was constructed, and it was shown that the superconducting regimes occur in conjunction with flavour polarization of moir´e bands bounded by a van Hove singularity (vHS) at high displacement fields.
Abstract: We construct a van der Waals heterostructure consisting of three graphene layers stacked with alternating twisting angles $\pm\theta$. At the average twist angle $\theta\sim 1.56^{\circ}$, a theoretically predicted magic angle for the formation of flat electron bands, narrow conduction and valence moir\'e bands appear together with a linearly dispersing Dirac band. Upon doping the half-filled moir\'e valence band with holes, or the half-filled moir\'e conduction band with electrons, displacement field tunable superconductivity emerges, reaching a maximum critical temperature of 2.1 K at optimal doping and displacement field. By tuning the doping level and displacement fields, we find that superconducting regimes occur in conjunction with flavour polarization of moir\'e bands bounded by a van Hove singularity (vHS) at high displacement fields. This experimental observation is found to be inconsistent with a weak coupling description, suggesting that the observed moir\'e superconductivity has an unconventional nature.
60 citations
TL;DR: In this paper, the effect of porosity distributions on the mechanics of nanostructures is investigated based on the higher-order nonlocal strain gradient theory, where the displacements gradients are assumed to be small so that the components of the Green-Lagrange strain tensor are linear and infinitesimal.
57 citations
TL;DR: In this article, the authors investigated the stress evolution, displacement field, local deformation and its overall distribution, and failure characteristics of the anchorage structure of surrounding rock with different rockbolt spacing through the model experiments.
Abstract: This paper investigated the stress evolution, displacement field, local deformation and its overall distribution, and failure characteristics of the anchorage structure of surrounding rock with different rockbolt spacing through the model experiments The influences of the pre-tightening force and spacing of rockbolt on the support strength of the anchorage structure of surrounding rock were analyzed by the simulation using FLAC3D numerical software The support scheme of the excavated roadway was then designed, and the effectiveness of this support scheme was further verified by the displacement measurement of the roadway The results showed that the maximum displacement between the roof and floor of the west wing track roadway in Kouzidong coal mine, China is about 42 mm, and the maximum displacement between its both sides is about 72 mm, indicating that the support scheme proposed in this study can ensure the stability and safety of the excavated roadway
56 citations
TL;DR: This article tends to investigate and optimize critical buckling loads of thin/thick sandwich functionally graded (FG) beam with porous core, for the first time, and examines influences of porosity function, porosity percentage, distribution gradation index, load types and boundary conditions on bucking loads.
Abstract: Static stability of beams subjected to nonuniform axial compressive and shear loads is essential in many industrial applications, such as aircraft, automotive, mechanical, civil and naval. Thus, this article tends to investigate and optimize critical buckling loads of thin/thick sandwich functionally graded (FG) beam with porous core, for the first time. The proposed model is developed to consider a sandwich beam with three layers, which has top and bottom FG layers reinforced by single-walled carbon nanotubes (SWCNTs) and core porous layer with various porosity distributions. The variable in-plane compressive load is described by different distributed functions. Parabolic higher-order shear deformation theory of Reddy is adopted to describe kinematic displacement field and consider both thin and thick structures. The equilibrium governing variable-coefficient differential equations are obtained in detail by generalized variational principle. Equilibrium equations are solved numerically by differential quadrature method to get critical buckling loads. Numerical results are illustrated to examine influences of porosity function, porosity percentage, distribution gradation index, load types and boundary conditions on buckling loads of sandwich FG SWCNTs beam with porous core. Particle swarm optimization algorithm is adopted to get optimal axial load function.
TL;DR: The three main shape sensing methods, the Modal Method, the Ko's displacements theory and the inverse Finite Element Method, are presented and show different characteristics that make them suitable for different applications, depending on the level of accuracy and the number of strain information required.
TL;DR: In this paper, a method to determine crack tip position and fracture process zone (FPZ) in concrete was proposed based on Bažant Crack Band Model (CBM) and digital image correlation (DIC) technique.
TL;DR: In this paper, a three-variable high-order shear deformation plate theory (THSDT) was proposed for free vibration, buckling and instability analysis of functionally graded porous (FGP) plates reinforced by graphene platelets (GPLs).
TL;DR: In this paper, the effects of material properties, nonlocal parameter, Lorentz and electric forces on maximum static deflections and natural frequencies of actuated hybrid carbon/boron-nitride nanotubes (CBNNT) subjected to thermal loads are studied for the first time.
TL;DR: In this paper, the authors proposed an effective computational approach to analyze and active control of geometrically nonlinear responses of functionally graded (FG) porous plates with graphene nanoplatelets (GPLs) reinforcement integrated with piezoelectric layers.
TL;DR: In this article, the authors developed a numerical framework for the simulation of damage in composite structures using explicit time integration, where Lagrange polynomials are used to represent the displacement field through the thickness of each ply, resulting in a layer-wise element model.
Abstract: The objective of the current work is the development of a numerical framework for the simulation of damage in composite structures using explicit time integration. The progressive damage is described using a Continuum Damage Mechanics (CDM) based material model, CODAM2, in which the damage initiation and progression are modelled using Hashin's failure criteria and crack-band theory, respectively. The structural modelling uses higher-order theories based on the Carrera Unified Formulation (CUF). The current work considers 2D-CUF models where Lagrange polynomials are used to represent the displacement field through the thickness of each ply, resulting in a layer-wise element model. Numerical assessments are performed on coupon-level specimens, and the results are shown to be in good agreement with reference numerical predictions and experimental data, thus verifying the current implementation for progressive tensile damage. The capability of the proposed framework in increasing the polynomial expansion order through the ply thickness, and its influence on the global behaviour of the structure in the damaged state, is demonstrated. The advantages of using higher-order structural models in achieving significant improvements in computational efficiency are highlighted.
TL;DR: A novel thermoelasticity model based on the Moore–Gibson–Thompson equation is considered in cases where some of these models fail to be positive, and is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source.
Abstract: Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore-Gibson-Thompson equation in cases where some of these models fail to be positive. This thermomechanical model has been constructed in combination with a hyperbolic partial differential equation for the variation of the displacement field and a parabolic differential equation for the temperature increment. The presented model is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source. To solve this problem, together with Laplace and Hankel transform methods, the potential function approach has been used. Laplace and Hankel inverse transformations are used to find solutions to different physical fields in the space-time domain. The problem is validated by calculating the numerical calculations of the physical fields for a given material. The numerical and theoretical results of other thermoelastic models have been compared with those described previously.
TL;DR: In this article, a non-polynomial based higher-order shear deformation theory with inverse tangent hyperbolic shape function is used to define the displacement field.
Abstract: In the present paper, for the first time, an attempt has been made to obtain the solution for bending and stress under the thermal environment using Galerkin Vlasov's method. A non-polynomial based higher-order shear deformation theory with inverse tangent hyperbolic shape function is used to define the displacement field. The formulation is performed for the author's recently developed sandwich plate using a new modified sigmoid function-based functionally graded material (S-FGM) plate of different symmetric and non-symmetric configurations. Using a one-dimensional steady-state heat conduction equation, a new temperature distribution through the thickness based on modified sigmoid law is proposed. Three different types of porosity are considered viz. even, uneven but symmetric and uneven but non-symmetric. A new uneven non-symmetric porosity model is used in which micro-voids are varied in accordance with material property variation in the thickness direction in order to capture the accurate distribution of voids on the plate. The principle of virtual work is employed to derive equilibrium equations. An exact solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions. From the present study on static analysis, it is deduced that more refined and accurate results for plate in thermal environment, it is necessary to include the thermal effect on the stiffness of the plate in addition to the initial deflection of the plate. The effect of boundary conditions on stress and deflection distribution along the surface of the porous plate is studied, and it is observed that the distribution is prominently affected by the type of symmetric or asymmetric boundary conditions. The considerable increase in deflection and stress can be seen for even porosity distribution (P-1) in comparison to uneven symmetric (P-2) or uneven non-symmetric (P-3) porosity distribution. In addition, the maximum transverse shear stresses are offset more from the center of the sandwich plate with an increase in temperature differences with a maximum offset at ΔT = 300 K and minimum offset at ΔT = 0 K. Different examples are considered to check the accuracy and validation of the present formulation. The calculated outcomes and interpretations can be useful as a validation study for the imminent investigation of sandwich S-FGM plates having porosities in the thermal environment.
TL;DR: In this paper, a new phase field method was proposed to describe quasi-static hydraulic fracture propagation in porous media subjected to stress boundary conditions, and the new method is more in line with engineering practice.
TL;DR: In this paper, the displacement field of variable cross-section beam was reconstructed using the inverse finite element method (IFEM) based on isogeometric analysis, and the least square method was used to establish the strain-displacement relation.
TL;DR: In this article, a variational phase-field approximation of a discontinuous function field is proposed to obtain the crack opening (displacement jump) and verify the approximation against a closed solution.
TL;DR: In this paper, the static stability and mode-shapes of composite laminated beams under varying axial in-plane loads were investigated, and the effect of axial load functions on the buckling mode-shape was presented for the first time.
Abstract: This article investigates the static stability and mode-shapes of composite laminated beams under varying axial in-plane loads. The kinematic displacement field is described by unified higher-order shear deformation theory. Six functions are assumed to describe the distribution of axial in-plane load, which are one-constant function, two-linear functions, and three-parabolic functions. The Hamilton's principle is proposed to get the equilibrium equations of unified composite laminated beams. An efficient numerical differential quadrature method (DQM) is proposed to solve the govern equations. The obtained equations are solved as an eigenvalue problem to find critical buckling loads and their corresponding mode-shapes. The validation studies are compared with published works. Numerical results illustrate effects of in-plane load type, beam thickness, orthotopy ratio, fiber orientations, and boundary conditions on the critical buckling loads. The effect of axial load functions on the buckling mode-shapes is presented for the first time. These effects play very important role on the static stability and mode-shapes of composite beam structures. The proposed model may be important in design of aircraft, civil and ship-building when non-uniform in-plane compressive load is important.
TL;DR: In this article, the applicability of the digital image correlation (DIC) method in deriving the notch stress intensity factors (NSIFs) is examined for sharp V-notched components under mixed mode I/II loading.
TL;DR: In this article, a stochastic partial differential equation in space and time governing time-evolution of the relevant displacement field is characterized by a dynamic problem, which is characterized with stochastically partial differential equations.
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 (MEMS and NEMS).
TL;DR: In this article, a phase-field description for simulation of fracture in nearly incompressible materials is developed, based on a mixed form of the displacement equation with two unknowns: a displacement field and a hydro-static pressure variable.
Abstract: Within this work, we develop a phase-field description for simulating fractures in nearly incompressible materials. It is well-known that low-order approximations generally lead to volume-locking behaviors. We propose an approach that builds on a mixed form of the displacement equation with two unknowns: a displacement field and a hydro-static pressure variable. Corresponding function spaces have to be chosen properly. On the discrete level, stable Taylor–Hood elements are employed for the displacement-pressure system. Two additional variables describe the phase-field solution and the crack irreversibility constraint. Therefore, the final system contains four variables: displacements, pressure, phase-field, and a Lagrange multiplier. The resulting discrete system is nonlinear and solved monolithically with a Newton-type method. Our proposed model is demonstrated by means of several numerical studies based on three numerical tests. First, different finite element choices are compared in order to investigate the influence of higher-order elements in the proposed settings. Further, numerical results including spatial mesh refinement studies and variations in Poisson’s ratio approximating the incompressible limit, are presented.
TL;DR: It is shown that the leading-order term of the perturbed elastic wave field is determined by the Neumann-Poincare operator associated to the Lam\'e system and the polariton resonance for the elastic system is studied.
Abstract: This paper is concerned with the analysis of surface polariton resonance for nanoparticles in linear elasticity. With the presence of nanoparticles, we first derive the perturbed displacement field...
TL;DR: In this paper, the analysis for the anticlastic bending under constant curvature of nonlinear solids and beams, presented by Lanzoni, Tarantino and Elast, is extended and further developed for the class of slender beams.
Abstract: In this paper the analysis for the anticlastic bending under constant curvature of nonlinear solids and beams, presented by Lanzoni, Tarantino (J. Elast. 131:137–170, 2018), is extended and further developed for the class of slender beams. Following a semi-inverse approach, the problem is studied by a three-dimensional kinematic model for the longitudinal inflexion, which is based on the hypothesis that cross sections deform preserving their planarity. A compressible Mooney-Rivlin law is assumed for the stored energy function and from the equilibrium equations, the free parameter of the kinematic model is computed. Thus, taking into account the three-dimensionality of the beam, explicit formulae for the displacement field, the stretches and stresses in every point of the body, following both Lagrangian and Eulerian description, are derived. Subsequently, slender beams under variable curvature were examined, focusing on the local determination of the curvature and bending moment along the deformed beam axis. The governing equations take the form of a coupled system of three equations in integral form, which is solved numerically. The proposed analysis allows to study a very wide class of equilibrium problems for nonlinear beams under different restraint conditions and subject to generic external load systems. By way of example, the Euler beam and a cantilever beam loaded by a dead or live (follower) concentrated force applied at the free end have been considered, showing the shape assumed by the beam as the load multiplier increases.
TL;DR: In this article, the vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak's foundation is presented, and the constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping.
Abstract: The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented. The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping. The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory (ECBT), Timoshenko’s first-order beam theory (TFBT), Reddy’s third-order shear deformation beam theory, and the simple sinusoidal shear deformation beam theory. Hamilton’s principle is utilized to give the equations of motion and then to describe the vibration of the current beam. Based on Navier’s approach, the solution of the dynamic system is obtained. The effects of the material properties, the modes, the thickness ratios, the lamination schemes, the magnitudes of the feedback coefficient, the position of magnetostrictive layers at the structure, and the foundation modules are extensively studied and discussed.
TL;DR: In this article, a semi-analytical method is developed for the analysis of composite stiffened panels, where stiffness variability is achieved through a combination of fiber steering and curvilinear stringers.