Showing papers on "Displacement field published in 2018"

Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles

Abstract: In this paper, three-dimensional (3D) elasticity theory in conjunction with nonlocal strain gradient theory (NSGT) is developed for mechanical analysis of anisotropic nanoparticles. The present model incorporates two scale coefficients to examine the mechanical characteristics much accurately. All the elastic constants are considered and assumed to be the functions of (r, θ, φ), so all kind of anisotropic structures can be modeled. Moreover, all types of functionally graded spherical structures can be investigated. To justify our model, our results for the radial vibration of spherical nanoparticles are compared with experimental results available in the literature and great agreement is achieved. Next, several examples of the radial vibration and wave propagation in spherical nanoparticles including nonlocal strain gradient parameters are presented for more than 10 different anisotropic nanoparticles. From the best knowledge of authors, it is the first time that 3D elasticity theory and NSGT are used together with no approximation to derive the governing equations in the spherical coordinate. Moreover, up to now, the NSGT has not been used for spherical anisotropic nanoparticles. It is also the first time that all the 36 elastic constants as functions of (r, θ, φ) are considered for anisotropic and functionally graded nanostructures including size effects. According to the lack of any common approximations in the displacement field or in elastic constant, present theory can be assumed as a benchmark for future works.

Helical network model for twisted bilayer graphene

Abstract: In the presence of a finite interlayer displacement field, bilayer graphene has an energy gap that is dependent on stacking and largest for the stable AB and BA stacking arrangements. When the relative orientations between layers are twisted through a small angle to form a moir\'e pattern, the local stacking arrangement changes slowly. We show that for nonzero displacement fields the low-energy physics of twisted bilayers is captured by a phenomenological helical network model that describes electrons localized on domain walls separating regions with approximate AB and BA stacking. The network band structure is gapless and has of a series of two-dimensional bands with Dirac band-touching points and a density of states that is periodic in energy with one zero and one divergence per period.

Influence of Porosity on the Flexural and Free Vibration Responses of Functionally Graded Plates in Thermal Environment

Abstract: This paper examines the influence of porosities on the flexural and free vibration response of functionally graded material (FGM) plates based on the authors’ recently developed non-polynomial higher-order shear and normal deformation theory. The theory accommodates the nonlinear variation in the in-plane and transverse displacements in the thickness coordinates. It also contains the hyperbolic shear strain shape function in the displacement field with only four unknowns. A new mathematical model has also been proposed to incorporate the effects of porosity in the FGM plate. Various numerical examples have been solved to ascertain the accuracy, efficiency, and applicability of the present formulation. The effects of porosity, volume fraction index, plate thickness, aspect ratio, boundary conditions and temperature have been discussed in details. The obtained results can be treated as a benchmark for future studies.

Three-dimensional exact solution for vibration analysis of thick functionally graded porous (FGP) rectangular plates with arbitrary boundary conditions

Abstract: In this paper, a novel three-dimensional exact solution is performed for vibration analysis of thick functionally graded porous rectangular plates subject to arbitrary boundary conditions The theoretical model is based on the three-dimensional elastic theory Three kinds of porosity distributions including even, uneven and the logarithmic-uneven are performed Non consideration boundary conditions, all displacements of the rectangular plate are unified expanded as a improve Fourier series, which consists of standard three-dimensional (3-D) Fourier cosine series supplemented with closed-form auxiliary functions introduced to eliminate all the relevant discontinuities with the displacements and its derivatives at the edges As the displacement field is sufficiently smooth in the entire solution domain, the exact solution of the energy function of the plate is obtained through the Rayleigh Ritz process The numerical examples are given to verify the accuracy and reliability of the present method, in which both the present results and those reported in the literature are provided Besides, several numerous new results for thick FGP plates with elastic boundary conditions are also presented

Quantitative Assessment of Digital Image Correlation Methods to Detect and Monitor Surface Displacements of Large Slope Instabilities

Abstract: We evaluate the capability of three different digital image correlation (DIC) algorithms to measure long-term surface displacement caused by a large slope instability in the Swiss Alps. DIC was applied to high-resolution optical imagery taken by airborne sensors, and the accuracy of the displacements assessed against global navigation satellite system measurements. A dynamic radiometric correction of the input images prior to DIC application was shown to enhance both the correlation success and accuracy. Moreover, a newly developed spatial filter considering the displacement direction and magnitude proved to be an effective tool to enhance DIC performance and accuracy. Our results show that all algorithms are capable of quantifying slope instability displacements, with average errors ranging from 8 to 12% of the observed maximum displacement, depending on the DIC processing parameters, and the pre- and postprocessing of the in- and output. Among the tested approaches, the results based on a fast Fourier transform correlation approach provide a considerably better spatial coverage of the displacement field of the slope instability. The findings of this study are relevant for slope instability detection and monitoring via DIC, especially in the context of an ever-increasing availability of high-resolution air- and spaceborne imagery.

Analysis of functionally graded sandwich plates using a higher-order layerwise theory

Abstract: A higher-order layerwise finite element formulation is presented for static and dynamic analyses of functionally graded material (FGM) sandwich plates. A higher-order displacement field is assumed for core and first-order displacement field is assumed for top and bottom facesheets maintaining a continuity of displacement at layer interface. An eight noded isoparametric element using a C0 based finite element formulation with thirteen degrees of freedom per node has been considered in the present work. Two configurations of FGM sandwich plates, one with FGM core and homogenous facesheets and second having top and bottom layers made of FGM and homogenous core are considered. Effective material properties of the FGM are computed using rule of mixture (ROM). In order to establish the correctness of the present finite element formulation for wide range of problems for two configurations of FGM sandwich plates, comparison studies are presented. Next, parametric studies are taken up to investigate the effects of volume fraction index, span to thickness ratio and boundary conditions on static and dynamic behavior of FGM sandwich plate. It is shown here that present formulation is simple, straightforward and accurate for static and dynamic analyses of functionally graded material (FGM) sandwich plates.

A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells

Abstract: In this work, the bending and free vibration analysis of multilayered plates and shells is presented by utilizing a new higher order shear deformation theory (HSDT). The proposed involves only four unknowns, which is even less than the first shear deformation theory (FSDT) and without requiring the shear correction coefficient. Unlike the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral variables. The equations of motion are derived by using the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. Bending and vibration results are found for cylindrical and spherical shells and plates for simply supported boundary conditions. Bending and vibration problems are treated as individual cases. Panels are subjected to sinusoidal, distributed and point loads. Results are presented for thick to thin as well as shallow and deep shells. The computed results are compared with the exact 3D elasticity theory and with several other conventional HSDTs. The proposed HSDT is found to be precise compared to other several existing ones for investigating the static and dynamic response of isotropic and multilayered composite shell and plate structures.

A new nonlocal HSDT for analysis of stability of single layer graphene sheet

Abstract: A new nonlocal higher order shear deformation theory (HSDT) is developed for buckling properties of single graphene sheet. The proposed nonlocal HSDT contains a new displacement field which incorporates undetermined integral terms and contains only two variables. The length scale parameter is considered in the present formulation by employing the nonlocal differential constitutive relations of Eringen. Closed-form solutions for critical buckling forces of the graphene sheets are obtained. Nonlocal elasticity theories are used to bring out the small scale influence on the critical buckling force of graphene sheets. Influences of length scale parameter, length, thickness of the graphene sheets and shear deformation on the critical buckling force have been examined.

Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates

Abstract: In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton\'s principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

Approximation of a Brittle Fracture Energy with a Constraint of Non-interpenetration

Abstract: Linear fracture mechanics (or at least the initiation part of that theory) can be framed in a variational context as a minimization problem over a SBD type space. The corresponding functional can in turn be approximated in the sense of Γ-convergence by a sequence of functionals involving a phase field as well as the displacement field. We show that a similar approximation persists if additionally imposing a non-interpenetration constraint in the minimization, namely that only nonnegative normal jumps should be permissible. 2010 Mathematics subject classification: 26A45

An iterative reconstruction of cosmological initial density fields

Abstract: We present an iterative method to reconstruct the linear-theory initial conditions from the late-time cosmological matter density field, with the intent of improving the recovery of the cosmic distance scale from the baryon acoustic oscillations (BAOs). We present tests using the dark matter density field in both real and redshift space generated from an $N$-body simulation. In redshift space at $z = 0.5$, we find that the reconstructed displacement field using our iterative method are more than 80\% correlated with the true displacement field of the dark matter particles on scales $k < 0.10h\ {\rm Mpc}^{-1}$. Furthermore, we show that the two-point correlation function of our reconstructed density field matches that of the initial density field substantially better, especially on small scales ($< 40h^{-1}\ {\rm Mpc}$). Our redshift-space results are improved if we use an anisotropic smoothing so as to account for the reduced small-scale information along the line of sight in redshift space.

Isogeometric analysis of first and second strain gradient elasticity

Abstract: The elastic energy in the conventional Cauchy continuum model depends on the gradient of the displacement field, which is not adequate to show the behavior of a system under point and line forces. Applying these kinds of boundary conditions to the continuum will lead to singularities. To overcome this problem, a generalization of the Cauchy continuum concept is a choice. In this paper, isogeometric analysis is used to simulate the behavior of second- and third-gradient materials. As expected, a significant improvement in the efficiency and accuracy of the attained results compared to the conventional finite element method is noticed.