Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium

As a first endeavor, the small scale effect on the thermal buckling characteristic of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium is investigated. The surrounding elastic medium is modeled as the two-parameter elastic foundation. The formulation is derived using the classical plate theory (CPT) in conjunction with the nonlocal elasticity theory. The solution procedure is based on the transformation of the governing equations from physical domain to computational domain and then discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Then, the influence of small scale parameter in combination with the elastic medium parameters, geometrical shape and the boundary conditions on the thermal buckling load of the nanoplates is investigated.     

Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates

As a first endeavor, the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates is investigated using the nonlocal elasticity theory. The formulation is derived based on the first order shear deformation theory (FSDT). The solution procedure is based on the transformation of the governing equations from physical domain to computational domain and then discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. The formulation and the method of the solution are firstly validated by carrying out the comparison studies for the isotropic and orthotropic rectangular plates against existing results in literature. Then, the effects of nonlocal parameter in combination with the geometrical shape parameters, thickness-to-length ratio and the boundary conditions on the frequency parameters of the nanoplates are investigated.     

Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics

Buckling response of orthotropic single layered graphene sheet (SLGS) is investigated using the nonlocal elasticity theory. Two opposite edges of the plate are subjected to linearly varying normal stresses. Small scale effects are taken into consideration. The nonlocal theory of Eringen and the equilibrium equations of a rectangular plate are employed to derive the governing equations. Differential quadrature method (DQM) has been used to solve the governing equations for various boundary conditions. To verify the accuracy of the present results, a power series (PS) solution is also developed. DQM results are successfully verified with those of the PS method. It is shown that the nonlocal effects play a prominent role in the stability behavior of orthotropic nanoplates. Furthermore, for the case of pure in-plane bending, the nonlocal effects are relatively more than other cases (other load factors) and the difference in the effect of small scale between this case and other cases is significant even for larger lengths.     

Wavelet analysis of DEM simulations of samples under biaxial compression

The results of a wavelet analysis of data from discrete element modelling (DEM) simulations of samples under biaxial compression are presented. We show how a wavelet technique may be used to find the strain scales on which critical events occur and to identify regions both in space and in strain when particles in the sample undergo significant activity. The wavelet analysis indicates that most activity occurs along a line, and this line coincides with a localization or shear band that develops in the specimen during compression. The location of this shear band can be visually identified by considering the cumulative particle rotation. Furthermore, using cross-correlation we show that the principal stress ratio is correlated with the porosity of the sample along this line. In order to investigate the robustness of the technique, the wavelet analysis is carried out on two different size specimens that both show the same general phenomena.     

A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes

This paper reviews recent research studies on the application of the nonlocal continuum theory in modeling of carbon nanotubes and graphene sheets. A variety of nonlocal continuum models in modeling of the two materials under static and dynamic loadings are introduced and reviewed. The superiority of nonlocal continuum models to their local counterparts, the necessity of the calibration of the small-scale parameter, and the applicability of nonlocal continuum models are discussed. A brief introduction of the nonlocal beam, plate, and shell models is particularly presented. Summary and recommendations for future research are also provided. This paper is intended to provide an introduction of the development of the nonlocal continuum theory in modeling the two nano-materials, review the different nonlocal continuum models, and inspire further applications of the nonlocal continuum theory to nano-material modeling.     

Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects

This article presents the buckling analysis of isotropic nanoplates using the two variable refined plate theory and nonlocal small scale effects. The two variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the nanoplate are derived from the principle of virtual displacements. The closed-form solution for buckling load of a simply supported rectangular nanoplate subjected to in-plane loading has been obtained by using the Navier’s method. Numerical results obtained by the present theory are compared with available exact solutions in the literature. The effect of nonlocal scaling parameter, mode numbers and aspect ratios of the nanoplates on buckling load are investigated and discussed in detail in the present work. It can be concluded that the present theory, which does not require shear correction factor, is not only simple but also comparable to the first-order and higher order shear deformable theory.     

Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method

The small scale effect on the vibration analysis of orthotropic single layered graphene sheets (SLGS) is studied. Elastic theory of the graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived for the graphene sheets. Differential quadrature method (DQM) is employed to solve the governing differential equations for various boundary conditions. Nonlocal theories are employed to bring out the small scale effect of the nonlocal parameter on the natural frequencies of the orthotropic graphene sheets. Further, effects of (i) nonlocal parameter, (ii) size of the graphene sheets, (iii) material properties and (iv) boundary conditions on nondimensional vibration frequencies are investigated.     

Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity

A nonlocal elastic plate model accounting for the small scale effects is developed to investigate the vibrational behavior of multi-layered graphene sheets under various boundary conditions. Based upon the constitutive equations of nonlocal elasticity, derived are the Reissner–Mindlin-type field equations which include the interaction of van der Waals forces between adjacent and non-adjacent layers and the reaction from the surrounding media. The set of coupled governing equations of motion for the multi-layered graphene sheets are then numerically solved by the generalized differential quadrature method. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions in a multi-layered graphene sheet. Based on exact solution, explicit expressions for the nonlocal frequencies of a double-layered graphene sheet with all edges simply supported are also obtained. The results from the present numerical solution, where possible, are indicated to be in excellent agreement with the existing data from the literature.     

Does vibration amplitude influence the evaluation of nonlocal small scale parameter of single layered graphene sheets?

ABSTRACT

This study aims to evaluate the nonlocal small scale parameter for large amplitude vibration of single layered graphene sheets (SLGSs) comparing nonlinear resonant frequencies obtained via nonlocal continuum and molecular dynamics (MD) simulations. Nonlinear governing equations of motion are numerically solved employing the pseudo-spectral method to obtain the frequency response. Results reveal that the calibrated small scale parameter decreases when the vibration amplitude increases. Also, from MD simulations it is seen that for all length sizes after an ultimate vibration amplitude around 31% length size, the graphene sheets start to fracture.     

Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory

The natural frequencies of the flapwise bending vibrations of a nonuniform rotating nanocantilever has been calculated, considering the true spatial variation of the axial force due to the rotation. The area of the nanobeam cross-section is assumed to change linearly. The problem has been formulated using the nonlocal Eringen elasticity theory and it was solved by a pseudo-spectral collocation method based on Chebyshev polynomials. The effect of the nonlocal small-scale, angular speed, nonuniformity of the section and hub radius on the vibration behavior of the nanocantilever is discussed.     

Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation

Atomic vibration in the Carbon Nanotubes (CNTs) gives rise to non-local interactions. In this paper, an expression for the non-local scaling parameter is derived as a function of the geometric and electronic properties of the rolled graphene sheet in single-walled CNTs. A self-consistent method is developed for the linearization of the problem of ultrasonic wave propagation in CNTs. We show that (i) the general three-dimensional elastic problem leads to a single non-local scaling parameter (e₀), (ii) e₀ is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e₀ is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e₀ in the case of coupled longitudinal-torsional modes of wave propagation, is a function which exponentially converges to that of axial mode at large diameters and to torsional mode at smaller diameters. These results are valid in the long-wavelength limit.     

Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory

In this article, the small-scale effect on the vibration behavior of orthotropic single-layered graphene sheets is studied based on the nonlocal Reddy's plate theory embedded in elastic medium considering initial shear stress. Elastic theory of the graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. To simulate the interaction between the graphene sheet and surrounding elastic medium we used both Winkler-type and Pasternak-type foundation models. The effects of initial shear stress and surrounding elastic medium and boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets are studied considering five different boundary conditions. Numerical approach of the obtained equation is derived by differential quadrature method. Effects of shear stress, nonlocal parameter, size of the graphene sheets, stiffness of surrounding elastic medium, and boundary conditions on vibration frequency rate are investigated. The results reveal that as the stiffness of the surrounding elastic medium increases, the nonlocal effect decreases. Further, the nonlocal effect increases as the size of the graphene sheet is decreased. It is also found that the frequency ratios decrease with an increase in vibration modes.     

Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory

In this study, the free vibration behavior of circular graphene sheet under in-plane pre-load is studied. By using the nonlocal elasticity theory and Kirchhoff plate theory, the governing equation is derived for single-layered graphene sheets (SLGSs). The closed-form solution for frequency vibration of circular graphene sheets under in-plane pre-load has been obtained and nonlocal parameter appears into arguments of Bessel functions. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, mode number and boundary conditions on natural frequencies are investigated. The results are shown that at smaller radius of circular nanoplate, the effect of in-plane pre-loads is more importance.     

Energy dissipation capacity of fibre reinforced concrete under biaxial tension–compression load. Part I: Test equipment and work of fracture

The objective of this research was to analyse the differences in the dissipated energy under uniaxial tension and biaxial tension–compression load of fibre reinforced concretes using the Wedge Splitting Test. Under biaxial load the specimens were subjected to compressive stress ratios from 10% to 50% of the concrete compressive strength perpendicular to the direction of the tensile load.Under biaxial tension–compression load the energy dissipation capacity of the specimens decreases compared to the uniaxial tension load case on average 20–30%. It is believed that the decrease is a result of the damage mechanism of the concrete matrix and deterioration of the fibre–matrix and/or aggregate–cement paste interfaces in case the section is additionally loaded with compression stresses. This indicates that dimensioning of concrete elements under biaxial stress states using material parameters obtained from tests conducted on specimens under uniaxial tensile load is unsafe and could potentially lead to a non-conservative design.In the second part of this paper the extent of the fracture process zone under uniaxial tension and biaxial tension–compression load will be examined with the Acoustic Emission technique and the reasons for decrease of the energy dissipation capacity under biaxial load will be further discussed.     

The influence of constant axial compression pre-stress on the fatigue failure of torsion loaded tube springs

This paper reports the results of a series of biaxial static compression and torsion experiments performed to evaluate the effects of static compression stress on the fatigue life those smooth tubes made of high strength spring steel. Compression pre-stress was introduced by a solid steel bar inserted into a hollow spring and loaded with a screw-joint. The experimentally obtained results show a significant extension of fatigue strain life as a result of combining axial compression loading with torsion. Cracking behavior was observed and it was noted that compression pre-stresses contribute to retardation of the fatigue crack initiation process and, consequently, contribute to the extension of fatigue life. The fatigue shear crack initiated in a transverse direction. This crack continues to propagate in the same direction until it starts to propagate as a macro-crack on the maximum shear plane.     

大型内压缩流程空分设备的安全探讨

结合大型内压缩流程空分设备的设计、安装和调试经验，从主换热器和主冷等4方面分析了内压缩流程空分设备的安全因素，从主换热器1％液氧的排放和临时停车的操作等7方面介绍了大型内压缩流程空分设备的安全措施。     

大型内压缩流程空分设备的安全探讨

结合大型内压缩流程空分设备的设计、安装和调试经验,从主换热器和主冷等4方面分析了内压缩流程空分设备的安全因素,从主换热器1%液氧的排放和临时停车的操作等7方面介绍了大型内压缩流程空分设备的安全措施。     

Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory

This paper investigates the nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory and Timoshenko beam theory. The piezoelectric nanobeam is subjected to an applied voltage and a uniform temperature change. The nonlinear governing equations and boundary conditions are derived by using the Hamilton principle and discretized by using the differential quadrature (DQ) method. A direct iterative method is employed to determine the nonlinear frequencies and mode shapes of the piezoelectric nanobeams. A detailed parametric study is conducted to study the influences of the nonlocal parameter, temperature change and external electric voltage on the size-dependent nonlinear vibration characteristics of the piezoelectric nanobeams.     

Influences of elastic foundations and shear deformations on the buckling behavior of functionally graded material truncated conical shells under axial compression

This article presents an investigation on the buckling of functionally graded (FG) truncated conical shells under an axial load resting on elastic foundations within the shear deformation theory (SDT). The governing equations are solved using the Galerkin method, and the closed-form solution of the axial buckling load for FG conical shells on elastic foundations within the SDT is obtained. Various numerical examples are presented and discussed to verify the accuracy of the closed-form solution in predicting dimensionless buckling loads for FG conical shells on the Winkler–Pasternak elastic foundations within the SDT.     

三维机织碳/碳复合材料双轴压缩载荷下的力学行为

基于三维机织碳/碳复合材料的细观结构特征, 设计平板十字形试样, 在材料双轴力学性能试验机上开展了复合材料单轴、 双轴加载压缩试验, 对比分析了三维机织碳/碳复合材料在双轴压缩载荷下的力学行为。研究表明: 三维机织碳/碳复合材料的压缩行为表现为非线性、 脆性断裂; 双轴载荷作用下非线性特征更为显著, 压缩模量随应力的增加而增大, 强度与模量相较于单轴有较大幅度增加, 双轴压缩载荷作用下材料的强化效应显著; 试样破坏位置并未出现在试样中心区, 而是发生在试样的加载端部或十字形试样的加载分枝根部, 主要表现为基体开裂、 纤维断裂和层间脱粘, 碳布及其层间界面剪切强度的强弱直接影响材料的压缩强度。