Three-Dimensional Static Analysis of Nanoplates and Graphene Sheets by Using Eringen’s Nonlocal Elasticity Theory and the Perturbation Method

A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.

基于Poulos弹性理论的被动桩改进算法

传统的Poulos弹性理论仅适合于均质土中土体侧向位移时桩的性状分析,无法考虑土的层状特性。通过引入层状地基中作用一水平集中力的广义Mindlin解和地面作用有竖向荷载时的应力和位移通解,对Poulos方法进行了改进,使之扩展到多层土中,还用于研究堆载条件下的被动桩变形和受力响应。算例分析表明,改进弹性理论要比Poulos方法更为严密、合理,提高了计算精度,应用范围也更广。

On Axially Symmetric Vibrations of Fluid Filled Poroelastic Spherical Shells

Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic closed spherical shell filled with fluid are studied. The frequency equation of axially symmetric vibrations for a pervious and an impervious surface is obtained. Free vibrations of a closed spherical shell are studied as a particular case when the fluid is vanished. Frequency as a function of ratio of thickness to inner radius is computed in absence of dissipation for two types of poroelastic materials each for a pervious and an impervious surface. Results of previous works are obtained as a particular case of the present study.

Neumann＇s method for boundary problems of thin elastic shells

The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.

Memory response in a nonlocal micropolar double porous thermoelastic medium with variable conductivity under Moore-Gibson-Thompson thermoelasticity theory

The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.

Dynamic Design of Thick Orthotropic Cantilever Plates with Consideration of Bimoments

The paper is devoted to dynamic design of thick orthotropic cantilever plates by applying the bimoment theory of plates, which takes into account the forces, moments and bimoments;and the theory takes into account nonlinear law of displacements distribution in cross section of the plate. The methods for constructing bimoment theory are based on Hooke’s Law, three-dimensional equations of the theory of dynamic elasticity and the method of displacements expansion into Maclaurin series. The article gives the expressions to determine the forces, moments and bimoments. Bimoment theory of plates is described by two unrelated two-dimensional systems with nine equations in each. On each edge of the plate, depending on the type of fastening, nine boundary conditions are given. As an example, the solution of the problem of dynamic bending of thick isotropic and orthotropic plate under the influence of transverse dynamic loads in the form of the Heaviside function is given. The equations of motion of the plate are solved by numerical method of finite differences. The numerical results are obtained for isotropic and orthotropic plate. The graphs of changes of displacements and stresses of faces surfaces of the plate are presented. Maximum values of these displacements are found and analyzed. It is shown that by Timoshenko theory numerical values of stresses are much smaller compared to the ones obtained by bimoment theory of plates. Maximum numerical values of generalized displacements, forces, moments, and bimoments are obtained and presented in tabular form. The analysis of numerical results is done and the conclusions are drawn.

Einstein’s General Relativity and Pure Gravity in a Cosserat and De Sitter-Witten Spacetime Setting as the Explanation of Dark Energy and Cosmic Accelerated Expansion

Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.

两向不等压圆形孔口压缩与扩张问题的塑性区半径统一解

【目的】在地下工程中,隧道或水平定向钻井过程中的最大泥浆压力分析等所处真实应力场常为远处两向不等压应力场。为了求解两向不等压应力场下圆形孔口压缩和扩张问题的统一解析解,【方法】基于统一强度理论和弹脆塑性模型,借鉴鲁宾涅特解的求解方法,推导了两向不等压圆形孔口压缩和扩张问题的塑性区半径统一解,并与复变函数解、摄动解进行了对比,最后分析了各因素对塑性区半径的影响以及在实际工程中的应用。【结果】结果显示:当两向为不等压应力场时,弹塑性交界线均呈现类椭圆形状,对于压缩问题,类椭圆长轴方向与两向不等压应力场较小值处一致,并且弹塑性交界线在极角0°~90°范围内分成两段,在极角0°~30°范围内,弹塑性交界线随两向不等压应力场的应力比增加水平向左移动,在30°~90°范围内,弹塑性交界线随两向不等压应力场的应力比增加竖直向上移动,而对于扩张问题则相反;对于压缩问题,支护力、中间主应力、残余黏聚力和残余内摩擦角对塑性区半径影响显著,而对于扩张问题,扩孔压力、中间主应力、残余内摩擦角对塑性区半径影响显著,残余黏聚力对塑性区半径几乎无影响。【结论】在实际工程分析中,应充分考虑两向不等压应力场、中间主应力和弹脆塑性模型的影响,并且采用弹脆塑性模型比理想弹塑性模型计算的塑性区半径大,更适合岩土类材料弹塑性分析。

4 ,4′-二巯基二苯醚分子的电子输运性质研究

利用从头算方法和弹性散射格林函数理论,研究了4 ,4′-二巯基二苯醚分子的电输运性质.计算表明,当外加偏压少于0 .9 V时,该分子器件不导电.当外加偏压进一步增加时,该分子器件的电导呈现出平台特征.由于中间氧原子的存在,相对于4 ,4′-二巯基联苯分子来说,该分子的导电特性较差.

超声波在灰岩模拟材料强度测量中的应用

利用水泥、石膏和砂模拟灰岩的岩性,在室内进行小样配方试验的基础上,选择合适的配方,进行了室外岩溶顶板的模拟试验.利用声波仪,用超声波法检测了模拟岩溶顶板试样的纵波波速和横波波速,得出了相应试样的动弹性模量和动泊松比.结合试验数据,分析了纵波波速与横波波速之间的关系,以及它们与抗压强度、抗弯强度和动弹性模量之间的关系,证明纵波波速较横波波速能更好地反映模拟试样的抗压强度和抗弯强度,并且纵波波速随试样的强度和动弹性模量的增长而增大.

钢筋砼双向板弯矩系数的简捷计算方法

本文对按弹性理论确定的双向板弯矩系数进行回归分析，提出计算弯矩系数的简捷计算方法。文中计算公式适用于计算承受均布荷载的钢筋砼四边支承矩形板，具有计算简便和编写计算机程序简单的优点。

饱和土中单桩受移动荷载作用的动力响应

根据Biot动力理论,采用Fourier和Hankel变换方法得到了半空间饱和土受移动荷载及土体内受垂直简谐荷载作用下的变换域内基本解.再根据虚拟桩法,得出了移动载荷作用下桩基的第二类Fredholm积分方程.最后应用IFFT方法得到时间、空间域内单桩的动力响应.数值结果表明,移动荷载会引起桩身的负摩擦力;桩身最大轴力、孔压随移动荷载速度增加而增大;此外,在桩上端部会出现孔压集中现象.

求解饱和半空间上弹性圆板固结沉降的积分方程

本文采用解析方法分析了弹性圆板在饱和半空间上的固结沉降。考虑弹性圆板与饱和半空间的接触面上无摩擦力,且饱和半空间表面为全部透水的。运用Biot固结理论和积分方程技术,在Laplace变换域上建立了弹性圆板固结沉降的对偶积分方程,并化此对偶积分方程为第二类Fredholm积分方程。通过对其核函数的有效数值积分得到第二类Fredholm积分方程的解,再利用Laplace反演技术获得弹性板在时间域中的固结沉降值。文末给出弹性板中心点固结沉降的固结度的数值算例。

Unified solutions for stresses and displacements around circular tunnels using the Unified Strength Theory

The unified solutions are presented for stresses and displacements around a circular tunnel subjected to a hydrostatic stress field.The rock mass is assumed to be elastic-brittle-plastic and governed by the Unified Strength Theory.The displacements are obtained accounting for three different definitions for elastic strains and different Young's modulus in the plastic zone.The unified solutions obtained in this paper are especially versatile in reflecting the intermediate principal stress effect to different extents for different materials.The conventional solutions,based on the Mohr-Coulomb failure criterion and the Generalized Twin Shear Stress yield criterion,are special cases of the present unified solutions.The new unified solutions can compare with those computed by the latest generalized Hoek-Brown failure criterion.The results obtained demonstrate the importance of the intermediate principal stress influence for the stresses and displacements analysis.The effects of different definitions for elastic strains and different Young's modulus in the plastic zone on the displacements are significant.

天然气饱和度对岩石弹性参数影响的数值研究

基于三维数字岩心,对岩石的弹性模量、纵横波速度、拉梅常数、泊松比等参数随不同含气饱和度变化规律进行数值研究。研究结果表明岩石的含气饱和度对横波速度影响不大,含气饱和度的增加将引起横波速度的缓慢增加。岩石的拉梅常数、泊松比、纵波速度、弹性模量和纵横波速度比随含气饱和度的增加而减小,当含气饱和度较低时,它们随含气饱和度增加急剧降低。将各弹性参数随含气饱和度的变化率进行比较,发现对天然气饱和度变化最敏感的参数是拉梅常数,其次是泊松比、体积模量和纵横波速度比等。该研究有助于选取对天然气饱和度变化敏感的参数计算储层的含气饱和度,从而提高计算精度。

采用俞茂宏统一强度理论求解套管的极限外压强

充分考虑拉压强度比和中间主应力系数,根据俞茂宏统一强度理论推导出在外压强下闭端、开端和平面应变套管弹塑性极限外压强的统一算法。数值仿真显示:随拉压强度比的减小和中间主应力系数的增大,弹性极限外压强增大;开端套管的弹性极限外压强最大,平面应变套管的次之,闭端套管的最小;塑性区的半径随外压强的增大而增大;当外压强增大时,套管由弹性状态进入弹塑性状态,塑性区的半径逐渐从内半径扩展到外半径;塑性极限外压强随拉压强度比的减小而增大;随外内半径比的增大,在同样的统一强度理论参数下,闭端、开端和平面应变的塑性极限外压强之间的差异增大,且塑性极限外压强大于弹性极限外压强;塑性极限外压强的计算值与试验测试值之间的相对误差为-4%^-9%,而国际标准化组织样板数据与试验测试值之间的相对误差为-12%^-25%,美国石油协会推荐数据与试验测试值之间的相对误差为-17%^-30%,表明文中的套管塑性极限外压强公式更接近试验值。

Effect of formulation of alginate beads on their mechanical behavior and stiffness

The aim of this work was to determine the effect of formulation of alginate beads on their mechanical behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and concentrations of alginate and gelling cations and were produced using an extrusiondripping method, Single wet beads were compressed at a speed of 40 mm/min, and their elastic limits were investigated, and the corresponding force versus displacement data were obtained. The Young＇s moduli of the beads were determined from the force versus displacement data using the Hertz＇s contact mechanics theory. The alginate beads were found to exhibit plastic behavior when they were compressed beyond 50% with the exception of copper-alginate beads for which yield occured at lower deformation, Alginate beads made of higher guluronic acid contents and gelling cations of higher chemical affinity were found to have greater stiffness. Increasing the concentration of alginate and gelling ions also generated a similar effect. At such a compression speed, the values of Young＇s modulus of the beads were found to be in the range between 250 and 900 kPa depending on the bead formulation.

考虑群桩加筋效应的桩基沉降计算方法研究

基于弹性半空间的Mindlin位移解的数值积分,结合叠加原理的Poulos弹性理论方法,对群桩进行沉降分析,但在工程应用中,对大型群桩的沉降结果偏大。为了得到合理的桩基沉降值,提出了三桩模型方法,该模型考虑了群桩加筋效应。为了进一步提高群桩加筋效应的计算效率,提出了加筋系数的概念,并推导了群桩加筋系数的矩阵表达式,进而提出了考虑遮拦-群桩加筋效应的群桩加筋系数分析法,并进行了相关的算例分析。结果表明:分析小型群桩沉降时,文中方法与Poulos法和Butterfield的边界元解结果均吻合较好;分析上海中心大厦的大型群桩沉降时,与Poulos法相比文中方法更接近实测值。

含孔隙流体夹杂岩石的等效弹性常数

一般岩石块体中包含若干孔隙,孔隙中含有不同的流体.孔隙和流体对岩块的弹性特性有较大的影响.本文构建了一种"岩石胞元",该胞元由一个孔隙流体夹杂和岩石基体组成.基于Eshelby等效夹杂原理推导出岩石胞元的等效弹性常数张量的表达式.当岩石胞元的孔隙占比与岩块孔隙率相等时,则岩石胞元布满岩块,此时岩块等效弹性常数与岩石胞元的弹性常数相等.当孔隙占比大于岩块孔隙率时,岩石胞元总体积小于岩块体积,岩块等效为岩石胞元和岩石基体的组合体,此时岩块的等效弹性常数为两者弹性常数的体积加权平均值.分析表明,岩石胞元的孔隙占比取值与岩块基体和孔隙流体的特性密切相关,可由试验确定;岩块等效弹性模量随着孔隙率的增大而减小,随着孔隙流体夹杂弹性模量的增大而增大.本文岩块弹性常数估计结果与已有理论和试验结果进行了比较,具有较好的一致性.

基于Mindlin解的转炉桩筏基础设计

以某炼钢厂房的桩筏基础设计为工程背景,采用Mindlin和Boussinesq弹性理论计算桩土刚度,Reissner厚板理论分析桩基筏板,并利用该方法对转炉桩基础和厂房柱基础共同组成桩筏体系的总体沉降、差异沉降、桩顶反力、筏板内力等结果进行了计算。此法较现有的桩基设计规范中基于筏板绝对刚性假定的计算方法有一定的优越性。通过分析计算结果总结变化规律,发现荷载密度对此类基础的局部沉降、桩顶反力影响较大。