Dynamic analysis of functionally graded truncated conical shells subjected to asymmetric moving loads

The dynamic behavior of functionally graded (FG) truncated conical shells subjected to asymmetric internal ring-shaped moving loads is studied. The material properties are assumed to have continuous variations in the shell thickness direction. The equations of motion are derived based on the first-order shear deformation theory (FSDT) using Hamilton׳s principle. The finite element method (FEM) together with Newmark׳s time integration scheme is employed to discretize the equations of motion in the spatial and temporal domain, respectively. The formulation and method of solution are validated by studying their convergence behavior and carrying out the comparison studies in the limit cases with existing solutions in the literature. Then, the influences of material graded index, radius-to-length ratio, semi-vertex angle, thickness, boundary conditions and moving load velocity on the dynamic behavior of the FG truncated conical shells are studied. In addition, the difference between the responses of the FG shells under symmetric and asymmetric loadings is compared.     

组合式基层路面结构弯沉指标研究

柔性基层或组合式基层沥青路面作为新型的路面结构,其弯沉指标控制与现有规范验收体系不相适应,本文通过大量的试验验证与分析,揭示了级配碎石基层顶面弯沉的发展规律及其与沥青路面顶层弯沉指标的相关关系,提出了新型路面结构弯沉指标的控制标准。     

基于传统板理论的智能圆形FGM薄板自由振动研究

基于传统板理论（CPT）对圆形功能梯度（FG）薄板的自由振动性能进行分析。这种板具有2个由压电（PZT4）材料构成的均布驱动器。对FG底层板的材料特性进行假定,考虑了材料体积分数的能量分布,将材料沿厚度方向进行分级,并采用二次方程模拟沿压电覆层厚度方向分布的电势场。采用运动微分方程来模拟板的固定端边界条件。介绍了详细的数学推导过程,并采用数值分析来研究FG板的梯度变化对结构自由振动的影响。其分析结果得到了三维有限元分析结果的证实。     

径向荷载作用下功能梯度柱壳非线性后屈曲研究

基于柱壳非线性大变形理论,研究承受径向荷载的功能梯度柱壳的非线性后屈曲性能。依据功能梯度参数,功能梯度材料沿厚度方向的属性有差异。考虑依赖温度的材料属性,比较不同温度的影响。研究了功能梯度参数与空间参数的影响。最后,利用试验结果对理论结果进行修正。     

Folding of a plastic fibre under combined shear and compression

Large deflection of an elastic–plastic, nonlinear strain-hardening clamped-sliding beam subjected to a combined compression and shear load is solved analytically. The solution requires only numerical evaluation of integrals. Analytical expressions for applied force, deflection, bending moment, and strain energy are obtained. Numerical examples are given for a single stainless steel fibre of the hybrid stainless steel assembly (HSSA). The contact condition of the beam with end platens is determined. It is shown that the normalized effective crush distance ranges from 0.85 to 1.00, and depends only on loading angles and material hardening exponents. The crushing load has a maximum for the case with a small material hardening exponent and a small loading angle. It is found that no plastic unloading will occur before the beam contacts with the end platens. Finite element simulations are performed to verify the accuracy of the analytical solution, and a rather good agreement is obtained.     

大挠度功能梯度压杆的后屈曲分析

对一端固定一端自由功能梯度压杆的后屈曲问题进行了分析。依据组份材料的体积含量,假设材料的物性参数沿杆件的厚度按幂函数变化。基于Kirchhoff大变形理论,推导了大挠度功能梯度压杆后屈曲分析的控制微分方程和边界条件。采用微分求积法对所得控制微分方程和边界条件进行数值计算,得到压杆后屈曲时的自由端转角和自由端位移。分析了载荷、梯度指数和截面边长比对杆件后屈曲平衡路径的影响。     

六边形孔蜂窝梁挠度的数值模拟与分析

利用有限元软件ANSYS,采用板壳单元和双线性随动模型,对六边形开孔的蜂窝梁在均布荷载作用下的挠度进行了数值模拟与分析,确定了影响其挠度的主要因素,并与实腹梁相对比,给出了适用于工程应用的挠度设计公式。     

Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets

Vibrations of non-uniform and functionally graded (FG) beams with various boundary conditions and varying cross-sections are investigated using the Euler-Bernoulli theory and Haar matrices. It is assumed that the cross-section and material properties vary along the beam in the axial direction. The system of the governing equations is transformed with the aid of a set of simplest wavelets. To validate the present results, the non-homogeneity of the beams is discussed in detail and the calculated frequencies are compared with those of the existing literature. The results show that the Haar wavelet approach is capable of calculating frequencies for the beams with different shapes, rigidity, mass density, small or large translational and rotational boundary coefficients. The advantage of the novel approach consists in its simplicity, accuracy and swiftness.     

Coupled thermoelasticity of functionally graded plates based on the third-order shear deformation theory

In this paper, the analytical solution is presented for a plate made of functionally graded materials based on the third-order shear deformation theory and subjected to lateral thermal shock. The material properties of the plate, except Poisson's ratio, are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The solution is obtained under the coupled thermoelasticity assumptions. The temperature profile across the plate thickness is approximated by a third-order polynomial in terms of the variable z with four unknown multiplier functions of (x,y,t) to be calculated. The equations of motion and the conventional coupled energy equation are simultaneously solved to obtain the displacement components and the temperature distribution in the plate. The governing partial differential equations are solved using the double Fourier series expansion. Using the Laplace transform, the unknown variables are obtained in the Laplace domain. Applying the analytical Laplace inverse method, the solution in the time domain is derived. Results are presented for different power law indices and the coupling coefficients for a plate with simply supported boundary conditions. The results are validated based on the known data for thermomechanical responses of a functionally graded plate reported in the literature.     

Stability of elastic–plastic conical shells under shear loading

A method of determination of critical loads for thin-walled conical shells loaded by shear forces developed by moment of twist is presented. The three governing equations of neutral equilibrium with respect to basic displacement vector components u, v, and w are used. It is assumed that effective stress in the prebuckling state of stress in the shell can exceed the yield limit of the shell material. The use is made both of physical relations of Nadai–Hencky small elastic–plastic deformation theory of plasticity, and Prandtl–Reuss J₂ incremental plastic flow theory. Also, a bilinear stress–strain material model, material compressibility and Shanley approach will be accepted in the analysis. Galerkin method is applied to solve the problem equations and iterative techniques are accepted in numerical algorithm to determine critical loads for elastic–plastic shells.     

新型非接触式桥梁挠度和变形的检测方法

介绍了一种非接触式桥梁挠度变形的检测装置及测量方法。其核心技术为借助视频测量的图像散斑识别技术和二维图像处理技术,通过像素分析和已知几何尺寸的成像标定进行结构位移的测量。以某三跨预应力混凝土连续箱梁桥静载试验为背景,分别采用非接触式位移检测装置和传统的百分表测量方法进行对比测量研究,确认了非接触式桥梁位移测量精度可满足工程测量要求。结果表明非接触式位移检测法不仅测量时无需支架,省时省力,而且在100m以内对桥梁挠度具有较高的精度。     

火灾作用下混凝土双向简支板的挠度计算

小挠度薄板理论可以用来确定混凝土双向板正常使用时的挠度,当用于计算火灾作用下处于大挠度的双向混凝土板挠度时则会带来很大误差。在引入弹性板的大挠度微分控制方程后,考虑外加荷载与高温的共同作用,并计及高温下材料特性的变化,对火灾作用下钢筋混凝土双向简支板的挠度随温度的变化进行了分析。引入无量纲量,对大挠度微分控制方程进行无量纲化处理,并以无量纲板均布荷载为摄动参数,结合Galerkin方法提出了钢筋混凝土双向简支板火灾作用下挠度的计算式,计算结果与试验结果吻合较好,可为火灾作用下板的大挠度分析提供依据。研究结果表明：火灾作用下混凝土板的挠度与外加荷载和热弯矩均有关,与热弯矩成线性关系,而与外荷载则成非线性关系;当没有热弯矩时,挠度主要由外加荷载确定;当外加荷载恒定时,挠度则主要由热弯矩引起。     

夹层玻璃板大挠度弯曲分析

文章在夹层玻璃板小挠度理论基础上研究了大挠度情况下的非线性弯曲问题,提出了以5个位移分量表示的夹层玻璃板大挠度控制微分方程。文章同时指出该微分方程的解可由夹层板大挠度的解类比得出,能直接应用于实际工程设计。     

Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection

Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on von Kármán's plate theory, equilibrium equations governing a large axi-symmetric deformation of the FGM circular plate under thermomechanical loads are derived. In the analysis, the geometric imperfections of the plate are taken into account. By using a shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved numerically. Responses for the nonlinear thermomechanical post-buckling responses of the FGM plate are obtained. Numerical examples are presented that relate to the performances of perfect and imperfect, homogenous and graded plates. Characteristic curves of the post-buckling deformation of the imperfect FGM circular plate varying with thermal loads, imperfection parameters and volume fraction index are plotted. And then effects of the load parameters, materials constitution, and the geometric imperfection of the plate on the deformation are discussed in detail.     

Optimum design of laminated composite plates to maximize buckling load using MFD method

This paper presents optimal design of simply supported laminated composite plates subject to given in-plane static loads for which the critical failure mode is buckling. The objective function is to maximize the buckling load capacity of laminated plates and the fiber orientation is considered as design variable. The first-order shear deformation theory is used for the finite element analysis. In this paper, the effects of bending–twisting coupling are also included for the buckling optimization. The modified feasible direction method is used as an optimization method. Also, computer programs are coded in MATLAB and Golden Section method is adapted in this program for the optimal design of laminated plates for maximum buckling load. The effect of width-to-thickness ratio, aspect ratio, number of layers, material anisotropy, load ratios (N_y/N_x), uncertainties in material properties and functionally graded materials on the results is investigated and compared.     

既有桥梁挠度的研究

应用结构力学理论,考虑荷载横向分布的影响,得出对于不同截面形式的主梁在外荷载作用下的跨中挠度的计算方法。并结合实际的工程实例进行验证,将计算的跨中挠度值与实测的跨中挠度值进行比较,满足规范要求,则表明采用该方法来计算既有桥梁的挠度是可行的。     

对带几何缺陷的FGM圆板的非线性热力学后屈曲现象的分析

带有几何缺陷FGM圆板的非线性热力学后屈曲现象是由力学荷载及横向不均匀温度升高导致的。基于组成材料的体积分数导致的能量分布法则,FGM板的材料特性假定在板厚度方向呈梯度变化。根据VonK偄rm偄n平板理论,推导出FGM板在温度荷载作用下的轴对称大变形的计算公式。在此分析中同时考虑了板的几何缺陷。通过运用目标法,解决了那些带有固定边界条件的非线性方程。数值算例中考虑了是否带有几何缺陷、均质或非均质的钢板。带缺陷FGM圆板的后屈曲变形特征曲线根据温度荷载、缺陷参数和体积分数的变化绘制而成。文中同时讨论了荷载参数、材料构成及板的几何缺陷对变形的影响。     

Non-linear in-plane stability analysis of FG circular shallow arches under uniform radial pressure

In this paper, non-linear stability behavior of functionally graded (FG) circular shallow arches subjected to a uniform radial pressure is investigated by an analytical method. For this purpose, the classical single layer assumption is used to approximate the displacement field through the arch. Donnell׳s non-linear model for shallow shells is employed to derive the strain–displacement relations. The material properties vary smoothly through the thickness of the arch according to a power-law distribution. The governing equilibrium equations and the complete set of boundary conditions are extracted employing the principle of virtual displacements and variational calculus. Because of considerable pre-buckling deformations of shallow arches, the stability analysis is accomplished considering the pre-buckling deformations. The non-linear equilibrium paths are presented for two symmetric types of boundary conditions. Results show the influences of properties dispersion, geometrical characteristics, and boundary conditions on the stability behavior of the FG circular shallow arches. Also, the results of the paper are compared with the known data in literature.     

Static analysis of superelliptical clamped plates by Galerkin's method

In this study, clamped superelliptical plates under uniformly distributed surface load are statically analyzed. Linearly elastic, homogeneous, and isotropic material is considered. The classical thin plate model (Kirchhoff) is employed. The lack of contributions on the static behavior of this sort of plate shapes is the fundamental motivation of the current study. Galerkin's method is used to obtain solutions. The method is conducted for polynomial series at powers ranging from 2 to 8 in order to get converging solutions. Maximum deflections of the plates and mid-point moments are obtained and the results are arranged in tabular form. For purpose of understanding, the behavior trend of the structure with respect to the parameters, some of the solutions are organized in graphical form. The study is performed for a wide range of superelliptical plates. The results are also examined with respect to the parameters a/b ratios and n, which are the plate aspect ratio and the superelliptical power, respectively.     

大变形条件下单桩水平承载性状分析

针对大变形条件下承受水平荷载的单桩基础,采用沿深度线性增加并能较好的反映上部土体抵抗侧向变形能力的地基反力系数,及简化的土体弹塑性本构关系,推导出桩身变形和内力的计算公式,并用FORTRAN语言编制了计算程序。算例表明：桩的水平位移和弯矩随水平力和力矩的增加而非线性增大;桩身位移随距离地面的距离的增加而减小,距地面的距离超过10倍桩径时桩身响应极小,可忽略不计;桩顶约束是桩身响应沿桩身分布的重要影响因素;随着桩周土体力学性质的改善,桩的最大位移和最大弯矩均明显减小。计算值与现场实测值吻合度很高,且比已有解计算结果更优,所得解及程序是可靠的。