AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.

Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method

The three-dimensional free vibration analysis of a multi-directional func- tionally graded piezoelectric （FGP） annular plate resting on two parameter （Pasternak） elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method （SSDQM） is used to provide an analytical solution along the thickness using the state space method （SSM） and an approximate solution along the radial direction using the one-dimensional differential quadrature method （DQM）. The influence of the Winkler and shear stiffness of the foundation~ the material property graded variations, and the circumferential wave number on the nomdimensional natural frequency of multi-directional FGP annular plates is studied.

3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials

The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.

Magneto-elastic dynamics and bifurcation of rotating annular plate

In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton＇s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincare′ maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions,and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos.

NON-SYMMETRICAL BENDING PROBLEMS OF INFINITE ANNULAR PLATES SUPPORTED ON INNER EDGE

For non-asymmetrical bending problems of elastic annular plates, the exact solutions are not fond. To bending problems of infinite annular plate with two different boundary conditions, based on the boundary integral formula,the natural boundary integral equation for the boundary value problems of the biharmonic equation and the condition of bending moment in infinity,bending solutions under non-symmetrical loads are gained by the Fourier series and convolution formulae. The formula for the solutions has nicer convergence velocity and high computational accuracy, and the calculating process is simpler. Solutions of the given examples are compared with the finite element method. The textual solutions of moments near the loads are better than the finite element method to the fact that near the concentrative loads the inners forces trend to infinite.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

Free vibration of piezoelectric annular plate

General solutions for coupled three dimensional equations of piezoelectric media were used in this work to obtain some analytical solutions for free vibration of piezoelectric annular plates. These solutions not only satisfy the governing equations at every point in the concerned region but also satisfy the prescribed boundary conditions at every point on the boundaries. Therefore, they are three-dimensional exact. Numerical results are finally tabulated.

3D thermally induced analysis of annular plates of functionally graded materials

Within the framework of three-dimensional elasticity theory,this paper investigates the thermal response of functionally graded annular plates in which the material can be transversely isotropic and vary along the thickness direction in an arbitrary manner.The generalized Mian and Spencer method is utilized to obtain the analytical solutions of annular plates under a through-thickness steady temperature field.The present analytical solutions are validated through comparisons against those available in open literature.A parametric study is conducted to examine the effects of gradient distribution,different temperature fields,different diameter ratio and boundary conditions on the deformation and stress fields of the plate.The results show that these factors can have obvious effects on the thermo-elastic behavior of functionally gradient materials(FGM)annular plates.

Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions

This paper presents a unified approach for predicting the free and forced (steady-state and transient) vibration analyses of annular sector and annular plates with various combinations of classical and non-classical boundary supports. In spite of the types of the boundary restraints and the shapes of the plates, the admissible displacement function is described as a modified trigonometric series expansion, and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. Mathematically, the unification of various boundary value problems for annular sector and annular plates is physically realized by setting a set of coupling springs to ensure appropriate continuity conditions along the radial edges of concern. Numerous examples are presented for the free vibration analyses of annular sector and annular plates with different boundary restraints. With regard to the forced vibration analysis, annular sector and annular plates with different external excitations are examined. The accuracy, convergence and numerical robustness of the current approach are extensively demonstrated and verified through numerical examples which involve plates with various shapes and boundary conditions. © 2017, Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg.

BUCKLING ANALYSIS OF POLAR ORTHOTROPIC ANNULAR PLATES UNDER UNIFORM PRESSURES

The title problem is systematically analyzed by the differential quadrature (DQ) method. Estimates of the critical buckling loads are obtained for combinations of various boundary conditions, internal and/or external Pressures, hole sizes,and rigidity ratios. A comparison is made with existing results for certain cases. Numerical investigation has been carried out with regard to the convergence of the solutions. It is found that accurate results are obtained with only nine or eleven grid points.

A THREE-DIMENSIONAL ELASTICITY SOLUTION FOR TWO-DIRECTIONAL FGM ANNULAR PLATES WITH NON-UNIFORM ELASTIC FOUNDATIONS SUBJECTED TO NORMAL AND SHEAR TRACTIONS

In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.

复合材料双层球壳与环板耦合结构振动特性研究

以一阶剪切变形理论为基础,采用谱几何法对不同边界条件下复合材料双层球壳与环板耦合结构振动特性分析模型进行构建,其中采用人工虚拟弹簧技术模拟耦合结构的边界条件。根据耦合处的连接关系,通过布置耦合弹簧模拟器对子结构之间的耦合关系进行模拟。应用哈密顿原理对复合材料双层球壳与环板耦合结构的特征方程进行推导,对耦合结构的固有特性和稳态响应进行求解。将所得结果与有限元结果进行对比,验证了计算的正确性。分析了几何参数、材料参数对复合材料双层球壳与环板耦合结构振动响应的影响。

深圳岗厦北综合交通枢纽大尺寸钢管混凝土半埋 入式柱脚性能试验研究

深圳岗厦北综合交通枢纽位于地下空间资源紧张的城市核心区,规模巨大且荷载工况复杂,核心换乘区设有51.2m×48.0m的无柱超大跨中庭。为解决由场地条件限制导致的柱脚埋深不足问题,结合已有研究成果和工程实践经验,依托深圳岗厦北综合交通枢纽,提出并设计了半埋入式钢管混凝土柱脚节点。为检验节点可靠性,通过1/5大比例缩尺模型试验结合数值分析研究了轴力、剪力和弯矩共同作用下的半埋入式柱脚节点的力学响应,分析了柱脚内部的应力分布规律,揭示了同时设置环板和栓钉作为抗剪连接件时的工作机理。分析结果表明:设计荷载工况下,钢管混凝土柱轴力主要通过环板和柱脚底板传递,弯矩主要通过钢管侧壁承压传递;环板埋深较浅时可以获得较高的传力效率,但其下部混凝土易出现应力集中;钢管侧壁栓钉在埋置深度范围内均能够较好地发挥抗剪作用。承台下部桩基布置合理,设计荷载工况下未见承台冲切破坏特征、节点整体处于弹性工作状态;1.2倍设计荷载工况下节点刚度仍未见明显退化,节点混凝土未出现压溃或剥落,表面无可见裂缝发展,各关键位置钢材应力低于材料强度。设置环板和栓钉作为剪力连接件的半埋入式柱脚可以实现对钢管混凝土柱的可靠嵌固,提出的采用抗剪环板加强的钢管混凝土半埋入式柱脚节点设计与构造方案合理可行,满足结构安全要求。

温度场下功能梯度圆锥壳-环板振动特性分析

针对功能梯度圆锥壳-环板组合结构振动问题,本文采用一阶剪切变形理论和Rayleigh-Ritz法分析了温度场下组合结构的振动特性。组合结构位移变量采用谱几何法来表征,考虑材料参数与温度相关并引入人工边界弹簧建立了组合结构振动特性分析模型。数值算例中,通过将文中求解结果与文献解和有限元法结果进行对比验证了模型的正确性,进而分析尺寸、材料、温度和连接位置等参数对结构振动特性的影响。研究结果表明:组合结构基频随厚度增加而增加,随着幂律指数、半顶角和温度场参数增加而降低,随环板内径和连接位置变化会呈现非单一变化趋势。

膨胀剂和后浇带对超长环形底板混凝土防裂的影响研究

世界上亮度最高的第四代高能同步辐射光源的超长环形底板周长约1494 m、厚1 m,如何保证底板混凝土施工质量防止裂缝产生是工程的难点。建立有限元三维数值分析模型,按照实际施工过程仿真底板混凝土的跳仓浇筑过程,模拟分析底板混凝土温度及温度应力变化情况,同时将计算温度结果与实测温度结果进行对比,验证热学参数的合理性和准确性。在反演分析基础上,研究膨胀剂和后浇带的温控防裂效果。研究结果表明:早膨胀型自变(Ⅰ型)对混凝土早龄期应力的影响是有利的,但晚膨胀型自变(Ⅲ型)的延迟膨胀性补偿由于混凝土收缩和温降引起的应力,有利于减小底板冬季最大拉应力;设置后浇带能减小底板混凝土分缝分块长度,削减混凝土最大拉应力,削减幅度为6.65%。

聚合釜设备筒体导流板的结构分析

对含整体夹套的聚合釜设备的螺旋导流板进行分析建模计算,对螺旋导流板和同心环状导流板结构2种方式分别建模。通过分析结果可知,采用同心导流板结构代替螺旋导流板,提高了建模效率,网格使划分更容易,增加了仿真速度。

圆环型弹性阀片变形模型及厚度对溢流阀开度影响分析

先导溢流阀是阻尼连续可变减振器的关键部件,使减振器具有阻尼连续可调能力,而圆环型弹性阀片是影响先导溢流阀的开度、压力等参数的关键零件。为查明圆环型弹性阀片变形规律与先导溢流阀开度的映射机制,推导了圆环型弹性阀片变形的数学模型,在先导阀开度为0~0.25 mm,阀片厚度为0.1~0.3 mm的情况下进行计算分析,验证了变形模型的准确性,并揭示了先导溢流阀开阀压力、入口压力、溢流阀阀口内外压差和溢流阀开度的变化规律,获取了溢流阀开阀压力、压差、开度与圆环型弹性阀片厚度的关系曲线,为先导溢流阀的高精密设计及减振器阻尼匹配、优化提供理论指导。

CDC减振器阀片热变形建模研究

阀片变形极大地影响了减振器的阻尼特性,提高阀片变形量的计算精度,可进一步精确分析CDC减振器的阻尼特性。根据热弹性理论和大、小挠度理论,推导了环形阀片任意半径处的变形解析解,从而建立了温度-压力复合作用下的阀片变形数学模型,开展了温度场和静力学仿真验证,基于Simulink搭建了考虑阀片热变形的CDC减振器阻尼力的数学模型,并将仿真结果与实验结果进行对比。结果表明:阀片变形解析解与仿真结果误差在5%以内,阻尼力模型仿真结果与实验结果误差在10%以内。该阀片变形数学模型和阻尼力模型均提高了减振器阻尼特性的计算精度,为阀片变形计算和减振器阻尼特性的研究提供了理论基础。

复杂边界条件下功能梯度圆环板平稳随机振动响应特性分析

提出一种可用于分析复杂边界条件下功能梯度圆环板平稳随机振动响应特性的谱几何法‑虚拟激励法(spectro geometric method‑pseudo excitation method,SGM‑PEM)。采用沿圆环板边界均匀分布的边界约束弹簧来模拟复杂边界条件,通过虚拟激励法将平稳随机载荷转化为虚拟简谐载荷。在一阶剪切变形理论框架下,采用以简洁三角函数为内核的谱几何法来描述圆环板结构的位移容许函数。基于Rayleigh‑Ritz法推导了平稳随机激励作用下功能梯度圆环板的动力学分析模型。通过与有限元法结果对比分析,验证了文中构建的分析模型的有效性和准确性。分析了梯度指数、厚度参数、边界条件等因素对功能梯度圆环板平稳随机振动响应特性的影响规律。

CFRP对称铺层环形法兰连接拉伸刚度计算方法

为计算碳纤维增强复合材料(carbon fiber reinforced plastic,CFRP)对称铺层环形法兰连接的拉伸刚度,基于圆板对称弯曲和经典层合板理论提出一种考虑环向支撑、材料各向异性和撬力作用系数的计算方法。在制备过程中,采用预浸料手工铺设和模压成型的方法成型试件,而后开展了3组不同法兰板厚度(2.2,3.0,3.8 mm)连接件轴向拉伸试验。通过对比理论计算值与试验结果,验证了计算方法的正确性,误差均不大于13.61%。通过理论模型分析影响因素,结果表明:拉伸刚度随法兰板厚度、外径和内径的增大而增大,随螺栓所在的半径变大而减小;改变螺栓位置对于拉伸刚度的提升比改变法兰板内外径更显著,当螺栓位置由90 mm调整至85 mm时,拉伸刚度提升59.54%。