Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

Accurate Free Vibration of Functionally Graded Skew Plates

The present study aims to analyze free vibration of thin skew plates made of functionally graded material(FGM)by using the weak form quadrature element method.The material properties vary continuously through the thickness according to a power-law form.A novel FGM skew plate element is formulated according to the neutral surface based plate theory and with the help of the differential quadrature rule.For verifications,Numerical results are compared with available data in literature.Results reveal that the non-dimensional frequency parameters of the FGM skew plates are independent of the power-law exponent and always proportional to those of homogeneous isotropic ones when the coupling and rotary inertias are neglected.In addition,employing the physical neutral surface based plate theory is equivalent to using the middle plane based plate theory with the reduced flexural modulus matrix.

Nonlinear Free Vibration of Reinforced Skew Plates with SWCNs Due to Finite Strain

This paper is an attempt to investigate the nonlinear free vibration of skew plates reinforced by carbon nanotubes(CNTs)due to finite strain tensor.The material properties of the nano-composite are estimated using the molecular dynamic results and the rule of mixture.Also,the differential equations governing the motions are derived on the basis of Classical Plate Theory(CPT)regarding the nonlinear Green-Lagrange strain tensor.In order to solve the nonlinear equations,Galerkin’s method,Frechet derivative and differential quadrature method are used.The effects of volume fraction of functionally graded materials(FGM),skew angle,distribution of CNTs and geometrical features of the plate on the nonlinear vibration of system have been studied.The results of this study have been compared with other researches and a good agreement has been achieved.

NAVIER SOLUTION FOR THE ELASTIC EQUILIBRIUM PROBLEMS OF ANISOTROPIC SKEW THIN PLATE WITE VARIABLE THICKNESS IN NONLINEAR THEORIES

This paper discusses the elastic equilibrium problems of anisotropic skew thin plate of variable thickness simply supported on all four sides in nonlinear theories, and uses the Navier method to seek an approach to the problem, and to illustrate the solution with the examples. In conclusion, the mention is made of the scope of application and the convergency of the solution.

全框支厚板转换斜交高层结构抗震性能研究

设计制作1∶15全框支厚板转换高层结构的微粒混凝土振动台试验模型,进行7度小震、中震、大震以及8度大震作用下单向、双向、三向共计44组工况的振动台试验,研究动力特性、动力放大系数、层间位移角等性能指标,揭示结构塑性损伤发展机制,进一步采用数值模型研究上部塔楼斜交角度对结构抗震性能的影响。结果表明,全框支厚板转换高层结构具有优良的抗震性能,模型结构经历8度大震后,全框支层未见明显裂缝,处于轻微损坏与完好之间,塔楼剪力墙底部和连梁端部裂缝发生明显,薄弱部位集中在3~10层;模型结构动力放大系数沿高度呈“S”形分布模式,在塔楼顶部放大明显,而全框支层的动力放大系数在不同烈度地震作用下始终处于1~2之间;塔楼斜交角度对此类结构体系动力特性和动力响应的影响很小,全框支层均能对上部不同斜交角度的塔楼起到充分的约束作用,上部塔楼承担绝大部分地震输入能量,全框支层的动力放大系数和动力响应均远低于上部塔楼,全框支厚板转换斜交高层结构体系能够实现“强全框支层弱塔楼”设计理念。

基于Skew-t-GJRGARCH(1,1)模型的5G板块风险度量研究

本文对5G板块进行风险度量研究,结果表明:对数收益率序列存在有偏、尖峰厚尾、非正态的特征,同时具有ARCH效应;通过拟合不同分布下的GJRGARCH(1,1)模型,发现5G板块不存在杠杆效应;采用GJRGARCH(1,1)模型在不同分布下进行VaR计算,由Kupiec检验得到基于skew-t分布的GJRGARCH(1,1)模型可以更好地度量5G板块的金融风险,其可信度和稳健性强。

Free Vibration Analysis of Functionally Graded Plates with Multiple Circular and Non-circular Cutouts

Cutouts are inevitable in structures due to practical consideration.In order to investigate the free vibration of functionally graded plates with multiple circular and non-circular cutouts,finite element method is used.The volume fraction of the material constituents is assumed to follow a simple power law distribution.The parameters considered in this paper are as follows：cutout size,cutout location,number of cutouts and different boundary conditions.It should be mentioned that free vibration for FG plates（such as rectangular？skew？trapezoidal？circular plates） with multiple cutouts has not been studied yet and hence the results out coming from this paper may be used as bench marks for future works.

Prediction of Skewed Bridge Behaviors with Arbitrary Boundary Conditions—— Theoretical Approach and Its Design Application

In this paper, we report on an analytical solution for beam-type skewed highway bridges subjected to truck loading. To confirm the analysis derivation and the solution obtained, the moment and shear responses to the design truck load are acquired using the analytical method for a number of typical US highway bridges and compared with those from numerical finite element method （FEM） analysis. In addition, the lateral distribution factors for moment and shear used in routine design are investigated based on comparison of the analytical approach and FEM. The analytical solution is shown in good agreement with the FEM result. Furthermore, the relevant provisions in the American Association of State Highway Transportation Officials＇ （AASHTO＇s） LRFD Bridge Design Specifications are also discussed here for comparison, particularly with respect to design application. It is observed that the design code specified load distribution factor may not predict well, especially for shear and/or severe skew.

基于群速度校准的超声导波技术及在复合材料缺陷检测中的应用

由于在复合材料板中传播的超声导波具有偏斜效应,使得理论群速度与试验测得的群速度不一致,因此需要对群速度幅值和传播方向进行校准。数值计算复合材料板中超声导波频散方程得到S0模态各个方向的理论相速度频散曲线。运用群速度校准法则对S0模态群速度幅度和传播方向进行修正。校准后的理论群速度与试验测得的群速度较为吻合。试验中采用频率200 kHz的S0模态对碳纤维复合材料板中的模拟缺陷进行检测。结果显示采用校准后群速度和试验测得的群速度可准确定位缺陷,且具有很好的一致性。因此,采用群速度校准法则可有效提高各向异性复合材料结构中超声导波的缺陷定位和识别能力。

参数变化对简支斜板屈曲承载力的影响规律

针对斜向肋箱梁结构中的局部屈曲失稳问题,推导斜坐标系下简支边的弯矩计算公式、纵向面内载荷作用下斜板的屈曲平衡微分方程,将调和微分求积法和边界融入法相结合,给出调和边界融入微分求积法求解简支斜板局部稳定性的具体方法.最后以单向轴压或剪应力作用下的简支斜板为例,研究载荷变化系数、斜板边长比、倾角与屈曲临界载荷之间的关系.结果表明:单向轴压作用下简支斜板屈曲临界载荷随载荷变化系数的增大而增大,随倾角的增大而减小,随边长比的增大先增大后减小再增大;剪应力作用下简支斜板屈曲临界载荷随边长比的增大而增大,随倾角的增大先减小后增大.

有自由边的各向异性平行四边形板的弯曲、振动与屈曲的傅里叶分析

得到了有自由边的各向异性平行四边形板在面内张力和剪力作用下自由振动、屈曲和弯曲问题的精确解析解。首先给出五个重傅里叶级数叠加解,然后通过叠加得到六种不同边界的解,包括悬臂板和四边自由的板等。对一些典型情况考查了其收敛性,结果令人满意。与其它精确解析解比较,其结果非常一致。

平行四边形加肋板自由振动分析的无网格法

基于一阶剪切理论,提出一种求解平行四边形加肋板自由振动问题的无网格法,通过用一系列点来离散平板及肋条,得到加肋板的无网格模型。基于一阶剪切理论及移动最小二乘近似求出位移场,以梁模拟肋条,求出平行四边形加肋板总动能及总势能。再由Hamilton原理导出加肋板自由振动的控制方程,采用完全转换法引入边界条件,求解方程得出结构自振频率。以不同参数的加肋板为例,将该文解与ABAQUS有限元解进行比较分析。研究表明,该方法能有效地分析平行四边形加肋板自由振动问题,在肋条位置改变时,又避免了网格重构。

有面内张力和剪力作用的简支各向异性平行四边形板自由振动、屈曲和弯曲的精确解

对简支各向异性平行四边形板在面内张力和剪力作用下自由振动、屈曲和弯曲问题作了全面的研究。利用叠加法和本问题所固有的对称性优点得到了重富立叶级数解。与现有结果的比较验证了此法的精确性。文后给出了多种几何条件下的自由振动、屈曲和弯曲的数值结果。

斜交板弯曲理论的斜交坐标法

斜交板是工程中的一种常用结构,建立其弯曲微分方程是获得解析解的难点和关键.本文在正交坐标系的薄板弯曲理论的基础上,利用坐标转换,建立了斜交坐标系中各向同性、正交异性和斜交异性的斜板弯曲微分方程,并简要介绍该方法推广应用于平行四边形斜板有限元法的思路.较文献[1-3]的方法而言,利用本文提出的斜交坐标转换法可大大简化弯曲微分方程推导过程,且可方便地推广应用到斜交箱梁等其它结构中.

MY准则解析受均布载荷简支斜板极限载荷

为了得到斜板极限载荷的解析解,用平均屈服(MY)准则,对受均布载荷的简支金属斜板进行了塑性极限分析.首次获得MY准则下斜板极限载荷的解析解,该解是斜板几何参数长l1,宽l2以及长宽夹角θ的函数.研究表明:随着θ的增大,极限载荷先增大而后减小;斜板面积增加,极限载荷减小.得到了菱形、矩形和方形板的解析解,并将方形板的解析解与Tresca、Mises以及TSS提供的极限载荷进行比较,对比表明:方板的极限载荷与边长成反比关系,Tresca屈服准则提供极限载荷的下限,TSS屈服准则提供上限,MY准则预测结果恰居二者中间,且最靠近Mises解.

一种考虑剪切变形的平行四边形厚/薄板通用单元

根据Timoshenko二广义位移梁理论 ,构造了深梁位移场的插值函数。利用斜坐标系与直角坐标系的变换关系、有限条带思想和深梁位移插值函数 ,构造了一种考虑剪切变形的平行四边形厚 薄板弯曲通用单元的位移 (曲率、剪应变、转角、横向位移 )插值函数 ,导出了刚度矩阵和非结点荷载等效力。并对简支 固支方板、Razzaque斜板、四边简支斜交板弯曲进行了数值计算。算例表明此单元有较好的精度 ,对于薄板不出现剪切闭锁 。

关于斜交异性斜板的弯曲理论

作为对作者以前发表的外交各向异性极弯曲理论[1～3]的改进，文中对这种材料异性极的弯曲，从新的应变关系和物理方程出发，演引出新的弹性平衡微分方程，并提示其实用近似求解方法．

面内平动功能梯度斜板的主动振动控制

对新型功能梯度材料制成的面内平动斜板,通过直角坐标系和斜角坐标系的坐标变换,建立了在斜角坐标系下受多个集中控制力作用的横向振动控制微分方程。采用微分求积法,将微分方程和边界条件对空间坐标进行离散化处理,得到了时域内振动控制系统的状态方程。应用最优控制法,对面内平动功能梯度斜板的无量纲运动速度小于一阶无量纲临界速度时的等幅振动和大于一阶无量纲临界速度时的发散失稳两种情况进行了数值仿真,得到控制前后若干个节点挠度随时间的变化曲线。结果表明,该方法能够有效地控制面内平动功能梯度斜板的横向振动,特别是对于发散失稳的抑制。

FGM斜板的振动特性分析

对FGM斜板,通过坐标转换,在斜坐标系下建立了FGM斜板的横向振动微分方程。用微分求积法研究了四边简支和对边固支对边简支FGM斜板的自由振动特性,给出了不同角度和不同边长比下一阶固有频率与梯度指标之间的变化曲线,以及四边简支FGM斜板角度对固有频率的影响。

功能梯度斜板的屈曲分析

研究面内荷载作用下功能梯度斜板的屈曲问题。基于经典板理论,假设材料性质为板厚度方向坐标的幂函数,不考虑温度的影响,推导功能梯度板在纵向荷载作用下的平衡微分方程,运用坐标转换关系,建立斜坐标系下功能梯度斜板的屈曲微分方程。采用微分求积法,离散屈曲微分方程,结合边界条件,给出功能梯度斜板在两对边受有均布压力作用下临界屈曲荷载的无量纲数值解。在此基础上,讨论板的几何外形尺寸、夹角、梯度指标以及中面变形等因素对临界屈曲荷载的影响。结果表明:功能梯度板的临界屈曲荷载变化介于相应的均质各向同性板的临界屈曲荷载变化之间;功能梯度材料板的临界屈曲荷载变化随板的相对几何外形尺寸宽长比b/a的减小而减小,随梯度指标k和夹角θ的增加而减小;中面变形对夹角较小和梯度指标较高的板有较大影响。