正交各向异性中厚环形板轴对称弯曲问题的解析解

本文从中厚板理论出发,对正交各向异性环形板在轴对称横向荷载作用下的弯曲问题进行了探讨。     

中厚矩形夹层板稳定问题的一般解

本文基于Ｒｅｉｓｓｎｅｒ理论和胡海昌的简化计算方法,提出了矩形夹层板弹性稳定问题的一般解析解,它适用于各种边界条件下单向受压的中厚夹层板。从而使类问题的求解一般休、格式化。     

Reissner板弯曲问题的渐近解

本文从分析Ｒｅｉｓｓｎｅｒ板理论与Ｋｉｒｃｈｈｏｆｆ板理论的关系入手，导出了对Ｒｅｉｓｓｎｅｒ板问题的求解，可用摄动技术转化为相应边界条件下求解一系列Ｋｉｒｃｈｏｆｆ板问题，最后给出了算例也证明了本文方法具有简单，精度高的特点。     

正交各向异性中厚板轴对称弯曲问题

本文应用中厚板理论对正交各向异性板轴对弯曲问题进行探讨，导出了用平均位移和转角表示的内力和位移的表达式以及这类问题的一般解析解。     

双参数地基上弹性厚板弯曲的一般解析解

针对大型工程建设中水泥混凝土场坪的地基上的Reissner弹性厚板弯曲问题,本文采用复级数方法将其转化为常系数偏微分方程组的边值问题,并首次得到了任意边界条件下的一般解析解。该解形式简单,计算方便、可靠。以板的中部、板边中部和板角部位承受局部载荷为例进行了分析验算,与己有的计算结果相比,计算结果相当满意。     

复合材料夹层板弯曲修正的Reissner理论

本文对大高度、软夹芯的复合材料夹层板的弯曲问题,提出了一种新的修正的Reissner理论。该理论对Reissner的线性特性进行了非线性修正;引入夹芯弹性支撑作用对变形与应力的修正。修正项由Reissner理论结果确定,并最终归结为求解Reissner理论问题,使计算更精确而应用亦较方便。      

具有边梁的悬臂矩形板的弯曲问题

本文建议一个求解具有边梁悬臂矩形板弯曲问题的解析解法。该法将有边梁和无边梁悬臂矩形板弯曲问题的解融为一体,在有边梁悬臂矩形板的解中令边梁弯曲刚度为零即得到无国梁悬臂矩形板的解。     

压电扇形板弯曲的三维精确解

本文利用Ding et al^[1]提出的横观各向同性压电材料三维问题的通解,求得了压电扇形板在表面正应和和电位移或电势作用下的三维精确解,该解可退化为圆板情形。     

功能梯度曲梁弯曲问题的解析解

该文采用弹性力学逆解法,求得了功能梯度曲梁在端部受弯矩作用的解析解。假设弹性模量E=E₀rⁿ沿径向呈幂函数的梯度分布。根据弹性力学平面问题的基本方程,在极坐标系下,引入应力函数,得到了弯曲问题的解析解。进而将功能梯度曲梁问题进行扩展,求得了整环或厚壁圆筒以及向错问题的解析解。将所得到的解退化到均匀弹性情况,与经典的理论解一致。最后对梯度函数按幂函数变化的算例进行了分析,结果显示梯度因子n对应力及位移的分布产生了巨大的影响。该文所得到的结论可以作为功能梯度曲梁构件优化设计的理论基础。     

基于高阶剪切理论的复合材料格栅夹层板弯曲特性

基于高阶剪切弯曲理论,对含有软质芯材的复合材料格栅夹层板的弯曲特性进行了理论研究。基于能量法,推导了含有软质芯材的复合材料格栅的等效弹性参数计算式;基于高阶剪切弯曲理论,推导了夹层板的弯曲平衡微分方程,并采用Navier方法,给出了分布载荷作用下四边简支、上下表层为对称正交铺层的夹层板弯曲问题的理论解;用算例对典型格栅夹层板的理论解和有限元仿真解进行了对比,两者误差为7.1%,验证了本文理论方法的正确性;并分析了夹层板跨厚比、格栅厚度、格栅复合材料铺层角度、格栅间距等参量对含有软质芯材的典型复合材料格栅夹层板弯曲挠度的影响规律。      

四角点支承厚矩形板弯曲的功的互等定理法求解

本文应用功的互等定理法求解了在均布载荷作用下四角点支承厚矩形板的弯曲问题．首次给出了该问题的精确解析解及其可供工程实际参考的数值图表．     

功能梯度Levinson圆板弯曲解的均匀化和经典化表示

基于Levinson三阶剪切变形理论,研究了材料性质沿厚度任意连续变化的功能梯度材料圆板的轴对称弯曲问题。首先,建立了功能梯度材料圆板在Levinson板理论下轴对称弯曲问题位移形式的控制微分方程,其中考虑了拉-弯耦合和三阶剪切变形效应。然后,利用载荷等效关系以及均匀板的经典理论控制微分方程,导出功能梯度圆板在Levinson剪切变形理论下弯曲解与经典理论下均匀圆板的挠度之间的解析转换关系,给出了转换系数的计算公式。由此,可将功能梯度材料圆板在Levinson三阶剪切理论下的弯曲问题转化为相应均匀薄圆板在经典理论下的弯曲问题求解,以及转换系数的计算问题。     

Optimum distribution of smart stiffeners in sandwich plates subjected to bending or forced vibrations

The problems of optimum distribution of active stiffeners manufactured from piezoelectric or shape memory alloy materials and bonded to or embedded within the facings of a sandwich plate are considered. The sandwich plate consists of thin composite or isotropic facings which are in the state of plane stress and a thick shear deformable core. The amplitude of forced vibrations of the plate is reduced using symmetric couples of piezoelectric stiffeners subjected to out-of-phase dynamic voltages. Shape memory alloy stiffeners are used to reduce bending deformations. In the latter case, a desirable effect is achieved by activating the stiffeners on one side of the middle surface. Optimum design is considered based on the requirement of minimal transverse static or dynamic deflections subject to a constraint on the volume of smart stiffeners. The variables employed in the process of optimization are the ratios of the cross-sectional areas of the stiffeners in each direction to their respective spacings. It is shown, that, dependent on the load, materials, and geometry, optimum design can significantly reduce deflections, i.e. enhance the strength, of sandwich plates.     

Non-homogeneous response of cross-ply laminated elastic plates using a higher-order theory

A consistent formulation for the bending of cross-ply laminated composite plates that possess non-homogeneous elastic properties is presented. Based on a third-order shear deformation plate theory, the governing equations are obtained using the principle of virtual work. With the help of the small parameter method, a wide variety of results are presented for the symmetric and antisymmetric analysis of non-homogeneous rectangular laminated plates. The influence of non-homogeneity, lamination schemes, aspect ratio and material anisotropy on the deflections and stresses is investigated. The new results for non-homogeneous response of composite plates should serve as bench marks for future comparisons.     

基于修正单层梁理论的夹层梁最大弯曲正应力计算

目的计算夹层梁横截面的最大弯曲正应力。方法将夹层梁等效成等截面均质单层梁,进而推导出了理论计算公式,并在此基础上进行了三点弯曲试验的算例研究。结果当破坏载荷与夹层梁横截面的尺寸一定时,随着芯层与总厚度比的增加,修正单层梁理论计算的最大正应力值逐渐增加,而单层梁理论计算的结果为恒定值。对于同样结构的夹层梁,随着芯层弹性模量与表层模量比的增加,修正单层梁理论计算的最大正应力与单层梁理论的差异值越来越小。结论修正单层梁理论与层合梁理论计算的结果是一致的,该方法可有效进行最大弯曲正应力的预测与计算。     

板壳分析与应用

板壳分析是现代固体力学的一个重要分支。这门学科几乎与一切工程设计都有关联,对航天、航空、航海、机械、石化、建筑、水利、动力、仪表、交通等工程设计,尤其具有指导意义。现今,经典的薄板壳线性 理论已较成熟,并在各种工程设计中起着指导作用。然而,在薄板壳非线性领域和厚板壳线性领域,还有许多问题未被解决。章在介绍这门学科发展历史的基础上,概述了作近四十年结合工程实际对波纹板壳、单层板壳、双层金属旋转扁壳、网格扁壳、夹层板壳和复合材料层合板壳等六类薄板壳的非线性弯曲、稳定和振动问题以及厚、薄板壳弯曲问题进行理论探索的情况。     

Buckling Analysis of Composite Sandwich Plates with Flexible Core Using Improved High-Order Theory

A new improved high-order theory is presented for global and local buckling analysis of sandwich plates with soft orthotropic core. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of plate are satisfied. Overall buckling loads, as well as wrinkling loads, are obtained for various sandwich plates. Effect of geometrical parameters and material properties of face sheets and core are studied on the overall buckling and face wrinkling of sandwich plates.     

基于哈密顿解法的厚板边界效应典型算例分析

在平板弯曲问题中存在边界效应现象。这个现象用Reissner厚板理论可以论证,而经典薄板理论则无法解释。边界效应现象在板的自由边界附近表现最为典型。该文首先选取均载作用下的三边简支,一边自由的矩形厚板作为典型问题,采用哈密顿解法求出解析解。然后结合这个典型问题,对边界效应现象进行分析,对其影响因素和影响范围进行讨论。     

Bending analysis of functionally graded piezoelectric plates via quasi-3D trigonometric theory

Abstract

This work is devoted to the bending analysis of functionally graded piezoelectric (FGP) material plate by using a simple quasi-3D sinusoidal shear deformation theory under simply supported edge conditions. The governing equations and boundary conditions are derived by using the principle of virtual work. The impact of piezoelectric, electric loading, and gradient index on the displacement, electric displacement, electric potential, and stresses are explored numerically presented and discussed in detail. To check the accuracy and validity of bending results obtained from this analysis of FGP plates, results are compared with the analytical solution obtained by 3D, quasi-3D, and higher order shear deformation theories. Parametric studies are then performed to examine the effects of the thickness of the plate and the electric field on the overall electro-mechanical response of the FGP plates. The presented results are useful in design processes of smart structures and analysis from piezoelectric materials.