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1.
初曲矩形薄板的非线性动力屈曲研究   总被引:1,自引:0,他引:1  
对两参数冲击载荷面内压缩作用下初曲矩形薄板的非线性动力屈曲问题进行了理论研究。首先采用双重余弦函数的组合确定了面内冲击矩形薄板的艾雷应力函数和中面力的分布;其次根据伽辽金法求得了初曲矩形薄板非线性动力屈曲问题的控制方程,基于巴拿赫压缩映象原理,采用逐次逼近方法求解了该控制方程。最后,应用本文发展的理论,给出了面内两参数冲击载荷作用下初曲矩形薄板动力屈曲响应的计算实例,计算结果与已有的实验结果较吻合  相似文献   

2.
基于双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板的屈曲问题. 首先,基于能量法与变分原理,给出了梯度弹性基础上正交异性薄板的屈曲控制方程,并得到了梯度弹性基础刚度系数K1 与K2的计算式;进而,通过将位移函数采用三角函数展开的方法,给出了单向压缩载荷作用下、四边简支正交异性弹性基础板屈曲载荷的计算式;在算例中,通过将该文的解退化到单纯的正交异性板,并与经典弹性解比较,证明了理论的正确性;最后,求解了弹性模量在厚度方向上呈幂律分布的梯度基础上的薄板屈曲问题,分析了基础上下表层材料弹性模量比与体积分数指数对屈曲载荷的影响.  相似文献   

3.
多孔功能梯度材料(FGM)构件的特性与孔隙率和孔隙分布形式有密切关系。本文基于经典板理论,考虑不同孔隙分布形式时修正的混合率模型,研究Winkler弹性地基上四边受压多孔FGM矩形板的自由振动与临界屈曲载荷特性。首先利用Hamilton原理和物理中面的定义推导Winkler弹性地基上四边受压多孔FGM矩形板自由振动的控制微分方程并进行无量纲化,然后应用微分变换法(DTM)对无量纲控制微分方程和边界条件进行变换,得到计算无量纲固有频率和临界屈曲载荷的代数特征方程。将问题退化为孔隙率为零时的FGM矩形板并与已有文献进行对比以验证其有效性。最后计算并分析了梯度指数、孔隙率、地基刚度系数、长宽比、四边受压载荷及边界条件对多孔FGM矩形板无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。  相似文献   

4.
通过在Hellinger-Reissner广义势能中引入应变的非线性项,推导出了弹性力学Hamilton体系下的具有初应力的振动方程,并运用精细积分给出了两端简支的梁、组合梁和四边简支板及组合板在初应力下振动频率。本文结果是严格弹性力学意义(没有引入任何几何变形假设)下的精确解,为衡量各种计入剪切变形的薄板、中厚板理论的准确性提供了一个标准。  相似文献   

5.
针对强厚度矩形板四边简支情况,论文根据状态变量法思想,基于三维弹性理论基本方程,以3个位移分量及3个应力分量按双三角级数展开,将三维弹性力学控制方程转化为常微分方程边值问题.尽管一些各向异性弹性矩形厚板早已由状态空间法获得分析解,可是各向同性厚板的分析解至今难以获得,因为状态空间解法中特征方程有重根问题而不易于收敛.论文提出采用插值矩阵法直接对常微分方程进行求解,获得各向同性矩形厚板在四边简支边界条件下三维理论的位移和应力解,并与有限元精细结果进行比较,证明了本文解的准确性.  相似文献   

6.
矩形板屈曲问题的一个小波解   总被引:1,自引:0,他引:1  
利用Wavelet-Galerkin法分析了四边固支与四边简支矩形板的屈曲问题.以小波作为基函数表示板的挠度,推导出屈曲系数及屈曲模态的计算过程.数值计算给出了不同边长比的矩形板的屈曲系数及屈曲半波数.与传统的三角函数作基函数的Galerkin法及有限元法结果比较,结果表明在一定条件下小波可以作为试函数解决结构力学的屈...  相似文献   

7.
建立考虑横向剪切与转动惯量影响的矩形板的动力控制方程,应用Galerkin方法将其化为Mathieu方程,然后根据Lyapunov-Schmidt方法得到了系统在参数激励下的1/2亚谐分叉特性,并给出了四边简支与四边固支弹性薄板的非线性动力屈曲分叉条件。  相似文献   

8.
利用辛几何方法本文推导出了四边固支矩形弹性薄板弯曲问题的精确解析解.由于在求解过程中不需要事先人为的选取挠度函数,而是从弹性薄板的基本方程出发,首先将矩形薄板弯曲问题表示成Hamilton正则方程,然后利用分离变量和本征函数展开的方法求出可以完全满足四边固支边界条件的精确解析解.本文中所采用的方法突破了传统的半逆法的限制,使得问题的求解更加合理化.文中还给出了计算实例来证明推导结果的正确性.  相似文献   

9.
矩形屈曲板受微扰时的浑沌现象   总被引:6,自引:0,他引:6  
用Melniko-Holmes方法研究四边简支的弹性矩形薄板可能发生浑沌振动的临界条件,所提出的方法适用于具有各种边界条件和载荷工况 大量的其它类似问题。  相似文献   

10.
研究Winkler地基上正交各向异性矩形薄板弯曲方程所对应的Hamilton正则方程, 计算出其对边滑支条件下相应Hamilton算子的本征值和本征函数系, 证明该本征函数系的辛正交性以及在Cauchy主值意义下的完备性, 进而给出对边滑支边界条件下Hamilton正则方程的通解, 之后利用辛叠加方法求出Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的解析解. 最后通过两个具体算例验证了所得解析解的正确性.  相似文献   

11.
开孔平板的剪切稳定性实验   总被引:2,自引:0,他引:2  
查煜峰 《实验力学》1989,4(4):406-410
对四边简支和四周边受均匀剪切力的矩形薄平板的屈曲失稳,作了实验分析及数值计算.用作者所设计的剪切试验装置,对一组开孔及开孔后加强的薄平板进行了剪切稳定性试验,求得薄平板失稳时的载荷——挠度曲线及失稳波形,由曲线上拐点来确定平板失稳临界载荷,并将实验结果与有限元数值计算结果作了比较.  相似文献   

12.
角点支承矩形薄板的屈曲问题是板壳力学的一类重要课题,控制方程和边界条件的复杂性导致寻求该类问题的解析解十分困难。虽然各类近似/数值方法可用于解决此类难题,但作为基准的精确解析解在公开文献中鲜有报道。本文基于近年来提出的辛叠加方法,解析求解了四角点支承四边自由矩形薄板的屈曲问题。首先将问题拆分为两个子问题,接着利用分离变量与辛本征展开推导出子问题的解析解,最后通过叠加获得原问题的解。由于求解过程从基本控制方程出发,逐步严格推导,无需假定解的形式,因此本文解法是一种理性的解析方法。数值算例给出了不同长宽比和不同面内载荷比情况下,四角点支承四边自由矩形薄板的屈曲载荷和典型屈曲模态,并经有限元方法验证,确认了解析解的正确性。  相似文献   

13.
中面单向受拉(压)的阶梯式矩形薄板的振动   总被引:1,自引:0,他引:1  
张英世  顾煜炯 《力学季刊》1999,20(4):437-442
用奇异函数建立x=0与x=a两对边简支并受面内均布拉(压)力作用、加两边为任意支承、非单一材质的n级阶梯式矩形薄板自由振动和强迫振动的微分方程并求得其通解,用W算子给出振型了函数的表达式及常见支承条件下板的方程。文中给出的固有频率表达式表明,面内均布拉(压)力对固有的数值有影响。此处导出的各种情况下的影响函数,对于求解相应民政部下的阶梯式矩形薄板的静力弯曲和稳定性问题,也是适用的。  相似文献   

14.
DYNAMIC BUCKLING OF STIFFENED PLATES UNDER FLUID-SOLID IMPACT LOAD   总被引:1,自引:0,他引:1  
A simple solution of the dynamic buckling of stiffened plates under fluid-solid impact loading is presented. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton‘ s principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method, the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained from Budiansky-Roth ( B-R ) curves.  相似文献   

15.
In this research work, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the classical plate theory based on exact neutral surface position is employed to derive the governing stability equations. Considering Levy-type solution, the buckling equation reduces to an ordinary differential equation with variable coefficients. An exact analytical solution is obtained for this equation in the form of power series using the method of Frobenius. By considering sufficient terms in power series, the critical buckling load of functionally graded plate with different boundary conditions is determined. The accuracy of presented results is verified by appropriate convergence study, and the results are checked with those available in related literature. Furthermore, the effects of power of functionally graded material, aspect ratio, foundation stiffness coefficients and in-plane loading configuration together with different combinations of boundary conditions on the critical buckling load of functionally graded rectangular thin plate are studied.  相似文献   

16.
Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article. The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio, thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.  相似文献   

17.
Large deflection and postbuckling responses of functionally graded rectangular plates under transverse and in-plane loads are investigated by using a semi-analytical approach. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The plate is assumed to be clamped on two opposite edges and the remaining two edges may be simply supported or clamped or may have elastic rotational edge constraints. The formulations are based on the classical plate theory, accounting for the plate-foundation interaction effects by a two-parameter model (Pasternak-type), from which Winkler elastic foundation can be treated as a limiting case. A perturbation technique in conjunction with one-dimensional differential quadrature approximation and Galerkin procedure are employed in the present analysis. The numerical illustrations concern the large deflection and postbuckling behavior of functional graded plates with two pairs of constituent materials. Effects played by volume fraction, the character of boundary conditions, plate aspect ratio, foundation stiffness, initial compressive stress as well as initial transverse pressure are studied.  相似文献   

18.
基于Von Karman非线性板理论和Kachanov-Rabotnov损伤理论,建立了在横向和面内载荷共同作用下考虑蠕变损伤效应的矩形板的非线性控制平衡方程,采用有限差分法和时间增量算法对未知变量进行离散,对整个问题进行迭代求解,分析了几何非线性、荷载等因素对板非线性蠕变损伤特性的影响。  相似文献   

19.
The present paper deals with dynamic, coupled buckling of long, prismatic columns simply supported at the ends. This investigation concerns thin-walled structures of a square cross-section with or without intermediate stiffeners under in-plane pulse loading. The dynamic load of a rectangular shape has been assumed in the analysis. The structures are composed of rectangular plates interconnected along longitudinal edges. A plate model is adopted in the analysis. The material of the structure is isotropic. The problem has been investigated on the basis of the disturbance theory. The dynamic critical load factor DLF has been determined using the Budiansky and Hutchinson criterion. The results obtained with the analytical-numerical method (ANM), which employs the asymptotic perturbation theory, have been compared with the finite element method (FEM).  相似文献   

20.
A dynamic method is described for determining the linear buckling loads of elastic, perfectly flat, rectangular plates. The proposed method does not require the application of in-plane loads; it requires only vibrational excitation of the plate. The buckling load is determined from the measured normal modes of vibration. The method is applicable to isotropic as well as anisotropic plates with any type of edge support. The accuracy of the dynamic method was evaluated by tests in which buckling loads of aluminum and graphite fiber-reinforced-epoxy composite plates were determined both by the dynamic method and by imposing static in-plane loads on the plates. The results of the dynamic and static tests agree closely. A. Segall (on leave from RAFAEL, Israel)  相似文献   

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