弹性地基上正交各向异性变厚度圆薄板的大挠度问题

本文推出了均布载荷下弹性基地上的正交各向异性变厚度圆薄板大挠度问题的基本方程。利用修正迭代法获得了该问题的二阶近似解。     

变厚度圆薄板在均布载荷下大挠度问题

本文首先给出变厚度圆薄板大挠度方程,用小参数方法和修正迭代法联合求解此问题,得到三次近似解;给出特征曲线同线性理论进行了比较.     

变厚度圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题

本文首先导出变厚度圆柱型正交各向异性圆形薄板的非线性非对称弯曲的基本方程，利用“两变量法”，引进四个小参数，对厚度线性变化的圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题进行研究，得到了挠度函数W（r，θ）和应力函数F（r，θ）对ε1为N阶及对ε2为M阶的一致有效渐近解．     

变厚度各向导性斜形簿板的弹性平衡问题的Navier解

本文首先对变厚度各向异性斜形薄板有关非线性理论的弹性平衡问题进行了讨论,建立了变厚度各向异性斜形薄板的大挠度问题的基本方程,然后采用Navier法,给出了求解的一般途径,并以示例说明求解的具体方法,最后讨论了解的收敛性及本方法的应用范围.     

在复合载荷作用下变厚度圆薄板大挠度问题

本文用变厚度板壳大挠度理论的修正迭代法[1],对周边固定,在复合载荷下的变厚度圆薄板进行了求解,从而得到了精确度较高的二次近似解析解.将本文的结果退化到特殊情况就可以得到和文[1、2]完全一致的结果.本文还绘出特征曲线进行比较,其结果是理想的.     

正交各向异性板壳理论中的Schrǒdinger方程

本文是文[1～5]的继续。在本文中: (1) 将正交各向异性薄壳的小挠度振动问题或Winkler地基上正交各向异性薄板的小挠度振动问题所服从的Love-Kirchhoff方程化归为矩阵各向异性Schr(?)dinger方程的求解,由此可以利用文[1]和[3～5]中的方法得到这两类问题的通解; (2) 将正交各向异性扁壳大挠度问题的Von K(?)rm(?)n-BaacoB方程(其特例为正交各向异性薄板大挠度问题的von Karman方程)化归为AKNS方程即Dirac方程的形式,从而可以利用文[4～5]中的散射反演方法得到这两类问题的精确解。 波纹板壳和加肋板壳的小挠度问题的通解或大挠度问题的精确解,作为特例包含在本文中。     

极正交各向异性圆薄膜大挠度问题

本文主要用摄动法和积分方程的数值积分方法求解受预加张力的极正交各向异性圆薄膜在均布荷载作用下的轴对称大挠度问题,得到了荷载、薄膜力及挠度与中心挠度的关系,它们与材料系数的比K=E_■|E_r~(1/2)有关.当K→时,所得结果与各向同性圆薄膜的结果相吻合。     

对“变厚度圆薄板在均布载荷下大挠度问题”解法的讨论

文献[1]用小参数法和修正迭代法联合求解了“变厚度圆薄板在均布载荷下的大挠度问题”,文[1]中所得到的解以及各种特殊情况都是正确的.但文[1]中求解步骤仍属于摄动法的求解过程,并且文[1]中将载荷项设为:     

复合荷载下波纹圆板的非线性分析*

本文按照各向同性和正交各向异性圆板的大挠度理论,研究了具有光滑中心的波纹圆板在均布和中心集中荷载联合作用下的非线性弯曲问题.应用修正迭代法,我们得到了夹紧固定和滑动固定两种边界条件下十分精确的解析解.     

变厚度圆薄板非对称非线性弯曲问题

首先将直角坐标系中的横向变厚度薄板的大挠度方程,转化到极坐标系中的变厚度圆薄板的非对称大挠度方程·　此方程和极坐标系中径向、切向两个平衡方程联立求解·　将物理方程和中面应变非线性变形方程,代入3个平衡方程,可得用3个变形位移表示的3个非对称非线性方程·　用Fourier级数表示的解代入基本方程,获得相应的基本方程·　在周边夹紧边界条件下,用修正迭代法求解·　作为算例,研究了余弦形式载荷作用下的问题,还给出了载荷与挠度的特征曲线,曲线依据变厚度参数变化而变化,其结果和物理概念完全吻合·     

Chaotic and bifurcation dynamics of a simply-supported thermo-elastic circular plate with variable thickness in large deflection

This paper presents the conditions that can possibly lead to chaotic motion and bifurcation behavior for a simply-supported large deflection thermo-elastic circular plate with variable thickness by utilizing the criteria of fractal dimensions, maximum Lyapunov exponents and bifurcation diagrams. The governing partial differential equation of the simply supported thermo-elastic circular plate with variable thickness is first derived by means of Galerkin method. Several different features including Fourier spectra, phase plot, Poincar’e map and bifurcation diagrams are numerically computed. These features are used to characterize the dynamic behavior of the plate subjected to various excitations of lateral loads and thermal loads. Numerical examples are presented to verify the conditions that lead to chaotic motion and the effectiveness of the proposed modeling approach. Numerical modeling results indicate that large deflection motion of a thermo-elastic circular plate with variable thickness possesses chaotic motions and bifurcation motion under different lateral loads and thermal loads. The simulation results also indicate that the periodic motion of a circular plate can be obtained for the convex or the concave circular plate. The dynamic motion of the circular plate is periodic for the cases including (1) the lateral loading frequency is within a specific range, (2) thermal and lateral loadings are operated in a specific range and (3) the thickness parameter is less than a specific critical value for the convex circular plate or greater than a specific critical value for the concave circular plate. The modeling results show that the proposed method can be employed to predict the non-linear dynamics of any large deflection circular plate with variable thickness.     

Stochastic Normal Deflections of Orthotropic and Composite Rectangular Plates

A general method of analysis based on random variable transformations technique is presented for studying stochastic normal deflection of composite plates. A simply supported orthotropic rectangular thin plate model with indeterminate elastic coefficients is investigated to obtain the marginal density function of its maximum normal deflection under a uniform load. A general closed form marginal density function of the maximum normal deflection is obtained. The method of analysis is illustrated through studying different cases for the distributions of the considered stochastic variables. A numerical study of the uniform distribution case is performed.     

Transverse vibration of nonhomogeneous orthotropic viscoelastic circular plate of varying parabolic thickness

An analysis of the transverse vibration of nonhomogeneous orthotropic viscoelastic circular plates of parabolically varying thickness in the radial direction is presented. The thickness of a circular plate varies parabolically in a radial direction. For nonhomogeneity of the circular plate material, density is assumed to vary linearly in a radial direction. This paper used the method of separation of variables in solving the governing differential equation. In this paper, an approximate but quite convenient frequency equation is derived by using the Rayleigh–Ritz technique with a two‐term deflection function. Deflection, time period and logarithmic decrement for the first two modes of vibration are computed for the nonhomogeneous orthotropic viscoelastic circular plates of varying parabolic thickness with clamped edge conditions for various values of nonhomogeneity constants and taper constants and these are shown in tabular form for the Voigt–Kelvin model. Copyright © 2011 John Wiley & Sons, Ltd.     

四边固定变厚度正交各向异性矩形板的非线性非对称弯曲问题的一致有效渐近解

利用“修正的两变量法”和“混合摄动法”,引进4个小参数,对厚度线性变化的正交各向异性矩形板的非线性非对称弯曲问题进行了研究,得到了挠度函数W(x,y)和应力函数Φ(x,y)对ε1为N阶及对ε2为M阶的一致有效渐近解．     

修正多重尺度法在求解圆簿板具有很大挠度问题时的应用*

本文利用修正的多重尺度法[1～2]重新研究固支圆薄板在均匀压力作用下,挠度很大时解的渐近性态.结果表明与钱伟长教授用首创的合成展开法求解该问题[3]的结果相一致,但较后者更简捷.本文结果还表明文[4]中所指出文[1～2]方法的局限性是非本质的,并改正文[3]中一些计算错误.     

关于圆簿板大挠度问题的正交条件解法

本文重新考察了钱伟长教授求解圆薄板大挠度问题的系统近似法,发现此法实质上可视为奇异摄动理论中的变形参数法.以无量纲中心挠度为小参数,将挠度、中面薄膜力和载荷参数作渐近展开,我们对所得的递推方程给出了正交条件(可解性条件),据此可确定圆薄板的刚度特性.本文指出,利用圆薄板小挠度解和正交条件,可以不经求解方程而导得载荷参数与中心挠度关系的三阶近似以及中心点、边缘处的薄膜力的首项近似.文中对若干特例(均布载荷、复合载荷、各种边界条件)进行了具体计算,所得的结果与钱伟长、叶开沅、黄黔等人在文[1～4]中给出的结果完全相符.     

奇异摄动法应用于扁球壳的非线性稳定问题(Ⅱ)

本文对边缘固定夹紧在均布载荷作用下弹性圆底扁薄球壳的非线性稳定性问题进行了研究.利用奇异摄动法求出几何参数k较大时的一致有效的渐近解,并导得决定中心挠度和临界载荷的解析公式,作出了稳定性曲线.这篇文章是作者文章[11]的继续.     

复合载荷下圆薄板的大挠度问题

本文引入载荷分布函数使复合载荷依单参数变化,并选取平均挠角作为单一的位移摄动参数,给出了在均布载荷和中心集中力联合作用下边缘固定夹紧的圆薄板大挠度问题的摄动解,并讨论了中心点挠度为零的特殊情况.