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1.
双向压缩简支矩形板的后屈曲性态 总被引:2,自引:1,他引:2
本文从Karman板大挠度方程出发,以挠度为摄动参数,采用直接摄动法,研究了简支矩形板在面内双向压缩作用下的后屈曲性态.本文同时考虑了板初始几何缺陷的影响.计算结果与实验结果的比较表明二者是一致的. 相似文献
2.
含基体横向损伤的黏弹性板的蠕变后屈曲分析 总被引:2,自引:0,他引:2
基于Schapery三维黏弹性损伤本构关系,引入沈为和Kachanov损伤演化方程,建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型;应用von Karman板理论,导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散,时间上采用增量算法和Newton-Cotes积分法离散,控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响,且与已有文献的结果进行了比较. 数值结果表明:随着外载荷或者初始挠度的增大,板后屈曲趋于稳定时的挠度就愈大,损伤的影响愈明显;而随着长宽比的增大,板后屈曲趋于稳定时的挠度愈小,损伤的影响却随之增大. 相似文献
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1.引言 关于复合载荷作用下圆板的大挠度弯曲问题,文献[1,2]曾分别选取不同的参数用摄动方法给予求解。本文用一个简便的方法来分析此问题。即先假设一个挠度试函数,使相容方程完全满足,求出薄膜力;然后再用伽辽金加权残数法求解平衡微分方程。 已知均布荷载及中心集中力联合作用下圆板的大挠度方程为 相似文献
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板钢结构承载力分析最终可化简为对一任意边界的矩形板在面内荷载作用下的极限承载力分析.从含初始弯曲的大挠度方程出发,以板厚度的折减量为摄动参数,将残余应力考虑成等效荷载,根据实用板与理想板的比较,得出板的厚度折减量和板的极限承载力方程.通过与非线性有限元方法和已有试验数据的验证分析,表明折减厚度法适用范围广、安全、精度高,可作为非线性有限元方法的补充,大大简化了结构极限承载力分析的复杂性. 相似文献
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本文采用逐步加载法将圆板弯曲的非线性微分方程组线性化,再用变分方法求解线性化方程.文中推得各次加载时的载荷与挠度,应力与挠度关系的递推公式.圆形薄板在轴对称弯曲情况下的非线性问题可用卡门方程表示 相似文献
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将斜板在大挠度理论下的平衡方程和变形协调方程转化为斜坐标系下的表达式,并无量纲化,对于四边固支斜板,选用尺度小于1的二维bior3.1重构尺度函数与小波作试函数,满足板在平面外的几何与自然边界条件,利用小波-Galerkin法将板的无量纲平衡控制方程与变形协调方程转化为两个非线性方程组,从而将后屈曲路径的求解转化为两非线性方程组的求解问题.以载荷作为迭代步长,采用Newton-Raphson迭代算法求得承受单向压缩四边固支斜板在不同边长比、不同斜角下的后屈曲平衡路径及四级渐近解. 相似文献
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采用非线性有限元分析加筋板的几何非线性弹性稳定性问题。根据 Von Karman 大挠度板理论以及文献[1]所提出的方法,考虑了加筋偏心的影响,获得了非线性有限元分析所需的平衡方程和增量方程。为了提高编制程序和数字计算的效率,刚度矩阵均写成统一的形式。当板屈曲时,为了克服 Jacobi 矩阵的奇异性,采用了位移控制解法和修改的 Riks 方法。据此编写了计算机程序,分析了梁、板的大挠度以及轴压加筋板的几何非线性弹性稳定性问题。计算结果表明了所提出方法的正确性。 相似文献
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讨论了正交异性非线性变厚度混凝土环形板问题.建立了荷载为q(r)及q(r)*sinnθ条件下的环形板平衡条件式,导出了挠度表达的Euler方程.据此获得一组常系数微分方程和它们的特征值,可以求解正交异性非线性变厚度环形板的挠度及内力. 相似文献
11.
Zhang Shanyuan Wang Tiefeng 《Acta Mechanica Solida Sinica》1994,7(4):334-346
A study is presented for the large deflection dynamic response of rigid-plastic circular plate resting on potential fluid under a rectangular pressure pulse load.By virtue of Hankel integral transform technique,this interaction problem is reduced toa problem of dynamic plastic response of the plate in vacuum.The closed-formsolutions are derived for both middle and high pressure loads by solving the equationsof motion with the large deflection in the range where both bending moments andmembrane forces are important.Some numerical results are given. 相似文献
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A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases,the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any additional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the von Karman plate theories are identified with respect to the large deformation bending of circular plates. 相似文献
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分析了置于无旋不可压理想流体流面上的简支刚塑性圆板受矩形脉冲载荷作用的大挠度动力响应,借助Hankel变换,将液-固耦合作用为在空气中的圆板塑性动力响应问题,进而求解弯矩和膜力联合作用的大挠度运动方程,得到了中载及高载下各相运动的完全解,并提供了数值算例。 相似文献
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戴世强 《应用数学和力学(英文版)》1991,12(7):617-625
In this paper,we reexamine the method of successive approximation presented byProf.Chien Wei-zang for solving the problem of large deflection of a circular plate,and findthat the method could be regarded as the method of strained parameters in the singularperturbation theory.In terms of the parameter representing the ratio of the centerdeflection to the thickness of the plate,we make the asymptotic expansions of thedeflection,membrane stress and the parameter of load as in Ref.[1],and then give theorthogonality conditions(i.e.the solvability conditions)for the resulting equations,bywhich the stiffness characteristics of the plate could be determined.It is pointed out thatwith the solutions for the small deflection problem of the circular plate and theorthogonality conditions,we can derive the third order approximate relations between theparameter of load and the center deflection and the first-term approximation of membranestresses at the center and edge of the plate without solving the differential equ 相似文献
16.
R. S. Dhaliwal 《Applied Scientific Research》1964,13(1):43-54
Summary This paper presents a solution for the deflection, moments and shearing forces in a rectilinear regular polygonal plate, with even number of sides having a central circular hole, subjected to concentrated edge couples at two opposite points of the outer boundary. Complex variable technique has been employed to find the solution of the problem. The solution involves an infinite system of linear algebraic equations and a method of solving them is provided. The solution for a corresponding plane stress (strain) problem has been derived. Numerical results are presented in the form of tables and graphs. 相似文献
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ABSTRACT Application of the Galerkin method to various fluid and structural mechanics problems that are governed by a single linear or nonlinear differential equation is well known [1-5]. Recently, the method has been extended to finite element formulations [6-10], In this paper the suitability of the Galerkin method for solution of large deflection problems of plates is studied. The method is first applied to investigate large deflection behavior of clamped isotropic plates on elastic foundations. After validity of the method is established, it is then extended to analyze problems of large deflection of clamped skew sandwich plates, both with and without elastic foundations. The plates are considered to be subjected to uniformly distributed loads. The governing differential equations for the sandwich plate in terms of displacements in Cartesian coordinates are first established and then transformed into skew coordinates. The nonlinear differential equations of the plates are then transformed into nonlinear algebraic equations, using the Galerkin method. These equations are solved using a Newton-Raphson iterative procedure. The parameters considered herein for large deflection behavior of skew sandwich plates are the aspect ratio of the plate, Poisson's ratio, skew angle, shearing stiffnesses of the core, and foundation moduli. Numerical results are presented for skew sandwich plates for various skew angles and aspect ratios. Simplicity and quick convergence are the advantages of the method, in comparison with other much more laborious numerical methods that require extensive computer facilities. 相似文献
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I.IntroductionBecauseofthenonlinearityoflargedeflectionproblemofthinplates,itisquitedifficulttoobtainitsaccuratesolution.Thereforeanapproximatesolutiontoitobtainedbyanappropriatemethodisdesired.Thetechniquesocalledperturbation,beingabletogiveresultswithadequateprecision,isofaprevailingandeffectiveonetobegenerallyaccepted.W.Z.Chientl]succesfullyobtainedanapproximatesolutiontothelargedeflectionproblemofthincircularplatefie-curalaxisymmetricallybyperturbationtechnique.X.Z.Wangl'Jgainedthedispl… 相似文献
19.
A boundary element method is developed for the large deflection analysis of thin elastic plates resting on elastic foundation. The subgrade reaction may depend linearly (Winkler-type) or nonlinearly on the deflection as well as on the point coordinates (nonhomogeneous subgrade). Moderately large deflections are examined as described by the von Karman equations. The plate may have arbitrary shape and its boundary may be subjected to any type of boundary condition. The proposed method uses the fundamental solution of the linear plate theory and treats the nonlinearities as well as the subgrade reaction as unknown domain forces. Numerical results are presented to illustrate the method and demonstrate its effectiveness and accuracy. 相似文献
20.
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