双参数弹性地基上自由边矩形板

本文以迭加法[1]给出在V. Z. Vlazov双参数弹性地基上自由边矩形板的精确解.文中导出了在各种边界条件下的基本解式,迭加这些基本解式,求得了在双参数弹性地基上自由边矩形板的最一般的精确解.它严格满足双参数弹性地基上板的控制微分方程和自由边的边界条件和角点条件.给出了数值结果.计算结果表明:当板的平面尺寸一定,地基深度与板厚度之比H/h=15时,双参数弹性地基与Winkler弹性地基相接近,证明了Winkler地基模式适用于压缩尺寸比较薄的弹性地基.     

弹性地基上自由边矩形薄板几个问题的注记

对于弹性地基上自由边矩形薄板的弯曲、稳定和振动问题,本文选择了一个挠曲函数,它能精确满足自由边全部边界条件以及自由角点的条件.应用能量变分原理,给出了确定挠曲函数中待定参数的方程,以及稳定性方程和频率方程,给出了求最小临界力和最小固有频率的一般公式.     

求解弹性地基上自由矩形中厚板弯曲问题的辛-叠加方法

基于近年来提出的辛-叠加方法,解析求解了弹性地基上自由矩形中厚板的弯曲问题.首先将原问题拆分为3类子问题,在Hamilton体系下,运用辛几何方法推导出子问题对应的弹性地基上对边滑支矩形板弯曲问题的辛解析解;以此为基础,通过叠加法思想,求出弹性地基上四边自由矩形中厚板的弯曲解.与半逆法等传统解析方法相比,辛-叠加方法兼备了辛方法理性和叠加法规律性的优点,在求解过程中不需要预先假定解的形式,而是由弹性力学基本方程出发,经过逐步严格推导获得解析解,因而大大拓展了可求解问题的范围,成为一种求解以矩形板问题为代表的弹性力学高阶偏微分方程复杂边值问题的有效解析方法.     

分析各向异性板的各向同性化样条积分方程法

本文分别按Reissner理论和Kirchhoff理论导出各向导性板的各向同性化控制方程,并论证了它们间在正交各向异性简支矩形板中的相通性.在用样条积分方程法求解中采用的只是些简单的各向同性板基本解,在稀疏剖分下也能有良好的计算精度.对双参数弹性地基上的板也只需在板上虚载的取值上附加某些项而不致增加多大的工作量.     

弹性地基上自由边矩形板的弯曲、稳定和振动

本文讨论了在弹性地基上自由边矩形板的弯曲、稳定和振动的问题.本文选择了一个挠曲函数,它不但能满足自由边的全部边界条件,而且也满足了自由角点的条件,从而得到了较好的近似解,文中使用了能量法.     

弹性地基上的自由矩形板

在弹性地基上的自由矩形板的弯曲,在弹性薄板理论中也是个难题.本文以叠加法提供一个精确解.它满足微分方程,自由边界的条件以及自由角点条件.这样将导致一系列无穷联立方程.所解的问题为在板的中点作用一集中力这问题.我们并以地基反力应与这集中力相平衡.校核所作的计算是否正确.     

弹性半空间地基上四边自由矩形板稳态振动的解析解

采用双重Fourier变换,分析得到弹性半空间地基受竖向稳态荷载作用下的积分变换解．与四边自由矩形板的振动解析解相结合,得出弹性半空间地基上四边自由矩形板稳态振动的解析解．还给出算例及参数影响分析．     

弹性地基上矩形板弯曲的CC型级数解

本文利用双变量函数的Stockes变换,用CC型级数求弹性地基上矩形板弯曲问题的解析解.以弹性地基上四边自由矩形板中点作用一集中力为例给出数字计算结果.     

简支夹层矩形板的非线性弯曲

本文应用变分法导出了具有软夹心的夹层矩形板的非线性弯曲理论的基本方程和边界条件.然后,使用摄动法研究了均布横向载荷作作用下简支夹层矩形板的非线性弯曲问题,得到了相当精确的解析解.     

非线性弹性地基上的圆薄板的分岔与混沌问题

根据非线性弹性地基上圆薄板大幅度方程,弹性抗力有线性项,三次非线性项和抗弯曲弹性项。在周边固定的条件下,利用Galerkin法得到了一个非线性振动方程。在无外激励情况下,求出在平衡点处的Floquet指数。分析了其稳定性与可能发生的分岔条件。在外激励条件下,用Melnikov方法分析研究了可能发生的混沌振动。通过数字仿真给出了各种地基参数下混沌区域的临界曲线和相平面图。     

板弯曲断裂计算的边界配置解法

采用复变函数理论和边界配置方法,分析计算了Kirchhoff板的弯曲断裂问题.假设了位移及内力的复变函数式,它们能满足一系列的基本方程和支配条件,例如域内的平衡方程、裂纹表面的边界条件、裂纹尖端的应力奇异性质.这样,仅板边界的边界条件需要考虑.它们可用边界配置法和最小二乘法近似满足.对不同边界条件和载荷情形进行了分析计算.数值算例表明,本文方法精度较高,计算量小,是一种有效的半解析、半数值计算方法.     

Nonlinear flexural response of laminated composite plates under hygro-thermo-mechanical loading

The paper deals with Chebyshev series based analytical solution for the nonlinear flexural response of the elastically supported moderately thick laminated composite rectangular plates subjected to hygro-thermo-mechanical loading. The mathematical formulation is based on higher order shear deformation theory (HSDT) and von-Karman nonlinear kinematics. The elastic foundation is modeled as shear deformable with cubic nonlinearity. The elastic and hygrothermal properties of the fiber reinforced composite material are considered to be dependent on temperature and moisture concentration and have been evaluated utilizing micromechanics model. The quadratic extrapolation technique is used for linearization and fast converging finite double Chebyshev series is used for spatial discretization of the governing nonlinear equations of equilibrium. The effects of Winkler and Pasternak foundation parameters, temperature and moisture concentration on nonlinear flexural response of the laminated composite rectangular plate with different lamination scheme and boundary conditions are presented.     

考虑高阶横向剪切正交各向异性板非线性弯曲的微分求积分析

采用微分求积方法（DQ方法）讨论了计及高阶横向剪切的正交各向异性弹性板的非线性弯曲问题．导出了非线性控制方程的DQ形式,利用推广的DQWB技巧处理了高阶矩的边界条件．进一步推广并运用新的分析技术简化了非线性方程的计算．为说明该方法的可靠性和有效性,将考虑剪切变形及不计剪切变形的薄板的数值结果与三维弹性解析解及其它数值解进行了比较,同时研究了数值结果的收敛性,并考察了不同的节点分布对收敛速度的影响A·D2还考察了几何、材料参数及横向剪切效应对正交各向异性板非线性弯曲的影响．分析结果表明横向剪切效应对正交各向异性中厚板的影响是显著的．     

周边面内压力作用下夹层圆板的非线性振动

基于von Krmn薄板理论,讨论了滑动固定基础上周边面内压力作用下夹层圆板的非线性振动问题,应用变分法导出了该问题的非线性特征方程和边界条件,给出了其精确静态解,并使用修正迭代法求解了该方程,导出了夹层圆板振幅和非线性振频的解析关系式．当周边面力使夹层圆板的最低固有频率为零时,就可获得临界载荷的值．     

The postbuckling analysis of laminated circular plate with elliptic delamination

Based on the Von Karman plate theory, considering the effect of transverse shear deformation, and using the method of the dissociated three regions, the postbuckling governing equations for the axisymmetric laminated circular plates with elliptical delamination are derived. By using the orthogonal point collocation method, the governing equations, boundary conditions and continuity conditions are transformed into a group of nonlinear algebraically equation and the equations are solved with the alternative method. In the numerical examples, the effects of various elliptical in shape, delamination depth and different material properties on buckling and postbuckling of the laminated circular plates are discussed and the numerical results are compared with available data.     

Three-dimensional layerwise-finite element free vibration analysis of thick laminated annular plates on elastic foundation

Using a three-dimensional layerwise-finite element method, the free vibration of thick laminated circular and annular plates supported on the elastic foundation is studied. The Pasternak-type formulation is employed to model the interaction between the plate and the elastic foundation. The discretized governing equations are derived using the Hamilton’s principle in conjunction with the layerwise theory in the thickness direction, the finite element (FE) in the radial direction and trigonometric function in the circumferential direction, respectively. The fast rate of convergence of the method is demonstrated and to verify its accuracy, comparison studies with the available solutions in the literature are performed. The effects of the geometrical parameters, the material properties and the elastic foundation parameters on the natural frequency parameters of the laminated thick circular and annular plates subjected to various boundary conditions are presented.     

Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods

This article introduces a coupled methodology for the numerical solution of geometrically nonlinear static and dynamic problem of thin rectangular plates resting on elastic foundation. Winkler–Pasternak two-parameter foundation model is considered. Dynamic analogues Von Karman equations are used. The governing nonlinear partial differential equations of the plate are discretized in space and time domains using the discrete singular convolution (DSC) and harmonic differential quadrature (HDQ) methods, respectively. Two different realizations of singular kernels such as the regularized Shannon’s kernel (RSK) and Lagrange delta (LD) kernel are selected as singular convolution to illustrate the present DSC algorithm. The analysis provides for both clamped and simply supported plates with immovable inplane boundary conditions at the edges. Various types of dynamic loading, namely a step function, a sinusoidal pulse, an N-wave pulse, and a triangular load are investigated and the results are presented graphically. The effects of Winkler and Pasternak foundation parameters, influence of mass of foundation on the response have been investigated. In addition, the influence of damping on the dynamic analysis has been studied. The accuracy of the proposed DSC–HDQ coupled methodology is demonstrated by the numerical examples.     

Modeling large amplitude vibration of matrix cracked hybrid laminated plates containing CNTR-FG layers

This paper presents the mathematical modeling of the nonlinear vibration behavior of a hybrid laminated plate composed of carbon nanotube reinforced functionally graded (CNTR-FG) layers and conventional fiber reinforced composite (FRC) layers. Three type symmetric distributions of single walled carbon nanotubes (SWCNTs) through the thickness of layers are considered. The cracks are modeled as aligned slit cracks across the ply thickness and transverse to the laminate plane. The distribution of cracks is assumed to be statistically homogeneous corresponding to an average crack density. The obtained partial differential equations are solved by the element-free kp-Ritz method, and the iteration process is dealt with using the linearized updated mode method. Detailed parametric studies are conducted investigate the effects of matrix crack density, CNTs distributions, CNT volume fraction, plate aspect ratio and plate length-to-thickness ratio, boundary conditions and number of layers on the frequency-amplitude responses of hybrid laminated plates containing CNTR-FG layers.     

Geometrically nonlinear bending analysis of laminated composite plate

In this work, a transverse bending of shear deformable laminated composite plates in Green–Lagrange sense accounting for the transverse shear and large rotations are presented. Governing equations are developed in the framework of higher order shear deformation theory. All higher order terms arising from nonlinear strain–displacement relations are included in the formulation. The present plate theory satisfies zero transverse shear strains conditions at the top and bottom surfaces of the plate in von-Karman sense. A C⁰ isoparametric finite element is developed for the present nonlinear model. Numerical results for the laminated composite plates of orthotropic materials with different system parameters and boundary conditions are found out. The results are also compared with those available in the literature. Some new results with different parameters are also presented.     

Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory

The main objective of this research work is to present analytical solutions for free vibration analysis of moderately thick rectangular plates, which are composed of functionally graded materials (FGMs) and supported by either Winkler or Pasternak elastic foundations. The proposed rectangular plates have two opposite edges simply-supported, while all possible combinations of free, simply-supported and clamped boundary conditions are applied to the other two edges. In order to capture fundamental frequencies of the functionally graded (FG) rectangular plates resting on elastic foundation, the analysis procedure is based on the first-order shear deformation plate theory (FSDT) to derive and solve exactly the equations of motion. The mechanical properties of the FG plates are assumed to vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents, whereas Poisson’s ratio is set to be constant. First, a new formula for the shear correction factors, used in the Mindlin plate theory, is obtained for FG plates. Then the excellent accuracy of the present analytical solutions is confirmed by making some comparisons of the results with those available in literature. The effect of foundation stiffness parameters on the free vibration of the FG plates, constrained by different combinations of classical boundary conditions, is also presented for various values of aspect ratios, gradient indices, and thickness to length ratios.