双模量矩形板的大挠度弯曲计算分析

双模量矩形板在外载荷作用下,会形成各向同性的拉伸区和压缩区,把双模量矩形板看成两种各向同性材料组成的层合板,采用弹性力学理论建立了双模量矩形板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量矩形板的中性面位置,推导出了双模量矩形板的大挠度弯曲变形微分方程。用加权残值法求得了双模量矩形板的大挠度弯曲变形时板中点挠度,把该方法计算结果与有限元计算结果进行了比较,说明了该计算方法是可靠的,并讨论分析了双模量对矩形板大挠度弯曲变形的影响。     

在阻尼介质中简支矩形板的塑性动力响应

本文用矩量法求解简支矩形板的塑性动力响应,分析阻尼介质对简支矩形板塑性动力响应的影响,解出了矩形板的残余挠度和终止运动时间.     

弹性边界约束矩形板的振动特性分析：理论、有限元和实验

提出一种有效的理论方法研究弹性边界约束矩形板的振动特性,并设计实验测试不同边界矩形板的固有频率。矩形板的弹性边界约束采用一系列的均布线性弹簧模拟,用特征正交多项式来表示矩形板的位移容许函数,并采用瑞利?里茨法获得弹性边界约束矩形板的固有频率和固有振型。通过改变边界弹簧的刚度即可模拟矩形板不同的边界条件,提高计算效率。基于理论方法计算获得结构固有频率并和有限元及实验结果进行对比,验证所提理论方法的正确性。此外,通过实验测试的方法分析弹性?简支、弹性?固支等不同边界组合条件下矩形板的振动特性,分析调整不同边界弹簧刚度对矩形板振动特性的影响。     

矩形薄板自由振动的一般解析解

本文求得了矩形薄板弹性横向自由振动位型函数微分方程的一般解。可以求解任意边界矩形薄板的固有频率。以四边固定矩形板为例求解了板的基频及其位型。     

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。     

夹层板弯曲问题的Hoff理论的解析解

本文根据Ｈｏｆ提出的夹层板理论和胡海昌、柳春图对该理论的简化理论，提出了矩形夹层板弯曲问题的解析解的一般格式，它可以用于求解各种边界条件下矩形夹层板弯曲问题的Ｈｏｆ理论的解析解。从而，使得考虑表层抗弯刚度的矩形夹层板弯曲问题求解格式化。     

筋上有开口裂缝的加筋矩形板横向振动特性分析

利用能量法分析筋上含有开口裂缝的四边简支加筋矩形板的横向振动。将矩形板与加强筋沿交界面切开,再将加强筋沿裂缝分成多个子块,采用薄板弯曲和平面应力理论分别建立矩形板和各子块的横向振动能量方程,解决了传统分析方法需给定开裂处筋的弯曲刚度问题。采用第一类切比雪夫多项式构造矩形板和各子块的位移试函数,由Ritz法和板-筋界面变形连续条件得出含有开口裂缝的加筋矩形板的横向振动特征方程。计算结果与有限元分析结果吻合很好,详细分析了裂缝深度和裂缝位置对无量纲频率的影响。     

矩形悬壁板自由振动精确解法

本文提出矩形薄板振动主振方向的概念。根据振形正交性的思想,在主振方向上矩形板振动波形是唯一的,由此建立了符合矩形悬臂板边界条件所激发出的振动曲线形态的振形函数表达式,并推导出矩形板的频率方程及相应的振形曲线。计算表明,这种方法符合板实际振动的规律性。     

混合边界矩形板的自由振动分析

应用一块板的一般解析解来求解混合边界矩形板的自由振动问题。一块板的一般解析解适用于求解任意边界条件矩形板的振动问题。混合边界矩形板的求解过程是将整块板分解为若干块板,每块板仅有均匀的边界,每两块相连的板边则具有连续性条件。利用全部边界条件和连续性条件即可求解各阶固有频率和振型。对几种具有简支边、平夹边或自由边混合边界的板做了计算,并与其它文献结果进行了对比。     

四边弹性约束FGM矩形板面内自由振动的DQM求解

假设矩形板为正交各向异性,材料的物性沿矩形板的宽度方向按幂律连续分布,基于二维线弹性理论,建立了四边弹性约束功能梯度材料(Functionally Graded Material,FGM)矩形板面内自由振动的控制偏微分方程。控制方程为复杂耦合的变系数偏微分方程,采用微分求积法(Differential Quadrature Method,DQM)数值研究了四边弹性约束FGM矩形板面内自由振动的无量纲频率特性。通过设置弹性刚度系数为0或∞,梯度指数为0,问题退化为各种典型边界下矩形板的面内自由振动,与已有的各向同性矩形板自振频率结果进行比较,结果表明分析求解方法行之有效。最后考虑了FGM矩形板边界条件、长宽比、梯度指数及刚度系数对自振频率的影响。     

Levy Solution for Buckling Analysis of Functionally Graded Rectangular Plates

In this article, an analytical method for buckling analysis of thin functionally graded (FG) rectangular plates is presented. It is assumed that the material properties of the plate vary through the thickness of the plate as a power function. Based on the classical plate theory (Kirchhoff theory), the governing equations are obtained for functionally graded rectangular plates using the principle of minimum total potential energy. The resulting equations are decoupled and solved for rectangular plate with different loading conditions. It is assumed that the plate is simply supported along two opposite edges and has arbitrary boundary conditions along the other edges. The critical buckling loads are presented for a rectangular plate with different boundary conditions, various powers of FGM and some aspect ratios.     

具有中间支承的矩形板自由振动分析

应用一般解析解来求解具有中间支承矩形板的自由振动问题。一般解析解能求解任意边界条件矩形板的振动问题,求解过程是将整块板看成是沿中间支承分开的两块板,沿支承边两块板的挠度均等于零,斜度和弯矩均相等,再由全部边界条件和连续性条件可以求解各阶频率和振型。对几种具有简支边,平夹边或自由边的混合边界矩形板进行了计算。     

Buckling behavior of standing laminated Mindlin plates subjected to body force and vertical loading

In this article, an exact analytical solution for stability analysis of vertical moderately thick laminated rectangular plates subjected to selfweight and top load on the basis of the first-order shear deformation plate theory is presented. It is assumed that the symmetric laminated rectangular plate is composed of transversely isotropic layers. Employing an analytical approach, the coupled governing stability equations of the laminated plate are converted into two uncoupled partial differential equations in terms of transverse displacement and an auxiliary function. It is considered that the vertical sides of the laminated plate are simply supported. Using Levy-type solution, the decoupled equations are reduced to two ordinary differential equations. One of these equations has variable coefficients, for which an exact analytical solution is obtained in the form of power series method of Frobenius. After appropriate convergence study, the present analysis is validated by comparing the results with the existing data reported in the literature. Furthermore, the effects of aspect ratio, plate thickness, boundary conditions, weight of plate and top load on the stability of laminated rectangular plates are investigated and discussed in details. The presented formulations and results can be used as benchmark for future research studies.     

Plate bending for frame analysis by coupling method of singular integral operators method with finite elements

The coupling of the Singular Integral Operators Method (SIOM) and the Finite Element Method (FEM) is proposed and investigated for the solution of plate bending problems. Such combination of the above two numerical methods gives more accurate results for the solution of plate bending problems in structural analysis. The plates are basic units of building frame structures, as well as to underground structures and thus the determination of bending moments around the plates is very important for the analysis of all kinds of structures. An application of plate bending problems is finally given to the determination of the bending moments in a rectangular plate with a rectangular hole in the center of the plate.     

将薄板矩形单元扩展为厚薄板通用单元的一般方法

本文提出将已有的薄板矩形单元扩展为无剪切闭锁现象的厚薄板通用单元的一般方法。对于薄板极限情况,这种厚薄板通用单元自动退化为原有的薄板单元,完全无剪切闭锁现象发生。应用此法构造的两个厚薄板通用矩形单元ＡＤＳ１和ＡＤＳ２自由度少,只含有角点挠度和转角,推导简明并具有一般性,能够通过分片检验。数值算例表明这两个单元对薄板和厚板都具有较高的精度,适用于实际工程计算。     

横向磁场中对边简支对边固支矩形薄板的分岔与混沌

研究了力磁耦合作用下对边简支对边固支矩形薄板的分岔与混沌问题。在给出横向稳恒磁场和载荷共同作用下的矩形薄板的非线性磁弹性耦合运动学方程的基础上,得到了对边简支对边固支的矩形薄板的磁弹性振动方程。用Melnikov函数法给出该系统发生混沌运动的条件,并用数值方法求解该系统振动方程。通过具体算例,得到了系统的分岔图、Lyapunov指数图,并给出了相应位移波形图、相平面轨迹图、庞伽莱截面图。分析了电磁场参量及外载荷对系统运动状态的影响。     

Mass-frequency influence surface, mode shapes, and frequency spectrum of a rectangular AT-cut quartz plate

The mass-frequency influence surface and frequency spectrum of a rectangular AT-cut quartz plate are studied. The mass-frequency influence surface is defined as a surface giving the frequency change due to a small localized mass applied on the plate surface. Finite-element solutions of R.D. Mindlin's (1963) two-dimensional plate equations for thickness-shear, thickness-twist, and flexural vibrations are given. Spectrum splicing, and an efficient eigenvalue solver using the C. Lanczos (1950) algorithm are incorporated into the finite-element program. A convergence study of the fundamental thickness-shear mode and its first symmetric, anharmonic overtone is performed for finite-element meshes of increasing fineness. As a general rule, more than two elements must span any half-wave in the plate or spurious mode shapes will be obtained. Two-dimensional (2D) mode shapes and frequency spectrum of a rectangular AT-cut plate in the region of the fundamental thickness-shear frequency are presented. The mass-frequency influence surface for a 5-MHz rectangular, AT-cut plate with patch electrodes is obtained by calculating the frequency change due to a small mass layer moving over the plate surface. The frequency change is proportional to the ratio of mass loading to mass of plate per unit area and is confined mostly within the electrode area, where the magnitude is on the order 10(8) Hz/g.     

Buckling analysis of rectangular composite plates with rectangular cutout subjected to linearly varying in-plane loading using fem

A numerical study is carried out using finite element method, to examine the effects of square and rectangular cutout on the buckling behavior of a sixteen ply quasi-isotropic graphite/epoxy symmetrically laminated rectangular composite plate [0°/+45°/-45°/90°]_2s, subjected to various linearly varying in-plane compressive loads. Further, this paper addresses the effects of size of square/rectangular cutout, orientation of square/rectangular cutout, plate aspect ratio(a/b), plate length/thickness ratio(a/t), boundary conditions on the buckling bahaviour of symmetrically laminated rectangular composite plates subjected to various linearly varying in-plane compressive loading. It is observed that the various linearly varying in-plane loads and boundary conditions have a substantial influence on buckling strength of rectangular composite plate with square/rectangular cutout.