内边界支承环板在边缘弯矩和线性荷载作用下塑性极限分析

1.计算方法简介对于环板,其平衡方程为式中(?)为环板内半径.对于内边界支承的环板,在最大弯矩极限条件下,其极限条件为 M_θ=-M_p,M_p,为塑性极限弯矩.于是,设     

板弯曲与平面弹性有限元的同一性

本文建立平面弹性与板弯曲的相似理论，并用于将平面弹性的单元移植到板弯曲元，从而其分片试验，收敛性等性质也同时移植到板弯曲元，使两者处于同一水平上，同时又将此基于力法的板弯曲元入位移法的轨道，找出共相应的位移系统，并证明其适定性，从而为将此类单元装入位移法通用程序系统创造了条件。     

Reissner板弯曲的复变函数分析方法

本文建立了Reissner板弯曲问题的复变函数分析方法,它可以有效地用于分析含一般孔洞板弯曲的应力集中问题。作为应用,文中还给出了一些计算实例。     

用奇异函数法简化计算具有悬臂端环板的极限荷载

本文应用奇异函数简化计算具有悬臂端环板的极限荷载.文中分别以具有内悬臂或外悬臂的环板的塑性极限分析为例,给出简化计算的方法及结果.算例表明了本文方法的可行性及简便性.     

Green函数法解点支承任意板自由振动频率

1 引言板是工程中经常采用的结构形式之一.沿边界呈对称点支承的悬臂板在土木工程中不乏常见.这种板的自由振动构成了典型板自振问题的一种特殊形式,由于解析法对自由边界条件及支承点的约束条件难以满足,所以常令科技人员感到棘手.H.T.Saliba 曾用4种级数迭加对这种板进行过分析、计算,得出几组计算结果.计算中每个级数取30     

利用奇异函数求解薄圆板的轴对称弯曲问题

本文利用奇异函数求解等厚度和台阶式变厚度薄圆板的轴对称弯曲问题,求解时无需分段,较传统方法简便实用。     

Green函数法解非均匀弹性地基板的自由振动

把板在特定域中的Green函数当作影响函数,根据实际板的边界条件首先求出虚拟域中的Green函数“源”,继而确定板内任意点的挠度及内力。在板的振动问题中及板的分布惯性力的影响后就可得到其自振频率的本征方程,从而计算出其各阶自振频率的值。文中附有算例,并把其计算结果与已有解析解作了比较,表明它们之间具有良好的吻合。     

用点源函数解受集中力圆板的非对称弯曲

本文将作用于板上任意位置的一个垂直于板中面的集中力看作一个点源,用δ函数表示,导出了受集中力作用的圆板非对称弯曲微分方程的封闭式特解和级数式齐次解,从而得出了适用于全板的统一的位移表达式。     

弹性体的正则方程和加筋板的固有频率分析

应用弹性力学的Hamilton正则方程理论和其半解析法，为整体加筋板的固有频率分析提出了一种新颖的数学模型. 采用同一种平面元素离散板和加强筋，并分别建立板和加强筋的线性方程组. 考虑到板和加强筋连接界面上应力和位移的连续性，联立板和加强筋的方程得到全结构的方程组和求解固有频率的特征方程. 主要优越性表现为：结构的旋转惯性、剪切变形等都得到了考虑，且不限制结构的板厚度和加强筋的高度. 多个数值实例的收敛分析和结果证明了方法是可靠的. 该方法很容易被修改用来分析加筋壳、加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳问题.     

On the elastodynamics of stiffened plates

Summary A method of determining the response of a stiffened elastic plate to a dynamic excitation is presented here. Green's function for such a combined system has been systematically derived based on the eigenfunctions of the system obtained through the application of Galerkin's method. With that Green's function a wide range of dynamic forcing functions can be considered.

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Zur elastodynamik versteifter platten

Übersicht Vorgestellt wird eine Methode zur Ermittlung der Antwort versteifter Platten auf dynamische Erregungen. Mit Hilfe der Eigenfunktionen des Systems, die durch Anwendung der Galerkin-Methode gewonnen werden, wird die Greensche Funktion solcher kombinierten Tragwerke systematisch hergeleitet. Damit kann ein weiter Bereich dynamischer Anregungsfunktionen behandelt werden.

     

Free vibration analysis of stiffened laminated plates

Based on the semi-analytical solution of the state-vector equation theory, a novel mathematical model for free vibration analysis of stiffened laminated plates is developed by separate consideration of plate and stiffeners. The method accounts for the compatibility of displacements and stresses on the interface between the plate and stiffeners, the transverse shear deformation, and naturally the rotary inertia of the plate and stiffeners. Meanwhile, there is no restriction on the thickness of plate and the height of stiffeners. To demonstrate the excellent predictive capability of the model, several examples are analyzed numerically. The model presented in this paper can also be easily modified to solve the problems of stiffened piezolaminated plates and shells, or plates and shells with piezoelectric material patches.     

Linear and nonlinear analysis of stiffened plates

An analysis is presented for the large deflection of clamped laterally loaded skew plates with stiffeners parallel to the skew directions. The governing nonlinear differential equations are derived taking into account the eccentricity of the stiffeners. A numerical procedure involving the use of integral equations of beams and the Newton-Raphson method is employed to get the solution. Numerical work has been done. The effect of variation of skew angle and size of stiffener on the behaviour of the stiffened skew plate has been studied.     

Tests on interactive buckling of stiffened plates

Tee-section columns have been tested under conditions that provide a close relationship between the results so obtained and the behavior of certain classes of stiffenedplate structures. It is shown that severe imperfection sensitivity arises when the overall column critical load is coincident, or nearly coincident, with the local torsional critical load of the stiffener. And, although the present results are clearly not directly applicable to stiffened-plate design, it is suggested that, it these systems are to be designed with even greater material efficiencies than at present, the interactive mechanics observed could acquire increasing design importance. Accordingly, suggestions are made as to the form of research needed to provide a rational basis for the design of such ‘optimized’ stiffened-plate structures.     

Sound transmission from stiffened double laminated composite plates

An analytical model is developed to investigate the sound transmission loss from orthogonally rib-stiffened double laminated composite plates structure under a plane sound wave excitation, in which first order shear deformation theory is presented for laminated composite plates. By using the space harmonic approach and virtual work principle, the sound transmission loss is described analytically. The validity and feasibility of the model are verified by comparing the present theoretical predictions with numerical results published previously. The influences of structure geometrical parameters on sound transmission loss are subsequently presented. Through numerical results, it can be concluded that the proposed analytical model is accurate and simple in solving the vibroacoustic behavior of an orthogonally rib-stiffened double laminated composite plates.     

水下爆炸载荷作用下加筋板的毁伤模式

为研究加筋板结构在水下爆炸载荷作用下的破坏模式,进行了一系列模型试验。通过对试验结果的分析,将加筋板的毁伤模式总体分为塑性大变形（模式I）、拉伸破坏（模式II）和剪切破坏（模式III）等3大类。又根据载荷强弱和加强筋的相对强度,将每种破坏模式细分为3种子模式。提出了一个量纲一的损伤因子,作为预报毁伤模式的判据。     

考虑面内破坏过程的含分层损伤复合材料加筋层合板的动力响应

基于复合材料层合板一阶剪切理论，推导了复合材料层合板单元的刚度阵和质量阵列式；同时采用了Adams应交能法与Rayleigh阻尼模型相结合的方法，构造了相应的阻尼阵列式；为了防止在低阶模态中分层处出现的上、下子板不合理的嵌入现象，建立了含分层损伤复合材料加筋层合板动力分析的分层分析模型和虚拟界面联接模型。在上述模型和理论基础上，采用了Tsai提出的刚度退化准则和动力响应分析的精细积分法，对含分层损伤复合材料加筋层合板结构进行了动力响应和破坏分析。通过算例，分别讨论了外载频率、分层位置，以及破坏过程的刚度退化对含损伤复合材料加筋层合板动力响应特征的影响，得到了一些具有理论和工程价值的结论。     

Dynamic buckling of stiffened plates under fluid-solid impact load

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.     

Shear deformation effect in plates stiffened by parallel beams

In this paper a general solution for the analysis of shear deformable stiffened plates subjected to arbitrary loading is presented. According to the proposed model, the arbitrarily placed parallel stiffening beams of arbitrary doubly symmetric cross section are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. The analysis of the plate is based on Reissner’s theory, which may be considered as the standard thick plate theory with which all others are compared, while the analysis of the beams is performed employing the linearized second order theory taking into account shear deformation effect. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM based method. The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical methods. The adopted model permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. The effectiveness, the range of applications of the proposed method and the influence of shear deformation effect are illustrated by working out numerical examples with great practical interest.