Buckling and multiple equilibrium states of viscoelastic rectangular plates

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Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness

The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.     

Nonlinear vibration of circular plate with variable thickness

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Dynamic stiffness for thin-walled structures by power series

INTRODUCTION Thin-walled structures have considerable tech-nological importance in many situations of engi-neering practice. The rotary and warping inertia terms should be considered in the analyses of thin-walled structures (Alwis and Wang, 1996), although it is difficult to obtain the analytical solutions of govern-ing differential equations, especially of thin-walled frame and spatial twisted structure. The finite element method (FEM) is widely used for vibration and sta-bility analy…     

Distribution of Welding Residual Stress of Mixed Steel U-Rib-Stiffened Plates

To analyze the effects of width and thickness of each composition element of mixed steel U-rib-stiffened plates on the welding residual stress distribution, the distribution of the U-rib and the plate residual stress was calculated using a simplified calculation method. The method involved welding the mixed steel U-rib-stiffened plates for a structure with different sizes and different strength ratios of U-rib to plate. Based on a welding residual stress numerical simulation method validated by the blind hole method test, the distribution law of the mixed steel U-rib stiffened plate was studied. The results showed that the change of plate width has little impact on the welding residual stress and that the ratio of the thicknesses of the plate to U-rib stiffeners, the thickness of the plate, and the thickness of the U-rib has a great influence on the distribution of the welding residual stress. The thickness of plate and steel strength also greatly influenced the distribution width of the residual tensile stress. While analyzing the compression capacity of U-rib-stiffened plates, the simplified distribution of welding residual stress was used.     

Axisymmetrical Nonlinear Bending and Buckling of a Circular Plate Under Large Load

With the terms of the exact series solution taken as trial functions, the method of point collocation was used to calculate the large deflection of a circular plate. The axisymmetrical bending formulae were developed for the calculation of a circular plate subjected to polynomial distributed loads, a concentrated load at the center, uniform radial forces and moments along the edge or their combinations. The support may be elastic. The buckling load was calculated. Under action of uniformly distributed load, central load or their compound load, solutions were compared with those obtained by other methods, Buckling beyond critical thrust was compared with that calculated by the power series method. The method presented in this paper has advantages of wide convergent range, high precision and short computing time. Moreover, the computing time is nearly independent of the complexity of the loads.     

复合材料加筋圆柱曲板总体失稳分析及试验研究

通过建立“非离散模型”对复合材料加筋圆柱曲板进行了总体失稳分析研究,重点研究了边界条件影响和简化方法,推导了加筋圆柱曲板整体失稳的筋条“抹平”计算方法,并通过算例与试验结果进行了比较。结果表明该算法对筋条两对边为简支或固支时的总体失稳分析具有较高精确度,同时对实验的加载方法有一定指导意义。     

薄板结构振动声辐射特性分析及优化

利用有限元法与边界元法结合对薄板进行振动声辐射特性分析,研究了薄板结构在简谐力作用下表面声压分布状况,分析了不同边界条件、材料以及加筋形式等因素对薄板结构振动声辐射特性的影响,并对简支矩形薄板厚度进行了优化。研究表明,边界约束的增加会导致薄板刚度变大,进而导致薄板辐射声功率与辐射效率随之改变?不同材料对结构的辐射声功率均有影响,而对辐射效率影响很小?加筋对薄板声辐射特性影响显著,十字型加筋形式减震降噪效果最好?对薄板厚度进行优化,优化后薄板辐射声功率级下降了4.29dB。     

复合材料叠层板非线性动力稳定性理论的几个基本问题

本文研究了复合材料叠层板在周期性动力谐载荷作用下的非线性动力稳定性理论中的几个基本问题。其内容包括：用Hamilton原理建立一般性基本方程,考虑了大挠度非线性;惯性力的影响;耦合效应影响,横向剪切效应的影响,以及几何初始缺陷困数等。     

半解析法求解含轴向浅槽复合材料圆柱壳的非线性动力响应及屈曲问题

The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation theory （FSDT）, the nonlinear dynamic equations involving the transverse shear deformation and initial geometric imperfections were derived with the Hamilton philosophy. The axial shallow groove of the laminated composite cylindrical shell was treated as the initial geometric imperfections in the dynamic equations. A semi-analytical method of expanding displacements and loads along the circumferential direction and employing the finite difference method along the axial direction and in the time domain is used to solve the governing equations and obtain the dynamic response of the laminated shell. The B-R criterion was employed to determine the critical loads of dynamic buckling of the shell. The effects of the parameters of the shallow groove on the dynamic response and buckling were discussed in this paper and the results show that the axial shallow grooves greatly affect the dynamic response and buckling.     

弹性有限长度杆在轴向应力波传播和反射过程中的屈曲

讨论弹性有限长度杆端部受冲击载荷作用，在轴向应为波传播和反射过程中的动态屈曲问题．利用扰动方程的解、端部支承条件和应力波反射前后波阵面相容条件得到了动态屈曲的分叉条件，临界载荷和屈曲模态．数值结果表明：临界载荷有多个分支且随时间增加而降低；由于应力波在端部的反射，使临界载荷进一步下降．这个结果就解释了实验中的一些现象．     

Exact thickness-shear resonance frequency of electroded piezoelectric crystal plates

INTRODUCTION In quartz crystal resonator design, the mass effec of the electrodes must be considered to achieve ac curate prediction of the fundamental thickness-shea frequency, as analyzed and demonstrated b Bleustein and Tiersten (1968), which is considered t be the exact frequency solutions in making necessar comparisons with solutions from two-dimensiona plate equations and deriving the correspondent cor rection factors (Mindlin, 1972). When the crysta plate is relatively thick or the…     

考虑剪切效应有限变形粘弹性板的动力稳定性

Based on Reddy‘s theory of plates with higher-order shear deformations and the Boltzmann superposition principles,the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects,The Galerkin method was applied to simplify the set of equations.The numerical methods in nonlinear dynamics were used to solve the simplified system.It could e seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads.The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelatic plates were investigated.     

纵横载荷联合作用下弯曲薄板的功的互等定理

本文将功的互等定理应用于形状、大小和材料均相同又处于真实状态的两个薄板系统之间，得出了纵横载荷联合作用下弯曲薄板的功的互等定理，并给出了简洁的数学表达式。该式既可以用于横向载荷作用下弯曲薄板问题的求解，又可以用于薄板稳定问题的求解。定理推导过程中没有对薄板的形状和边界条件加以限制，因而使该定理具有较广的适用范围。     

Three-dimensional vibration of thick plate

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Prediction of Buckling of Plain Knitted Fabric Sheets Subjected to Simple Shear in Wale Direction

Knitted fabric is very different from woven fabric due to its more complicated knitting structures. The buckling of knitted fabric sheets subjected to simple shear in the wale direction is investigated analytically in consideration of the large deformation of fabric sheet in critical configuration. The theory on instability of finite deformation is applied to the analysis. All the stress boundary conditions of knitted fabric sheet are satisfied. An equation to determine the buckling direction angle is derived. It is shown that there are two possible buckling modes, flexural mode and barreling mode. The buckling condition equations for the flexural mode and barreling mode are also obtained respectively. Numerical illustrations reveal that only the flexural mode can actually occur and the barreling mode cannot, which agrees with the experimental observations. For a permitted buckling mode on margin boundaries, the critical value of shear amount and the buckling direction angle can be determined.     

复合材料的强度和稳定性理论中的几个近代问题

本文论述了复合材料的强度和稳定性理论中的三个近代问题:复合材料迭层板的强度准则,多层复合材料圆柱壳的非线性稳定性理论,以及复合材料板的动力稳定性理论。关于迭层板的强度准则,论述了目前以张量多项式形式所表述的唯象性破坏准则,着重讨论和比较了各种近代理论在确定耦合系数方面的特点和差别。提出了近代理论中所存在的困难和发展趋势。在多层复合材料圆柱壳的非线性稳定性理论分析中,主要的问题在于如何研究和考虑那些非线性因素,诸如由材料的剪切模量所引起的物理非线性,横向剪切变形的影响,壳体结构的初始缺陷和几何非线性,以及前屈曲变形和边界支承条件的影响等。本文指出了考虑这些因素的方法以及它们的影响程度。复合材料板的动力屈曲性能研究是一个重要的近代研究方向。本文提出了关于复合材料本身的阻尼系数,纵向和转动惯性力影响,横向剪切效应,迭层板的初始几何缺陷,以及增强纤维的铺设方向等因素对于动力屈曲性能的影响。同时提出了计算这些影响的方法,指出这些因素在复合材料板的动力稳定性分析中有着重要作用。     

Analysis modeling for plate buckling load of vibration test

In view of the recent technological development, the pursuit of safe high-precision structural designs has been the goal of most structural designers. To bridge the gap between the construction theories and the actual construction techniques, safety factors are adopted for designing the strength loading of structural members. If safety factors are too conservative, the extra building materials necessary will result in high construction cost. Thus, there has been a tendency in the construction field to derive a precise buckling load analysis model of member in order to establish accurate safety factors. A numerical analysis model, using modal analysis to acquire the dynamic function calculated by dynamic parameter to get the buckling load of member, is proposed in this paper. The fixed and simple supports around the circular plate are analyzed by this proposed method. And then, the Monte Carlo method and the normal distribution method are used for random sampling and measuring errors of numerical simulati     

变厚度矩形薄板弯曲问题的DQ法研究

针对矩形薄板的线性挠曲控制微分方程及其边界条件,在空间域采用DQ法离散,得到以板各节点弯曲挠度为全部待定参数的线性方程组,只需一次求解该方程组即得到各节点的弯曲挠度,再由高阶Lagrange插值得到薄板全域内的任意点挠度。     

应用大挠度薄板功的互等定理求解四边固定矩形板的挠曲方程

应用大挠度弯曲薄板的第二类功的互等定理,求解均载四边固定大挠度弯曲矩形板的挠曲面方程。