关于Reissner厚板模型的解——对“关于简支厚板与薄板的关系”的讨论

In this paper, the method proposed in [2] is extended to the case of thickplate, the problem in the solution of Reissner model of thick plate is reduced to a solution oftwo displacement functions ω and f, and the general form of the solution of this model isderived. For a simply supported polygonal thick plate, f vanishes identically, and hence therelation between the solution of thick plate and that of similar thin plate can be established.According to this relation, the solutions of a class of thick plates may be derived from thecorresponding solutions of thin plates.     

Asymptotic Behavior of a Structure Made by a Plate and a Straight Rod

This paper is devoted to describing the asymptotic behavior of a structure made by a thin plate and a thin perpendicular rod in the framework of nonlinear elasticity. The authors scale the applied forces in such a way that the level of the total elastic energy leads to the Von-K′arm′an’s equations (or the linear model for smaller forces) in the plate and to a one-dimensional rod-model at the limit. The junction conditions include in particular the continuity of the bending in the plate and the stretching in the rod at the junction.     

Second-order two-scale method for bending behavior analysis of composite plate with 3-D periodic configuration and its approximation

This paper considers the bending behaviors of composite plate with 3-D periodic configuration.A second-order two-scale(SOTS)computational method is designed by means of construction way.First,by 3-D elastic composite plate model,the cell functions which are defined on the reference cell are constructed.Then the effective homogenization parameters of composites are calculated,and the homogenized plate problem on original domain is defined.Based on the Reissner-Mindlin deformation pattern,the homogenization solution is obtained.And then the SOTS’s approximate solution is obtained by the cell functions and the homogenization solution.Second,the approximation of the SOTS’s solution in energy norm is analyzed and the residual of SOTS’s solution for 3-D original in the pointwise sense is investigated.Finally,the procedure of SOTS’s method is given.A set of numerical results are demonstrated for predicting the effective parameters and the displacement and strains of composite plate.It shows that SOTS’s method can capture the 3-D local behaviors caused by3-D micro-structures well.     

Mathematical Justification of an Obstacle Problem in the Case of a Plate

In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified.Starting from the three-dimensional nonlinear Signorini problem,by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied.It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.     

THE QUADRATIC SPECHT TRIANGLE

We propose a class of 12 degrees of freedom triangular plate bending elements with quadratic rate of convergence.They may be viewed as the second order Specht triangle,while the Specht triangle is one of the best first order plate bending element.The convergence result is proved under minimal smoothness assumption on the solution.Numerical results for both the smooth solution and nonsmmoth solution confirm the theoretical prediction.     

NONCONFORMING QUADRILATERAL ROTATED Q1 ELEMENT FOR REISSNER－MINDLIN PLATE

In this paper,we extend two rectangular elements for Reissner-Mindlin plate[9] to the quadrilateral case,Optimal H^1 and L^2 error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.     

WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D

In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models.We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that,via operator splitting,decouples the system into two sub-problems,one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure.To prove the convergence of the approximate quasilinear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.     

A COMBINED HYBRID FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS

In this paper,a combined hybrid method is applied to finite element discretization of plate bending problems.It is shown that the resultant schemes are stabilized,i.e., the convergence of the schemes is independent of inf-sup conditions and any other patch test.Based on this,two new series of plate elements are proposed.     

关于高精度12参矩形板元的分析

It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini's element's, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.     

Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance

Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method.The rectangular thin plate is subject to transversal and i...     

关于简支厚板与薄板的关系

厚板的数学理论是建立在与薄板不同的力学假定的基础上的。本文分析了厚板与薄板之间静力学方面的关系。对于任意的简支多边形板,得到了厚板解通过薄板解的显式表达式,从而证明了:Reissner模型的厚板解与薄板解具有相同的剪力,但弯矩、转角、挠度有差别;而washizu模型的厚板解则与薄板解不仅剪力相同,连弯矩与转角亦相同,只是挠度有差别。     

Simulating thin plate bending problems by a family of two-parameter homogenization functions

This study develops a simple and effective numerical technique, which aims to accurately and quickly address thin plate bending problems. Based on the given boundary conditions, the thin plate homogenization function is constructed and a family of two-parameter homogenization functions are derived. Then, the superposition of homogenization functions method for the thin plate, the clamped plate, and the simply supported plate is obtained, which is meshless without numerical integration and iteration with the merits of easy-to-program and easy-to-implement. Six numerical experiments are employed to verify the effectiveness, accuracy and convergence of the proposed novel strategy. The proposed method is evaluated by the comparisons with the analytical solutions and the referenced solutions. It can be observed that the proposed method is quite accurate for the thin plate, the clamped plate, and the simply supported plate problems.     

The effect of periodic surface pressure on a rectangular elastic plate floating on shallow water

The steady-state behaviour of a floating elastic plate of bounded dimensions acted upon by a localized external load is investigated using linear shallow water theory. In the case of a plate of arbitrary shape, the problem reduces to solving a system of boundary-value integral equations supplemented with differential relations for the free edge of the plate. Using a rectangular plate as the example, the effect of the frequency of the periodic actions and the positions at which they are applied on the amplitudes of the normal flexures of the plate and of the directional pattern of surface waves far from the plate is investigated. It is shown that waveguide properties occur for an elongated plate.     

不同理论下圆板特征值之间的解析关系

基于经典板理论（CPT）、一阶剪切变形板理论（FPT）以及Reddy三阶剪切变形板理论（RPT）之间，圆板轴对称特征值问题在数学上的相似性，研究了不同理论之间圆板特征值间的解析关系．将特征值问题的求解转化为代数方程的求解，并导出了不同理论之间圆板特征值的显式精确解析关系．从而。只要已知圆板特征值（临界屈曲载荷和固有频率）的经典结果，便很容易从这些解析关系中得到一阶和三阶理论下圆板特征值的相应结果。这便于工程应用，同时也可检验一阶和三阶理论下板特征值的数值结果的有效性、收敛性以及精确性等问题．     

Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem

This paper analyses the large deflections of an orthotropic rectangular clamped and simply supported thin plate. A hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations describing the large deflections of the orthotropic plate to a set of algebraic equations. The simulation results indicate that significant errors are present in the numerical results obtained for the deflections of the orthotropic plate in the transient state when a step force is applied. The magnitude of the numerical error is found to reduce, and the deflection of the orthotropic plate to converge, as the number of sub-domains considered in the solution procedure increases. The deflection of the simply supported orthotropic plate is great than the clamped orthotropic plate. The current modeling results confirm the applicability of the proposed hybrid method to the solution of the large deflections of a rectangular orthotropic plate.     

周期性正弦凸起凹凸板等效刚度的研究

针对构造正交各向异性周期性正弦凸起结构凹凸板的等效刚度问题，根据经典弹性薄板理论，基于对单胞结构力学特性分析和单胞结构在板宏观结构上周期性均匀化分布的特点，推导了正弦凸起凹凸板的等效刚度解析公式.以四边简支周期性正弦凸起结构凹凸板为例，将该文计算结果与有限元模拟结果进行对比，验证了该文等效刚度的合理性和精确性.最后，分析了正弦凸起凹凸板几何参数对等效刚度特性的影响，给出了结构几何参数与等效刚度之间的关系.结果表明:应用该文方法可以有效计算周期性正弦凸起凹凸板的等效刚度；由于凹凸板在构造上的几何结构变化，与基础平板相比其弯曲刚度和抗扭刚度都有明显的提升.该研究结果对凹凸板静力学和动力学的进一步研究以及实际工程应用具有指导意义.     

Concentrated force solutions for an inhomogeneous thick elastic plate

The technique developed in refs. [1-5] is applied to the problem of a concentrated line force acting in the interior of an infinite plate. The plate is of arbitrary thickness, is isotropic, but is inhomogeneous in that the elastic moduli are any specified functions, not necessarily continuous, of the through-thickness coordinate. The mechanical properties of the plate are not necessarily symmetric about the mid-surface. The solution is based on the classical solution for a concentrated force in a thin elastic plate. This classical solution is extended to give exact closed form solutions for the displacement and stress in the thick inhomogeneous plate. For a plate that is not symmetric an in-plane force gives rise to bending as well as stretching deformations. Higher order force singularities are also considered, as is the problem of a concentrated force on the boundary of a semi-infinite symmetric plate.     

Effect of bottom topography on the unsteady behaviour of an elastic plate floating on shallow water

The unsteady behaviour of a thin elastic plate in the form of a strip of constant width and infinite length, floating on the surface of an ideal and incompressible liquid, is investigated within the limits of the linear shallow-water theory. The unsteady behaviour of the plate is caused by initial disturbances or an external load. The depth of the liquid under the plate is variable. It is assumed that all the flow characteristics are independent of the coordinate along the plate. The deflection of the plate is sought in the form of an expansion in eigenfunctions of the oscillations in a vacuum with time-varying amplitudes. The problem reduces to solving an infinite system of ordinary differential equations for the unknown amplitudes. The behaviour of the plate is investigated for different actions and shapes of bottom irregularities. It is shown that the bottom topography can have a considerable effect on the deformation of the plate.     

The uniform heating and bending of a two-layer plate

The problem of the uniform heating of a two-layer plate is solved. The transversely isotropic layer considered (a soft plate) is in ideal contact with a rigid isotropic thin elastically deformed layer. The ends of the plate are load-free. A boundary layer of the soft plate (a thin contact layer) is introduced, which enables the boundary conditions on the ends of the plate to be formulated in such a way that the problem has a bounded smooth solution [1]. The two-layer plate, generally speaking, is bounded along the axis perpendicular to the axes directed along the length and thickness of the plate. The resultant force and the resultant moment, applied to the end transverse sections, are equal to zero. The exact solution of the temperature problem is sought using the equations of the theory of elasticity. The plane problem of the bending of a two-layer plate acted upon by a uniformly distributed pressure applied to the side surface of an anisotropic layer is solved by a similar method. The ends of the rigid isotropic layer are clamped.     

基于数学形态学与Radon变换的车牌定位法

从粗定位和精定位方面考虑车牌定位.利用腐蚀、膨胀和差运算将RGB车牌图像转换为车牌图像位置为彩色的而其余位置是灰色的图像,将所获得的图像转化为灰度图像,利用Robert算子进行边缘检测,再进行腐蚀和膨胀运算,根据阈值获得连通区域,利用颜色特征实现车牌的粗定位.将粗定位后的图像进行二值化、差运算、Radon变换,再进行腐蚀运算,图像的填充等步骤,再考虑图像的上下左右边界实现车牌的精定位,对185幅车牌图像进行定位.通过实验,车牌定位准确率达到91.89%.说明所提出的方法简单易行,具有一定的实效性.