Boundary integral equations for bending problem of Reissener's plates on two-parameter foundation

Two fundamental solutions for bending problem of Reissner's plates on two-parameter foundation are derived by means of Fourier integral transformation of generalized function in this paper. On the basis of virtual work principles, three boundar integral equations which fit for arbitrary shapes, lods and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates. It provides the fundamental theories for the application of BEM. A numerical example is given for clamped, simply supported and free boundary conditions. The results obtained are satisfactory as compared with the analytical methods. Project supported by the P.H.D. Foundation of National Education Committee of China     

A boundary integral equation formulation for the Reissner's plates resting on two-parameter foundation

In this paper a boundary integral equation formulation for the Reissner's plates resting on a two-parameter foundation is established. With the aid of the Hormander Operator method, the equations of the corresponding fundamental solutions are converted into a sixth order partial differential equation with a scale function as an unknown. In order to reduce the equation further, two auxiliary functions are introduced. They satisfy a second and a fourth order equation respectively. The expressions of the auxiliary functions can be derived easily. The fundamental solutions of the Reissnei's plates on the two-parameter foundation arc expressed by a linear combination of the auxiliary functions and their derivatives. The boundary integral equations are formulated by the use of the weighted residual procedure. The fundamental solutions obtained are taken as the kernel functions of the boundary integral equations. A few examples are studied. The numerical results show high accuacy and efficiency of the present formulation.This work was supported by the National Natural Science Foundation of China.     

Postbuckling behavior of rectangular moderately thick plates and sandwich plates

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The complex variable boundary element method for solving sandwich plate problems

The objective of this paper is to develop a new complex variable boundary element method for sandwich plates of Reissner's type and Hoff's type. The general solution of Helmhotz equation in complex field is given. Based on the Vekua's complex integral representation of the analytic function, the new boundary integral equations are formulated. The density function in the integral equation is determined directly by boundary element method. Some standard examples are presented, and the results of numerical solutions are accurate everywhere in the plate. The approach presented is only applicable for bounded simply connected regions. The project is supported by the National Science Foundation of China.     

Isotropicalized spline integral equation method for the analysis of anisotropic plates

In the view of Reissner’s and Kirchhoff’s theories,respectively,we formulate theisotropicalized governing equations for the anisotropic plates,and give the proof of theequivalence relation between these two plate-models for the simply-supported rectangularorthotropic plates.The well-known fundamental solutions of the isotropic plates are utlizedfor the spline integral equation analysis of anisotropic plates.Even with sparse meshes thesatisfactory results can be obtained.The analysis of plates on two-parameter elasticfoundation is so simple as the common case that only a few terms should be added to theformulas of fictitious loads.     

域内具有支承及集中质量的薄板自由振动的边界元分析

本文基于薄板小挠度弯曲问题的基本解,建立了任意边界条件、域内具有支承及附有征意个集中质量的薄板自山振动的边界积分方程,文中计算了若干算例,其精度是实际工程中所允许的。     

Boundary element analysis for bending elastic plates with three generalized displacements

In this paper, the two fundamental differential equations for bending elastic plates with three generalized displacements are transformed into a set of boundary integral equations by Green formula. Three kinds of boundary conditions on edges have been strictly derived. So this paper gives a satisfactory method of boundary element analysis for solving the problem of bending elastic plates.     

Boundary integral equations for the bending problem of plates on two-parameter foundation

By means of Fourier integral transformation of generalized fimction, the fimdamental solution for the bending problem of plales on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series.On the basis of the above work, two boundary integral eguations which are suitable to arhitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem.     

Boundary element method for orthotropic thick plates

The fundamental solutions of the orthotropic thick plates taking into account the transverse shear deformation are derived by means of Hörmander's operator method and a plane-wave decomposition of the Dirac δ-function in this papey. The boundary integral equations of the thick plates have been formulated which are adapted to arbitrary boundary conditions and plane forms. The numerical calculation of the fundamental solutions is discussed in detail. Some numerical examples are analyzed with BEM.     

不连续Reissner矩形板的自由振动

用分区加权残值法研究Ressner矩形板在几何形状,边界条件等有突变时的自由振动问题,将研究对象按照结构几何形状和边界条件的具体情况划分为若干子域,在每个子域内用不同的试函数代入该域的内的控制方程到内部残值,并代入板的边界条件和各子域的协调条件得到边界残值和连续性残值,然后用最小二乘法消除残值,得到特征方程,文中讨论了该方法的收敛性和计算精度,求解了开孔矩形板的固有频率,并与已有结果进行了比较,结果表明：？该方法收敛性好,精度较高,适用范围广。     

复变形式的各向异性板弯曲问题的基本解

提出了求解各向异性板弯曲问题基本解的新方法。得到的基本解简捷明了，相应的法向弯矩和相当剪力的表达式易求，故便于应用在一般边界条件的各向异性板弯曲问题的边界积分方程。     

ANALYSIS OF SYMMETRIC LAMINATED RECTANGULAR PLATES IN PLANE STRESS

Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of boundary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.     

正交各向异性厚板的边界元解法

本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。     

Reissner型板表面裂纹应力强度因子的线弹簧-不连续位移边界积分方程解法

本文由Reissner型板的不连续位移基本解，根据Betti互换定理，导出了Reissuer型板的不连续位移边界积分方程；结合平面问题的不连续位移边界积分方程─—边界元方法和线弹簧模型，给出了Rrissner型板表面裂纹应力强度因子的线弹簧-不连续位移边界积分方程解法。     

Modified Kirchhoff's theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoff's boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis.     

Analysis of free vibration of coupled Reissner's plate-liquid-spring system

Based on Reissner's plate theory, the dynamic behaviour of an offshore circular plate with moderate thickness floating on a liquid of finite constant depth and anchored by uniformly distributed springs to the sea bed is investigated. The frequency equation governing the motion of the coupled Reissner's plate-liquid-spring system is analytically obtained by means of the linear potential flow theory and the expansion theorem in modal analysis. Several numerical examples are presented to illustrate the variation in fundamental frequencies of Reissner's floating circular plates with free edge due to the stiffnesses of distributed springs and the depths of liquid.The author is grateful to Mr. W.M. Cheng for his help in completing the numerical calculations.     

Bending of cantilever rectangular plates with the effect of transeverse shear deformation

On the basis of Reissner's theory, the exact solutions of the bending of cantilever rectangular plates are obtained by means of the concept of generalized simply-supported boundary. From the results obtained, it can be found that the method is valid.     

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。     

Free vibration of composite plates with mixed boundary conditions based on higher-order shear deformation theory

A global higher-order shear deformation theory is devised to obtain the governing equations of composite plates under dynamic excitation. The time-harmonic solution leads to an eigenvalue problem for the natural frequencies of plates. The eigenvalue problem for rectangular plates is converted to a set of homogenous algebraic equations using differential quadrature method. The formulation of the problem allows direct application of various boundary conditions. Therefore, rectangular plates with mixed boundary conditions are also considered. To show the validity of results, the fundamental natural frequencies of composite plates with different boundary conditions and those of isotropic plates with mixed boundary conditions are compared against the results available in the literature.     

各向异性柱体扭转的充分必要的边界积分方程

本文列出各向异性柱体扭转问题无量纲化后的有关方程的边界条件推导和验证了基本解，并指出一些书中基本解列式有误＾［９－１１］，列出了充分必要的边界积分方 程，进行了数据计算，并与习用的边界积分方程所得结果进行了比较，表明在退化值附近，习用的边界积分方程所得的边界剪应力会出现巨大的误差，扭转刚度的误差则要小得多，而充要的边界积分方程计算的结果则如终保持良好的精度，再次显示了它的优点。