带裂缝梁和板的应力分析

本文用迭代法分析了带裂缝的半无限大板。对于垂直于裂缝的集中力作用于角点的情况,文中得到了新的计算结果。带裂缝梁的解答由半无限大板的解迭加上边缘效应得到。在分析边缘效应时文中用最小功法计算了梁端面力的作用,提示了一个有用的应力函数.并就一典型梁求得了边缘效应的计算结果,这一计算结果也可以近似用于其他尺寸的梁。文中用改进了的数值积分方法计算了影响函数,并计算了几个典型算例。计算结果与文献中的已有结果或有限元分析结果非常符合。     

有限宽板边裂纹上作用一对集中力时的应力强度因子K_1

对于无限大板及半无限大板的带裂纹平面问题,可用积分变换和复变函数等解析方法得到解析解。但是,确定有限尺寸带裂纹体的应力场及应力强度因子,由于数学上存在着很大困难,目前还只能采用数值解法和近似分析解...     

夹杂对两相材料界面裂纹的影响

根据界面上应力和位移的连续条件,得到了单向拉伸状态下,含有椭圆夹杂的无限大双材料组合板的复势解。进一步通过求解Hilbert问题,得到了含有夹杂和半无限界面裂纹的无限大板的应力场,并由此给出了裂尖的应力强度因子K。计算了夹杂的形状、夹杂的位置、夹杂的材料选取以及上、下半平面材料与夹杂材料的不同组合对裂尖应力强度的影响。计算结果表明夹杂到裂尖的距离和夹杂材料的性质对K影响较大,对于不同材料组合,该影响有较大差异。夹杂距裂尖较近时,会对K产生明显屏蔽作用,随着夹杂远离裂尖,对K的影响也逐渐减小。另外,软夹杂对K有屏蔽作用,硬夹杂对K有反屏蔽作用,而夹杂形状对K几乎没有影响。     

弹性地基上无限大板的统一解

利用汉克尔变换法,推演得到了文克勒地基、双参数地基、弹性半空间体地基上无限大薄板,赖斯纳、汉盖、克罗姆等中厚板,在任意竖向荷载作用下的统一解;并给出了竖向轴对称荷载条件下的无限大板挠度、弯矩、剪力系数、地基反力系数的计算公式;最后,对圆形均布荷载作用下的不同地基和板模型的板挠度和弯矩进行了对比分析。结果表明:半空间体地基板与文克勒地基板的荷载圆中点的弯矩参数十分相近,但其荷载圆中点挠度系数较后者大1/3~1/2;中厚板理论对地基板挠度有更好地拟合和解析,但对板弯矩等内力的计算精度无改善。     

板下地基位移分布规律及参数确定

将弹性半空间地基受任意竖向荷载作用下的静力位移积分变换解与弹性半空间地基上四边自由矩形板受任意竖向荷载作用下的弯曲解析解相结合,建立了求解板下地基位移的一般方法.对一些算例,进行大量数值计算分析,得出弹性半空间地基上四边自由矩形板下地基水平位移和竖向位移的分布规律,地基影响深度,并由此分布规律确定了其相应的简化模型-双参数地基模型的两个参数.     

中心小裂纹的弹塑性分析

用修正能量法得到含中心小裂纹平板在均匀载荷作用下的J积分和张开位移的全塑性解。并用弹塑性分析的工程方法得到相应的弹塑性解。结果与无限大板的解作了比校,表明当a/b≤0.05时两者的差别小于5％。而对于a/b>0.05的情况,把无限大板的解用于中心小裂纹的板条可能会产生较大的误差。     

夹杂角端部奇异应力场分析

提出一种分析夹杂角端部奇异应力场的新型杂交有限元方法.构造了一个角端部奇异单元,该单元刚度建立不依赖数学解析解.用这种方法计算了单向载荷作用下无限大板含单个方形夹杂和菱形夹杂角端部奇异应力场,并与现有的数值解进行了比较,结果表明:目前的数值方法是可行的、有效的、数值结果精度高,适用范围广.作为应用讨论了双方形夹杂刚度和位置对夹杂角端部奇异应力场的影响.     

嵌入无限大弹性板中圆板的热屈曲分析

分析了嵌入无限大弹性板中的圆板在变温时的热屈曲问题。由于圆板的热膨胀系数与无限大弹性板的热膨胀系数不同,温度变化时圆板中会产生压应力。当压应力达到其临界值时,圆板会发生热屈曲。首先,基于弹性力学平面应力问题的基本理论,得到圆板和无限大弹性板的应力和位移;然后建立圆板热屈曲的控制微分方程,求得临界屈曲温度的解析解和数值解,着重讨论圆板和无限大弹性板的材料物性参数的关系对圆板临界屈曲温度的影响。     

膜-基复合材料界面剪应力的三维半解析计算

 采用影响系数法对膜-基复合材料的界面剪应力三维半解析进行 了分析研究.利用三维有限元方法对薄膜的影响系数进行了计算. 将 基体作为半无限大体，利用其平面边界作用单位力时的位移场解析 解，得到基体的影响系数. 结果表明，对膜-基复合材料界面剪应力 进行三维半解析计算，克服了完全用三维有限元对其进行计算的限 制，为该类问题的分析提供了新的途径.     

含孔曲板弹性波散射与动应力分析

基于敞口浅柱壳弹性波动方程及摄动方法，对无限大含孔曲板弹性波散射及动应力问题进行了分析研究，将经典薄板弯曲波动问题的分析解作为本问题的主项，给出了在稳态波下孔洞附近散射波的零阶渐近解。建立了求解含孔曲板弹性波散射与动应力问题的边界积分方程法，利用积分方程法可获得问题的近似分析解。并给出了无限大曲板圆孔附近动应力集中系数的数值结果，且对计算结果进行了分析与讨论。     

Analytical bending solutions of free orthotropic rectangular thin plates under arbitrary loading

This paper presents the analytical solutions for the bending of orthotropic rectangular thin plates by the double finite integral transform, which, as an effective tool in solving plate problems, should have received attention. As a representative and difficult problem in the theory of plates, free plates’ bending is successfully solved to demonstrate the accuracy of the method by comparing the present analytical solutions with those from the literature as well as those by the finite element method. With the proper integral transform kernels, the proposed solution procedure is applicable to the bending of orthotropic rectangular plates with all combinations of simply supported, clamped and free boundary conditions, which serves as an elegant approach to analytical solutions of plate bending problems.     

Vibrations of highly prestressed anisotropic plates via a numerical-perturbation technique

The method of matched asymptotic expansions is used to reduce the problem of the transverse vibrations of a highly prestressed anisotropic plate into the simpler problem of the vibration of an anisotropic membrane with modified boundary conditions that account for the bending effects. In the absence of an exact solution the membrane problem can be solved by any well-known numerical technique. The numerical-perturbation results for a clamped circular plate with rectangular orthotropy and a uniform tensile stress applied on its boundary show an excellent correlation with finite-element solutions for the original problem. Furthermore, the solutions obtained for annular plates form the basis for solutions to problems involving near-annular plates.     

Symplectic system based analytical solution for bending of rectangular orthotropic plates on Winkler elastic foundation

This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.     

功能梯度中厚圆/环板轴对称弯曲问题的解析解

基于一阶剪切变形板理论，导出了热/机载荷作用下，位移形式的功能梯度 中厚圆/环板轴对称弯曲问题的控制方程，获得了问题的位移和内力的一般解析解. 作为特 例，分别研究了边缘径向固定和可动的夹紧和简支的4种实心功能梯度圆板，给出了它们的 解，并分析了热/机载荷作用下解的形态，讨论了横向剪切变形、材料梯度常数和边界条件， 对板的轴对称弯曲行为的影响.     

Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material(FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching–bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-ofvariables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.     

On constructing a Green’s function for a semi-infinite beam with boundary damping

The main aim of this paper is to contribute to the construction of Green’s functions for initial boundary value problems for fourth order partial differential equations. In this paper, we consider a transversely vibrating homogeneous semi-infinite beam with classical boundary conditions such as pinned, sliding, clamped or with a non-classical boundary conditions such as dampers. This problem is of important interest in the context of the foundation of exact solutions for semi-infinite beams with boundary damping. The Green’s functions are explicitly given by using the method of Laplace transforms. The analytical results are validated by references and numerical methods. It is shown how the general solution for a semi-infinite beam equation with boundary damping can be constructed by the Green’s function method, and how damping properties can be obtained.     

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     

四种非正交边界板考虑初始荷载效应的后期荷载位移近似解

基于考虑初始荷载效应情况下板的一般形式的静力平衡微分方程,运用坐标变换得到了轴对称情形,考虑初始荷载效应后圆形板的极坐标形式的静力平衡微分方程。运用Galerkin法解得了简支等边三角形板、固支椭圆板、固支圆形板和简支圆形板四种非正交边界板考虑初始荷载效应的后期荷载位移近似解。运用相关文献提出的有限元法验证了近似解的正确性。各位移近似解表达式简单、物理意义明确,清楚地反映了初始荷载及相关因素对后期荷载位移的影响。计算分析表明：初始荷载效应提高了板的弯曲刚度,减小了板的后期荷载位移;板的初始荷载效应主要受初始荷载、跨厚比及边界条件等因素的影响。     

热/机械载荷下功能梯度材料矩形厚板的弯曲行为

采用Reddy高阶剪切板理论，考虑材料物性参数随坐标和温度变化的特性，研究在均匀变化的温度场内功能梯度材料矩形板在面内与横向载荷共同作用下的横向弯曲问题，基于一维DQ法和Galerkin技术，给出了一对边固支，另对边任意约束时板弯曲问题的半解析解，以Si3N4/SUS304板为例考察了材料组份，温度场，面内载荷及边界约束条件等对功能梯度材料板弯曲行为的影响。     

Variational approach to non-linear boundary value problems for elasto-plastic incompressible bending plate

Non-linear boundary value problems for inelastic isotropic homogeneous incompressible bending plate, within the range of J₂-deformation theory, are considered. An existence of the weak solution of the non-linear problem with clamped boundary condition is obtained in H²(Ω) by using monotone operator theory and Browder-Minty theorem. For linearization of the non-linear problem a monotone iteration scheme is constructed. It is shown that the sequence of potentials obtained from the sequence of approximate solutions (i.e. iterations), is a monotone decreasing one. Convergence of the iteration process in H²-norm is proved by using the convexity argument. Numerical solutions, based on finite-difference scheme, are given for linear bending problems with rigid clamped as well as simply supported boundary conditions. Further numerical examples are presented to illustrate the convergence of approximate solutions and monotonicity of the potentials as applied to the non-linear problems.