On stress concentration in rectangular plates having rectangular inserts

This paper deals with a study of stress-concentration factors in finite rectangular plates with rectangular inserts. The paper includes the effects of insert size and its orientation on stress concentrations. Photoelastic models for this investigation are made from hard and soft plastics having different elastic properties.     

各向异性矩形板的剪切屈曲分析

根据各向异性矩形薄板剪切屈曲横向位移函数的微分方程建立了一般性的解析解。该一般解包括三角函数和双曲线函数组成的解,它能满足四个边为任意边界条件的问题;该一般解还包括代数多项式解,它能满足四个角的边界条件问题。因此,这一解析解可用于精确地求解任意边界的各向异性矩形板的剪切屈曲问题。其中待定常数可由四边和四角的边界条件来确定,由此得出的齐次线性代数方程系数矩阵行列式等于零可以求得各阶临界载荷及其屈型。结合配点法,利用变形的对称和反对称性,以及对称迭层正方形板均可使计算更简单。以四边平夹的对称角铺设复合材料迭层板为例进行了计算和讨论。     

On the analysis of thick rectangular plates

Summary Thick rectangular plates are investigated using the method of initial functions proposed by Vlasov. The governing equations are derived from the three-dimensional elasticity equations using a MacLaurin series approach. As the governing equations can be obtained in the form of series, approximate theories of any desired order can be constructed easily by proper truncation. An exact solution is obtained for an allround simply supported thick plate using a Navier type solution. A Levy type solution for higher order theories is illustrated for the case of a thick plate with two opposite edges simply supported and other two edges clamped. Numerical results obtained are compared with those of classical, Reissner and Srinivas et al. solutions.

---

Übersicht Mit Hilfe der Methode der Initial-Funktionen von Vlasov werden rechteckige Platten untersucht. Die zugehörigen Gleichungen werden aus den Gleichungen für das dreidimensionale Problem durch eine Entwicklung in MacLaurin-Reihen gewonnen. Durch Abbrechen dieser Reihen können Näherungen beliebiger Ordnung erhalten werden. Für den Fall einer allseitig einfach gelagerten dicken Platte wird eine exakte Lösung erhalten, bei der eine Lösung vom Navier-Typ verwendet wird. Eine Lösung vom Levy-Typ höherer Ordnung wird am Beispiel einer dicken Platte abgeleitet, von der zwei gegenüberliegende Ecken einfach gelagert, die anderen fest eingespannt sind. Die numerischen Ergebnisse werden mit den klassischen, von Reissner, Srinivas u. a. erhaltenen Resultaten verglichen.

     

混合边界各向异性矩形板的静力分析

采用一般解析解和配点法相结合的方法,求解混合边界各向异性矩形板的弯曲问题.先由弯曲挠度的微分方程求出各种类型的齐次解和特解,然后组成一般解析解,再将板的每个边等分 为很多微小的段,仅对每一微段的中点建立应满足的边界条件,由全部边界条件方程式即可求得全部积分常数.以每边一半边界为平夹、另一半边界为简支或自由的方板为例进行了计算,并与四边均为简支的方板进行了对比,表明理论简单,结果实用.     

Perturbation analysis for the postbuckling of rectangular orthotropic plates

In this paper, applying perturbation method to von Kármán-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, thé postbuckling behavior of simply supported rectangular orthotropic plates under inplane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.     

Stability analysis of rectangular plates unidirectionally strengthened by ribs

The exact solution of the equations of neutral equilibrium is derived. The effect of the discrete arrangement of ribs on the behavior of the characteristics of the stress-strain state with distance from the plate edge is analyzed. The conditions of applicability of the theory of structurally orthotropic plates are formulated. The study was carried out in accordance with Project No. 614 of the Ukrainian Scientific and Technological Center. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 132–136, April, 2000.     

Numerical and experimental analysis of natural vibrations of rectangular plates with variable thickness

It is proposed to solve problems on natural vibrations of rectangular plates of variable thickness under complex boundary conditions using the numerical-analytical spline-collocation method in combination with the discrete-orthogonalization method and the experimental method of holographic interferometry. As a mathematical model, the problem on natural vibrations of a square plate with constant thickness and fixed ends is solved. The approximate solutions obtained are compared with experimental data. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 131–134, February 2000.     

Compression analysis of rectangular elastic layers bonded between rigid plates

An elastic layer bonded between two rigid plates has higher compression stiffness than the elastic layer without bonding. While the finite element method can be applied to calculate the stiffness, the compression stiffness of bonded rectangular layers derived through a theoretical approach in this paper provides a convenient way for parametric study. Based on two kinematics assumptions, the governing equation for the mean pressure is derived from the equilibrium equations. Using the approximate shear boundary condition, the mean pressure is solved and the compression stiffness of the bonded rectangular layer is then established in an explicit single-series form. Through the solved pressure, the horizontal displacements are derived from the corresponding equilibrium equations, from which the shear stress on the bonding surface can be found. It is found that the effect of the rectangular aspect on the compression stiffness is significant only when Poisson’s ratio is near 0.5. For the smaller Poisson’s ratio, the compression stiffness of the rectangular layer can be approximated by the formula for the infinite-strip layer of the same shape factor.     

Lateral instability of rectangular plates

This paper investigates the problems of lateral buckling of rectangular plates. In the text we discuss the minimum critical load of the lateral buckling occurring on under a concentrated force, uniformly distributed load and the concentrated couples, respectively. The energy method is used in this article.