Tensile and compressive buckling of plates weakened by cracks

Plates are susceptible to buckling under compression when the thickness dimension becomes sufficiently small. Such mode of structure failure can prevail even if the plates were extended in tension. Wribkling of stretched thin sheets is a commonly observed phenomenon that leads to complex deflection patterns, particularly in regions close to crack-like imperfections. Predictions of the buckled displacement modes for plates weakened by cracks will be made on the basis of a theory formulated by application of variational calculus. Finite element method is used such that defects of other shapes can also be analyzed. Various buckled displacement modes of a center-cracked plate are determined and displayed graphically. The critical buckling loads are found to decrease with increasing crack size. Moreover, local wrinkling of the plate surface becomes less pronounced for the higher buckling modes. The method of solution applies equally well to plates that are initially curved.     

A simple method for measuring local buckling of thin plates

A simple computer-interfaced optical system for measuring the dynamic-local-buckling deformation of thin-walled metal structural-plate elements is described in this paper with two sets of experimental results. The major advantage of this system is its simplicity and economy as well as its speedy automated process for data scanning, acquisition, and analyses by using a microcomputer.Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.     

Impact buckling of orthotropic shells of revolution with allowance for geometric nonlinearity

Scientific Research Institute of Mechanics, Gorky University, Gorky. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 43–50, May, 1990.     

黏弹性板的大挠度蠕变屈曲

研究了具有初始小挠度受轴向压载黏弹性板的蠕变屈曲问题,在建立控制方程时,利用了von Karman非线性应变-位移关系,并考虑了初始挠度,用标准线性固体模型描述材料的黏弹性特性,在求解非线性积分方程时,利用梯形公式计算记忆积分式,将非线性积分方程化为非线性代数方程进行数值求解,得到了结构的蠕变变形过程,又将问题退化到小挠度情况进行研究,得到了挠度随时间扩展的解析解,分析了瞬时失稳临界载荷、持久临界载荷的物理意义,讨论了考虑几何非线性对黏弹性板蠕变屈曲的影响。     

Scale effect in molding-composition plates with cracks

In [5–7], the influence of the relation between the plate width and the crack length on the limiting load for steel was investigated. The hazardous defect dimension in steel is determined by the grain size, and may be neglected in practice. For molding compositions reinforced by glassfiber or glass-strip sections, the hazardous defect dimension may be comparable with that of a visually observable crack. In that case, the failure criterion and the scale effect for a cracked plate depends on the relation between the plate width and the crack length, and on the crack-resistance characteristic of the material, which is the length of the crack equivalent to the hazardous defect in the material. The aim of the present work is to investigate this characteristic experimentally in various loading conditions, for the example of AG-4V molding composition and to develop a simple model permitting the prediction of the scale effect in analogous materials.S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 1, pp. 62–67, January, 1994.     

Creep of axisymmetrically loaded plates with allowance for damage accumulation in their material

The Rabotnov kinetic creep theory was used to calculate the stress-strain state and damage accumulation in the material of axisymmetrically loaded circular and ring plates at any time before the beginning of fracture. It is shown that the solution of the problem can be reduced to solving the same problem under the assumption of steady-state creep of the material. The unsteady creep problem is solved by multiplying the known solution of the steady-state creep problem by certain functions of the coordinates and time, which are determined from a corresponding system of equations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 157–168, September–October, 2006.     

Stiffness and buckling optimization of thin plates with BEM

The thickness optimization is used to maximize the stiffness or the buckling load of a Kirchhoff plate having constant volume. The shape of the plate is arbitrary and it is subjected to any type of admissible boundary conditions. The optimization consists in establishing the thickness variation law, for which either the stiffness of the plate or the buckling load is maximized. Beside the equality constraint of constant volume, the thickness variation is subjected also to inequality constraints resulting from serviceability requirements (upper and lower thickness bounds) as well as from the condition that the Kirchhoff plate theory remains valid. The latter constraint is new and it is derived herein by approximating the plate with a three-dimensional prismatic elastic body having curved upper and lower surface. The optimization problem is solved using the sequential quadratic programming algorithm. The bending and the plane stress problem of a plate with variable thickness, required for the evaluation of the objective function, are solved using the analog equation method. The thickness is approximated using integrated radial basis functions that approximate accurately not only the thickness function but also its first and second derivatives involved in the plate equation and in the constraints. Several plate optimization problems have been studied giving realistic and meaningful optimum designs without violating the validity of the thin plate theory.     

Local buckling of extended plates containing cracks and cracklike defects, subject to the influence of geometrical parameters of the plates and the defects

An experimental study of the local buckling of plates containing cracks and cracklike defects is reported, where the influence of the geometrical parameters of the plate and the defect are taken into account. An empirical curve is plotted to estimate the critical stresses at which buckling takes place. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 80–84, December, 1999.     

Stability of thin plates with cracks under biaxial tension

Conclusions A method has been developed for analyzing the stability of thin plates with cracks under biaxial tension which is based on measuring the local buckling of the plate in the crack region with pneumatic instruments and describing the results in the system of plate coordinates.It has been demonstrated that the critical stress corresponding to local loss of stability depends strongly on the magnitude of the force acting along the crack. Values of the bending factor have been determined experimentally for plates of the grade AMg6M aluminum alloy. Unlike in the case of no load along the crack, in the case of biaxial loading the value of this bending factor does depend on the geometrical parameters of the plate.An empirical expression has been derived for the bending factor which, for this particular material, yields values close to experimental ones.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 18, No. 10, pp. 80–85, October, 1982.     

Thermal buckling analysis of truss-core sandwich plates

Truss-core sandwich plates have received much attention in virtue of the high values of strength-to-weight and stifness-to-weight as well as the great ability of impulseresistance recently. It is necessary to study the stability of sandwich panels under the influence of the thermal load. However, the sandwich plates are such complex threedimensional(3D) systems that direct analytical solutions do not exist, and the finite element method(FEM) cannot represent the relationship between structural parameters and mechanical properties well. In this paper, an equivalent homogeneous continuous plate is idealized by obtaining the efective bending and transverse shear stifness based on the characteristics of periodically distributed unit cells. The first order shear deformation theory for plates is used to derive the stability equation. The buckling temperature of a simply supported sandwich plate is given and verified by the FEM. The efect of related parameters on mechanical properties is investigated. The geometric parameters of the unit cell are optimized to attain the maximum buckling temperature. It is shown that the optimized sandwich plate can improve the resistance to thermal buckling significantly.