Stability of a rectangular plate under biaxial tension

The stability problem of a rectangular plate undergoing uniform biaxial in-plane tensile strain is solved using the three-dimensional equations of nonlinear elasticity. The surfaces of the plate are stress-free, and special boundary conditions that allow one to separate variables in the linearized equilibrium equations are specified on the lateral surfaces. For three particular models of incompressible materials, the critical curves are constructed and the instability region is determined in the plane of the loading parameters (the multiplicities of elongations of the plate material in the unperturbed equilibrium state). The numerical results show that for thin plates loaded by tensile stresses, the size and shape of the instability region depend only slightly on the relation among the length, width, and thickness of the plate. Based on the results obtained, a simple approximate stability criterion is proposed for an elastic plate under tensile loads. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 94–103, July–August, 2007.     

正交各向异性薄板的弹塑性屈曲分析

本文应用混合硬化正交各向异性塑性理论和屈曲的能量法则，推导了正交各向异性薄板在面内压缩情况下的弹塑性稳定方程，计算了相应的临界荷载，并讨论几何形状、边界条件及诱导荷载比等对临界应力的影响。分析表明材料的各向异性性质对弹塑性临界应力的有较大的影响。     

Stability of clamped skew plates

The stability problems of clamped skew plates are considered with the inplane stresses represented in terms of oblique components. Deflection is expressed in terms of a double series of beam characteristic functions of clamped-clamped beam. Energy method is used to obtain buckling coefficients under individual loadings and for a few cases of combined loading. Convergence is examined in a few representative cases. For buckling in shear, two critical values exist the magnitude of negative shear being much larger than that of positive shear.     

Critical loads of shells with high-modulus reinforcement

The analytical method developed to determine the upper and lower critical stresses is applied to cylindrical shells reinforced with stringers and rings. Buckling modes typical of shells reinforced with discrete ribs are considered. The minimum critical loads are determined and compared with available experimental data. Perfect and imperfect ribbed shells with high-modulus reinforcement are studied. It is proved that the effect of small axisymmetric imperfections in such shells is not so drastic as in isotropic shells. Ribs made of a high-modulus material can enhance the stability of shells by a factor of tens     

Effect of the stiffness of ribs on the vibrations and stability of open cylindrical shells

The effect of the stiffness of ribs on the minimum natural frequencies and critical stresses of axially compressed open cylindrical shells reinforced with a quasiregular set of longitudinal ribs is analyzed by way of numerical examples. It is shown that the earlier discovered phenomenon of abrupt decrease in the minimum frequencies is independent of rib stiffness for certain modes and a small number of ribs     

黏弹性环形板的临界载荷及动力稳定性

利用线性黏弹性力学的Boltzmann叠加原理,在考察位移单值性条件的基础上,给出黏弹性环形板非线性动力学分析的初边值问题。通过Galerkin方法和引进新的状态变量,将其化归为四维非线性非自治常微分方程组,从而得到黏弹性环形板的四种临界载荷,同时考察了几何缺陷对黏弹性薄板临界载荷的影响。根据Floquet理论,得出黏弹性形板在周期激励下的线性动力稳定性判据。综合使用非线性动力学中的数值分析方法,研究了参数对黏弹性环形板非线性动力稳定性的影响。     

Exact solutions for variable-thickness inhomogeneous elastic plates under various boundary conditions

In this paper, an exact solution to the governing equations of the bending of a variable-thickness inhomogeneous rectangular plate is presented. The procedure is applicable to variable-thickness inhomogeneous rectangular plates with two opposite edges simply supported. The remaining ones subjected to a combination of clamped, simply supported, and free boundary conditions and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for variable-thickness inhomogeneous orthotropic plates as for uniform-thickness homogeneous isotropic plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of the inhomogeneity, aspect ratio, thickness parameter and degree of non-uniformity on the deflections and stresses are investigated. This paper is partially supported by the Deanship of Scientific Research at King AbdulAziz University (Grant no. 172/427).     

Buckling and cracking characteristics of two-layered plate in tension

This study is concerned with the loss of local stability of two-layered metal plates (steel–aluminium alloy) with a crack in tension. The critical stresses corresponding to the initiation of buckling are determined. The post-critical deformation and form of stability loss are investigated. The influence of buckling on the fracture characteristics is also estimated.     

Influence of discretely arranged longitudinal ribs on the stability and vibrations of open circular cylindrical shells

Open cylindrical shells reinforced with quasiregular sets of longitudinal ribs and hinged at all edges are considered. The effect of the discrete arrangement and number of ribs on the critical stresses that cause instability under longitudinal compression and on the minimum natural frequencies of vibrations is examined. Numerical results are analyzed     

局部载荷作用简支板屈曲分析

根据能量原理,引入大挠度Von-Karman方程,求解了应力不连续简支板的屈曲问题,得到了临界载荷和临界应力计算系数.     

Multi-mode wave propagation in ribbed plates. Part II: Predictions and comparisons

This paper addresses dispersion curve numerical computations for specific ribbed plates. Precisely, wave propagation in the direction parallel to the ribs is the main objective. First, analytical calculations are performed for such ribbed plates after which the results are compared to a more general numerical procedure. This procedure reuses a reduced finite element model of the ribbed plate and extracts guided multi-mode propagation parameters. Comparisons of analytical and numerical estimations show very good agreement. Finally, the experimental results obtained in the companion paper are considered. Specifically, experimental and numerical dispersion curves are compared over a wide frequency range. Close concordance is obtained allowing the dispersion curves to be fully interpreted.     

Fundamental solutions of the thermoelastic equations for transversely isotropic plates

The problem of thermoelasticity for transversely isotropic plates acted upon by concentrated heat sources is solved. The {1, 2}-order equations of thermoelasticity that incorporate the transverse shear and normal stresses are used. A bending heat source with symmetric heat transfer is considered. The dependence of thermal stress components on the thermal and thermomechanical parameters of transversely isotropic plates is studied     

Stability and vibrations of cylindrical shells discretely reinforced with rings

The linearized system of homogeneous equations of motion of cylindrical shells discretely reinforced with quasiregular sets of ring ribs is solved. Approximate formulas for the critical stresses and natural frequencies are presented     

Theoretical analysis of the sound absorption characteristics of periodically stiffened micro-perforated plates

The vibro-acoustic responses and sound absorption characteristics of two kinds of periodically stiffened micro-perforated plates are analyzed theoretically. The connected periodical structures of the stiffened plates can be ribs or block-like structures. Based on fundamental acoustic formulas of the micro-perforated plate of Maa and Takahashi, semi-analytical models of the vibrating stiffened plates are developed in this paper. Approaches like the space harmonic method, Fourier transforms and finite element method （FEM） are adopted to investigate both kinds of the stiffened plates. In the present work, the vibro-acoustic responses of micro-perforated stiffened plates in the wavenumber space are expressed as functions of plate displacement amplitudes. After approximate numerical solutions of the amplitudes, the vibration equations and sound absorption coefficients of the two kinds of stiffened plates in the physical space are then derived by employing the Fourier inverse transform. In numerical examples, the effects of some physical parameters, such as the perforation ratio, incident angles and periodical distances etc., on the sound absorption performance are examined. The proposed approaches are also validated by comparing the present results with solutions of Takahashi and previous studies of stiffened plates. Numerical results indicate that the flexural vibration of the plate has a signif- icant effect on the sound absorption coefficient in the water but has little influence in the air.     

Evaluation of Residual Stresses Induced by Robotized Hammer Peening by the Contour Method

Welded components suffer from high tensile residual stresses close to the weld beads. These stresses seem to be the origin of premature cracking which could result in a catastrophic rupture during operation and a reduction of the lifespan of these components. In this context, the Hydro-Québec’s Research Institute (IREQ) developed a technique of residual stresses relaxation by robotized hammer peening which makes it possible to release stresses close to surface and preserve the mechanical and dimensional properties of manufactured components. Robotized hammer peening was used to induce compressive residual stresses on initially stress free samples of austenitic stainless steel 304L. Hammer peening layers from one to nine were performed and the resulting residual stresses were evaluated thanks to the contour technique. Complete 2D residual stress fields on samples cross sections were obtained. The ability of hammer peening to relax residual stresses within welded plates was then quantified on austenitic stainless steel 304L plates welded with a 308 steel and hammer peened. These tests show the efficiency of hammer peening as a method to relax tensile residual stresses and induce compressive ones to a depth of a few millimetres. Process parameters were optimized such as the number of hammer peening layers to be applied to reduce processing time and maximization of the intensity and spatial distribution of the compressive residual stresses.     

Fracture mechanics based design procedures for pressurized components having part-through cracks

This paper presents a fracture mechanics based design procedure for pressurized components having part-through cracks. Fracture critical stresses are evaluated for the assumed crack configurations and the fracture envelopes are obtained for these configurations. For small size crack configurations, Feddersen's type correction is made for proper estimation of critical stress values. Residual strength of unbroken ligament is a more appropriate criterion for the design of thin sections with parth-through cracks. A criterion based on the ligament failure is defined for cases where the critical fracture stresses are above the material yield stress value. The procedure is illustrated by presenting an example of a pressurized tankage used in aerospace industry.     

Assessment of approximate models to evaluate transient and cyclical hygrothermoelastic stress in composite plates

The present paper aims at assessing an approximate model to evaluate hygrothermoelastic stress in composite laminated plates. The approximate model is based on straight hypotheses (classical lamination theory of plates) and is able to simulate the effects of complex hygrothermal conditionings, such as those encountered in the life of real structures. For the purpose of the assessment, a 3D analytical solution for hygrothermally stressed plates is employed. The approximate model for plates is also compared to an analytical model for cylinders under transient and cyclical hygrothermal loads [Jacquemin, F., Vautrin, A., 2002a. Modelling of the moisture concentration field due to cyclical hygrothermal conditions in thick laminated pipes. European Journal of Mechanics – A/Solids 21, 845–855; Jacquemin, F., Vautrin, A., 2002b. A closed-form solution for the internal stresses in thick composite cylinders induced by cyclical environmental conditions. Composite Structures 58, 1–9]. This is done in order to assess the capabilities and the limits of a simplified model for plates to represent also the behaviour of cylinders.     

Some features of the buckling of stringer shells

A technique for stability analysis of stringer shells is proposed. It is used to analyze the minimum critical stresses. The dependence of the dimensionless parameters σ_cr/σ_cl on the number of stringers is plotted. The linear and nonlinear theories of ribbed shells are used to examine the features of how stringer shells lose stability. It is shown that the minimum critical stresses determined using the theory of ribbed shells and a structurally orthotropic model are close within the range of stiffness parameters considered __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 59–64, February 2006.     

基于无网格法的非均匀弹性地基上变厚度加筋板弯曲与固有频率分析

采用基于移动最小二乘近似的无网格方法并结合一阶剪切变形理论,分析了非均匀弹性地基上变厚度加筋板的弯曲和固有频率问题.首先,用节点对变厚度板和筋条分别进行离散,导出变厚度板和筋条的势能;其次,利用筋条与变厚度板之间的位移协调条件将筋条的节点参数转换为板的节点参数,再将两者的势能进行叠加得到变厚度加筋板的总势能,并根据能量...     

联合载荷作用下简支矩形板的屈曲和过屈曲

本文研究了简支正交各向异性矩形板在两对板受中面压力作用下的屈曲和过屈曲性态,得到了载荷的稳定性区域,证明了临界载荷最多为二重的。利用多参数摄动方法求得临界载荷附近板的过屈曲状态的渐近解,分析了在二重临界载荷附近,当载荷按比例变化时,板的可能的过屈曲状态及其与参数的依赖关系。