复杂载荷下复合材料对称层合板的椭圆形分层屈曲

应用Ｒａｙｌｅｉｇｈ－Ｒｉｔｚ法对含有单个椭圆形分层的复合材料对称层板在压剪载荷联合作用下的脱层屈曲问题进行了分析计算。给出相应于不同的椭圆长短半轴之比ａ／ｂ值下及不同椭回主轴的偏角时，脱层屈曲的临界应变值。此计算考虑了层板的拉伸剪切藕合刚度影响及子层本身弯曲－扭转耦合刚度，和拉伸－弯曲耦合刚度的影响，给出有工程参考价值的计算结果。     

含椭圆孔的变角度复合材料层合板的屈曲性能研究

本文利用变角度复合材料的纤维方向角可沿平面位置任意连续变化的特点,提出在孔附近采用与孔同心的椭圆曲线作为纤维铺设路径的层合板铺层方案,以改善含椭圆孔的层合板的孔边应力集中,进而提高层合板的抗屈曲性能．主要研究内容有：利用ABAQUS软件分析本文提出的孔边特殊铺层方式下变角度复合材料层合板的面内应力分布及屈曲性能,通过与传统直线铺层方式以及线性变角度铺层方式进行比较,说明了本文提出的新铺层方式的优越性,并详细分析了椭圆孔的离心率、开孔尺寸及开孔方位对层合板的屈曲临界荷载的影响．研究结果可为含椭圆孔的变角度复合材料层合板的结构设计和优化提供一定的参考．     

Shock initiated instabilities in underwater cylindrical structures

An experimental investigation to understand the mechanisms of dynamic buckling instability in cylindrical structures due to underwater explosive loadings is conducted. In particular, the effects of initial hydrostatic pressure coupled with a dynamic pressure pulse on the stability of metallic cylindrical shells are evaluated. The experiments are conducted at varying initial hydrostatic pressures, below the critical buckling pressure, to estimate the threshold after which dynamic buckling will initiate. The transient underwater full-field deformations of the structures during shock wave loading are captured using high-speed stereo photography coupled with modified 3-D Digital Image Correlation (DIC) technique. Experimental results show that increasing initial hydrostatic pressure decreases the natural vibration frequency of the structure indicating loss in structural stiffness. DIC measurements reveal that the initial structural excitations primarily consist of axisymmetric vibrations due to symmetrical shock wave loading in the experiments. Following their decay after a few longitudinal reverberations, the primary mode of vibration evolves which continues throughout later in time. At the initial hydrostatic pressures below the threshold value, these vibrations are stable in nature. The analytical solutions for the vibration frequency and the transient response of cylindrical shell are discussed in the article by accounting for both (1) the added mass effect of the surrounding water and (2) the effect of initial stress on the shell imposed by the hydrostatic pressure. The analytical solutions match reasonably well with the experimental vibration frequencies. Later, the transient response of a cylindrical shell subjected to a general underwater pressure wave loading is derived which leads to the analytical prediction of dynamic stability.     

Determination of column-buckling criteria using vibratory data

A mathematical model is presented which describes a nondestructive testing procedure for determining buckling criteria for structures. The procedure requires identification of the structure's support boundary conditions using vibration data. Column-buckling experiments are presented which validate the model. The results illustrate the feasibility of using such models to predict the buckling load for structures whose support boundary conditions are not known in advance of service.     

The buckling behavior of uniformly heated thin circular cylindrical shells

The results of buckling tests on uniformly heated, clamped, thin circular cylindrical shells are presented and discussed. Particular attention is paid to both the actual buckling process and the ensuing post-buckling behavior. Load vs. end-shortening curves are included. The possibility of “snap-through” buckling which occurs at a value of end shortening greater than that corresponding to the maximum supported load is experimentally verified. A comparison of the present experimental results with available theory is made. It is observed that the experimental values of the buckling temperature can be substantially greater than the temperatures calculated by linear theory from the experimental buckling loads; however, the buckling stresses are the same whether the loading is thermal or mechanical.     

Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading

Free transverse vibration and buckling of a double-beam continuously joined by a Winkler elastic layer under compressive axial loading with the influence of rotary inertia and shear are considered in this paper. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli?CFourier method. The boundary value and initial value problems are solved. The natural frequencies and associated amplitude ratios of an elastically connected double-beam complex system and the analytical solution of the critical buckling load are determined. The presented theoretical analysis is illustrated by a numerical example, in which the effect of physical parameters characterizing the vibrating system on the natural frequency, the associated amplitude ratios and the critical buckling load are discussed.     

黏弹性薄板蠕变屈曲的载荷-时间特性研究

通过对黏弹性薄板压屈的稳定性分析,着重讨论了蠕变屈曲载荷－时间的特性,理论分析表明：黏弹性薄板蠕变屈曲与材料的力学性能密相关,屈曲载荷不像弹性薄板为一定值,而是与时间相关的;在一定载荷下,经过一段时间后出现延迟屈曲,相关的实验研究也证实这一重要结论;这种延迟失稳问题在工程中有其重要的意义。     

Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory

Analytical solutions for bending, buckling, and vibration of micro-sized plates on elastic medium using the modified couple stress theory are presented. The governing equations for bending, buckling and vibration are obtained via Hamilton’s principles in conjunctions with the modified couple stress and Kirchhoff plate theories. The surrounding elastic medium is modeled as the Winkler elastic foundation. Navier’s method is being employed and analytical solutions for the bending, buckling and free vibration problems are obtained. Influences of the elastic medium and the length scale parameter on the bending, buckling, and vibration properties are discussed.     

An experimental study of the parametric excitation of a tensioned sheet with a cracklike opening

The problem of the parametric excitation of a thins tensioned sheet with a cracklike opening is discussed Data obtained from an experimental investigation are presented and they indicated that both principal and secondary regions of instability are developed. Plts of the stability boundaries are presented in terms of excitation frequency, mean tensile load and alternating load. The principal region is observed to be significantly larger than the secondary region and the amplitudes of the oscillations associated with the principal region are also much larger than those of the secondary region. Oscillation amplitudes of the order of twelve times the thickness are reported and amplitude vs. excitation-frequency data are shown to exhibit an overhang behavior in the direciton of increasing frequency. This indicates the presence of a nonlinear stiff effect which is attributed to middle-surface stretching due to bending. Although damping and membrane effects were found to prevent the development of unbounded oscillations, it is noted that the large deflections associated with the principal region of instability could be expected to have a deterious effect on both crack nucleation and crack propagation.     

Predicting buckling loads from vibration data

There are analytical methods for predicting the buckling loads of columns with the boundaries ideally fixed, i.e., simply supported or built-in, or partially fixed. Vibration-test results may furnish a practical method of measuring the fixity. In this investigation a beam, that may or may not be loaded as a column, is assumed to have a torsional spring at each end such that a zero torsional stiffness corresponds to a simply supported end and an infinite torsional stiffness corresponds to a built-in end. From a Rayleigh-Ritz analysis, the buckling load and the fundamental frequency of the beam are each computed as a function of the torsional stiffness. This procedure leads to a one-to-one nondimensional relationship between the buckling load and the natural frequency. From these calculations, it is seen that regardless of the degree of clamping of one end relative to the other end, all that is needed to predict the buckling load within a 15-percent range is a knowledge of the theoretical buckling load of the simply supported column; the theoretical fundamental frequency of the simply supported beam; and the experimental fundamental frequency. Experimental results are presented to support the theory.     

Postbuckling of imperfect rectangular composite plates under inplane shear closed-form approximate solutions

In this paper, the postbuckling behavior of rectangular orthotropic laminated composite plates with initial imperfections under inplane shear load is investigated in a closed-form analytical manner. The plates under consideration are assumed to be infinitely long in the longitudinal direction. At the longitudinal edges, two different sets of boundary conditions are considered, specifically 1) simply supported edges and 2) fully clamped edges. Using Timoshenko-type shape functions for both the initial bifurcational buckling analysis and the subsequent Marguerre-type postbuckling studies, closed-form analytical solutions for the buckling loads and for the postbuckling state variables are derived. A comparison with geometrically non-linear finite element computations shows that the derived analysis approaches are suitable for postbuckling studies in load ranges not too far beyond bifurcational buckling as they are currently relevant for e.g., composite airframe structural analysis and design. Due to their strictly closed-form analytical nature, the presented analysis methods can be used conveniently in engineering practice for all application purposes where computational time is a crucial factor, especially for preliminary analysis and design or optimization procedures.     

Buckling behaviour of elliptical cylindrical shells and tubes under compression

This paper presents several issues that characterize the buckling behaviour of elliptical cylindrical shells and tubes under compression. First, a formulation of Generalised Beam Theory (GBT) developed to analyse the elastic buckling behaviour of non-circular hollow section (NCHS) members is presented. Since the radius varies along the cross-section mid-line, the main concepts involved in the determination of the deformation modes are adapted to account for the specific aspects related to elliptical cross-section geometry. After that, two independent sets of fully orthogonal deformation modes are determined: (i) local-shell modes satisfying the null membrane shear strain but exhibiting transverse extension and (ii) shell-type modes satisfying both assumptions of null membrane shear strain and null transverse extension. In order to illustrate the application, capabilities and versatility of the formulation, the local and global buckling behaviour of elliptical hollow section (EHS) members subjected to compression is analysed. In particular, in-depth studies concerning the influence of member length on the variation of the critical load and corresponding buckling mode shape are presented. Moreover, the GBT results are compared with estimates obtained by means of shell finite element analyses and are thoroughly discussed. The results show that short to intermediate length cylinders buckle mostly in local-shell modes, exhibiting only transverse extension, while intermediate length to long cylinders buckle mostly in shell-type modes (distortional and global modes), which are characterized by transverse bending and primary warping displacements. It is also shown that the present formulation is very efficient from the computational point of view since only three deformation modes (one local-shell, one distortional and one global) are required to evaluate the buckling behaviour of EHS cylinders for a wide range of lengths.     

Buckling of thin-walled columns accounting for initial geometrical imperfections

The paper is devoted to the effect of some geometrical imperfections on the critical buckling load of axially compressed thin-walled I-columns. The analytical formulas for the critical torsional and flexural buckling loads accounting for the initial curvature of the column axis or the twist angle respectively are derived. The classical assumptions of theory of thin-walled beams with non-deformable cross-sections are adopted. The non-linear differential equations are derived and the critical buckling loads are approximated by means of the Galerkin’s method. Comparison of analytical results to numerical analysis of simply supported I-columns by means of finite element method (FEM) is provided. Moreover the analytical formulas is adapted to I-columns with lipped flanges and satisfactory agreement of analytical and numerical results of stability analysis is observed.     

In-plane shear test of thin panels

Efficient application of thin-gage composite materials to helicopter fuselage structures necessitates that the materials be designed to operate at loads several times higher than initial buckling load. Methods are required to accurately measure and predict the response of thin-gage composites when subjected to these loads. This paper presents the results of an analytical and experimental study of the behavior of thin-gage composite panels subjected to in-plane shear loads. Finite-element stress analyses were used to aid in the design of an improved shear fixture that minimizes adverse corner stresses and tearing and crimping failure-modes characteristic of commonly used shear fixtures. Tests of thick buckle-resistant aluminum panels and thin aluminum and composite panels were conducted to verify the fixture design. Results of finite-element stress and buckling analyses and diagonal-tension-theory predictions are presented. Correlation of experimental data with analysis indicated that diagonal-tension theory can be used to predict the load-strain response of thin composite panels.     

微小缺口/孔洞的激光衍射无损检测

基于裂纹和孔洞的小尺寸特征,提出了微小缺口/孔洞的激光衍射无损探测技术,给出了解析表达式.通过这一技术,对单向拉伸试件中所含单边缺口和中心孔洞在外载作用下的演化过程进行了实时原位检测,获得了缺口/孔洞孔径随载荷的变化曲线及模拟裂纹时裂纹的张开位移、裂纹开裂长度及应力强度因子等一系列断裂参数.     

Thermal buckling of nanorod based on non-local elasticity theory

The buckling of nanostructures including as a nanobeam, nanorod, and nanotube in a temperature field is investigated based on the non-local elasticity field theory with non-linear strain gradients first proposed by Eringen. New higher-order governing differential equations both in transverse and axial direction for buckling of such nanostructures are derived based on the exact variational principle approach with corresponding higher-order non-local boundary conditions. Based on these new governing equations and boundary conditions, new analytical solutions for some practical examples on buckling of nanostructures are presented and analyzed in detail. Subsequently, the effects of non-local nanoscale and temperature change on critical buckling load are analyzed and discussed. It is observed that those factors have great influence on the critical buckling load of the nanostructures. In particular, the non-local stress very much affects the stiffness of nanostructures and the critical buckling load is significantly increased in the presence of non-local stress. The paper concludes that at low and room temperature the critical buckling load of nanostructures increases with increasing temperature change, while at high temperature the critical buckling load decreases with increasing temperature change. A critical temperature change which causes buckling without external load is also derived and discussed.     

一维六方准晶层合简支梁自由振动与屈曲的精确解

伪Stroh型公式能够将多场耦合材料的控制方程转化为线性特征系统来求解,从而获得多层结构简支边界条件的精确解.本文利用伪Stroh型公式,研究一维六方准晶层合简支梁的自由振动和屈曲问题,通过传递矩阵法,获得准晶层合梁自由振动固有频率与临界屈曲载荷的精确解.通过与已有梁的剪切变形理论结果比较,验证了本文伪Stroh型公式的正确性和有效性.通过数值算例,分析由两种不同准晶材料组成的三明治层合梁的叠层方式、高跨比、层厚比及层数对梁的固有频率、临界屈曲载荷及其模态的影响规律.结果表明,叠层顺序和梁的高跨比、层厚比对准晶层合梁的自由振动固有频率和临界屈曲载荷有很大影响,可通过调整梁的几何尺寸和叠层顺序得到准晶层合梁的最佳固有频率和临界屈曲载荷.本文给出的精确解可为工程上研究准晶梁的各种数值解法和实验方法提供理论参考.     

In-plane free vibration and stability of loaded and shear-deformable circular arches

The first known equations governing vibrations of preloaded, shear-deformable circular arches are derived according to a variational principle for dynamic problems concerning an elastic body under equilibrium initial stresses. The equations are three partial differential equations with variable coefficients. The governing equations are solved for arches statically preloaded with a uniformly distributed vertical loading, by obtaining a static, closed-form solution and an analytical dynamic solution from series solutions and dynamic stiffness matrices. Convergence to accurate results is obtained by increasing the number of elements or by increasing both the number of terms in the series solution and the number of terms in the Taylor expansion of the variable coefficients. Graphs of non-dimensional frequencies and buckling loads are presented for preloaded clamped arches. They clarify the effects of opening angle and thickness-to-radius ratio on vibration frequencies and buckling loads. The effects of static deformations on vibration frequencies are also investigated. This work also compares the results obtained from the proposed governing equations with those obtained from the classical theory neglecting shear deformation.     

The buckling of elastic spherical caps

The John equations are used to model the buckling of a simply-supported elastic spherical cap that is subjected to a constant uniform external load . The Liapunov-Schmidt method is used to solve these equations. We show that solutions possessing circular, pear-shaped, elliptical, triangular, square-shaped, pentagonal and a variety of other symmetries branch from the unbuckled state of the shell. The stability of these solutions is discussed. Some numerics that complement the analytical results are also included.     

Mechanical buckling of a functionally graded cylindrical shell with axial and circumferential stiffeners using the third-order shear deformation theory

This paper deals with an analytical approach of the buckling behavior of a functionally graded circular cylindrical shell under axial pressure with external axial and circumferential stiffeners. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations and equilibrium and stability equations are derived using the third-order shear deformation theory. The resulting equations are employed to obtain the closed-form solution for the critical buckling loads. A simply supported boundary condition is considered for both edges of the shell. The comparison of the results of this study with those in the literature validates the present analysis. The effects of material composition (volume fraction exponent), of the number of stiffeners and of shell geometry parameters on the characteristics of the critical buckling load are described. The analytical results are compared and validated using the finite-element method. The results show that the inhomogeneity parameter, the geometry of the shell and the number of stiffeners considerably affect the critical buckling loads.