冲击载荷作用下矩形薄板的弹性动力屈曲

为了研究冲击载荷作用下考虑应力波效应弹性矩形薄板的动力屈曲,根据动力屈曲发生瞬间的能量转换和守恒准则,导出板的屈曲控制方程和波阵面上的补充约束条件,真实的屈曲位移应同时满足控制方程和波阵面上的附加约束条件。满足上述条件,建立了该问题的完整数值解法,对屈曲过程中冲击载荷、屈曲模态和临界屈曲长度之间的关系进行研究,定量计算了横向惯性效应对提高薄板动力屈曲临界应力的贡献。研究表明：板的厚宽比一定时,临界屈曲长度随冲击载荷的增大而减小;由于屈曲时的横向惯性效应,应力波作用下薄板一阶临界力参数是相应边界板的静力失稳临界力参数的1.5倍;随着边界约束逐渐减弱,板临界力参数逐渐减小,动力特征参数逐渐增大。

     

功能梯度材料矩形中厚板的受压/热致屈曲

考虑材料组份沿板厚度方向按幂律变化的情形,研究了温度均匀变化时固支功能梯度材料(FGM)矩形中厚板的受压屈曲、热致屈曲和考虑热/机械预应力时的屈曲问题,给出了基于Reddy高阶剪切理论研究板屈曲荷载和屈曲临界温度的半解析数值方法.并以Si3N4/SUS304板为例考虑了材料组份、预加应力、横向剪切变形及面内位移约束条件等对FGM板屈曲承载能力的影响.     

任意变厚度矩形薄板的屈曲和振动

本文采用两步级数展开法获得了任意变厚度矩形薄板的屈曲和振动问题的一般解,并详细研究了四边简支变厚度矩形板的屈曲和振动问题的解.针对两种变厚度板,计算了失稳临界荷载、失稳波形以及基频,并与前人的结果做了比较,分析结果表明本文方法简单收敛快。     

中间支承对随从力作用下矩形薄板稳定性的影响

研究了切向均布随从力作用下,带有中间线支承的矩形薄板的稳定性问题.建立板的运动微分方程,利用微分求积法得到复特征方程.求解复特征方程,得出线支承板复频率随着随从力的变化关系,以及线支承刚度对板失稳形式和临界值的影响.对随从力作用下中间支承四边固支矩形薄板的计算结果表明:对于四边固支板,当边长比为1时,发现存在一个临界线支承刚度值,当线支承刚度小于该值时,板失稳为颤振失稳,当支承刚度大于该值时,板失稳为屈曲失稳;当边长比为2时,板失稳形式保持为屈曲失稳.     

考虑剪切变形的各向同性,正交各向异性矩形板的屈曲和后屈曲

本文讨论考虑横向剪切变形的各向同性、正交各向异性矩形板的屈曲和后屈曲性态。应用Reissner理论,采用文[1]提供的摄动方法,给出了完善和非完善各向同性、正交各向异性矩形板的后屈曲平衡路径,并与薄板理论结果作了比较。     

复合结构剪切板的屈曲与后屈曲研究

基于Ｒｅｉｓｓｎｅｒ剪切板理论，本文将现有理论模型推进了一步，导出了控制复合材料和构造矩形板平衡的广义Ｋａｒｍａｎ大挠度方程。此外，运用摄动技术，构造了一个单向压缩简支剪切矩形板的后屈曲渐近解，适用于面板和夹心材料都具正交各向异性的夹层板以及计及横向剪切变形对称铺设的层合板。文中给出了典型算例，并将当前结果与其它理论或数值解作了比较，显示出相当好的一致性。     

复合材料襟翼壁板屈曲失稳行为的栅线投影实验研究

本文利用栅线投影测量方法研究了蜂窝夹层板、工字型及T型加筋板三种不同结构形式复合材料襟翼壁板在压缩载荷下的屈曲失稳行为,得到了不同形式结构件屈曲的全场离面位移分布规律,分析了各自的屈曲失稳模式.研究结果表明,栅线投影测量方法在大尺度复合材料结构失稳变形测试中具有可行性;在相同面板尺寸条件下,工字型加筋复合材料襟翼壁板屈曲临界载荷最大,承载能力最强.本文结果可为飞机复合材料结构设计提供实验依据.     

轴向应力波作用下圆柱壳塑性轴对称动力屈曲

运用有限元特征值分析方法对应力波作用下圆柱壳塑性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的特征方程,在分析中同时考虑了应力波效应及横向惯性效应,把圆柱壳塑性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳塑性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

考虑横向拉伸影响的FGM夹层板动不稳定性分析

以受多种形式面内载荷作用下的功能梯度夹层矩形板为研究对象,夹层板的功能梯度层组分材料沿厚度方向按幂律分布,考虑组分材料物性参数的温度相关性.研究中所用的位移场在Reddy高阶剪切变形理论基础上考虑了横向拉伸的影响.利用能量原理和Galerkin法得到四边简支功能梯度材料夹层矩形板的动力学模型.运用Bolotin法求得了...     

硬夹心矩形夹层板的整体稳定性分析

论文在Reissner型理论给出的位移模式基础上,修正其软夹心假设,考虑夹心层面内刚度,给出了硬夹心夹层板的几何方程、物理方程,建立了硬夹心夹层板结构在面内纵向载荷作用下的平衡微分方程,并对方程进行了简化,通过理论计算得到了四边简支条件下硬夹心矩形夹层板整体失稳临界载荷的解析解,并分别计算了夹心层材料的弹性模量E、厚度h、泊松比μc对硬夹心夹层板临界载荷的影响,结果证明,对于硬夹心夹层结构,夹心层面内刚度对硬夹心夹层板整体失稳临界载荷的影响较大,考虑其面内刚度是必要的.     

MULTI-FIELD COUPLING BEHAVIOR OF SIMPLY-SUPPORTED CONDUCTIVE PLATE UNDER THE CONDITION OF A TRANSVERSE STRONG IMPULSIVE MAGNETIC FIELD

In order to study the multi-field coupling mechanical behavior of the simply-supported conductive rectangular thin plate under the condition of an externally lateral strong impulsive magnetic field, that is the dynamic buckling phenomenon of the thin plates in the effect of the magnetic volume forces produced by the interaction between the eddy current and the magnetic fields, a FEM analysis program is developed to characterize the phenomena of magnetuelastic buckling and instability of the plates. The critical values of magnetic field for the three different initial vibrating modes are obtained, with a detailed discussion made on the effects of the length-thickness ratio a/h of the plate and the length-width ratio a/b as well as the impulse parameterτon the critical value BOcr of the applied magnetic field.     

Bucklewaves

Motivated by a selection of results on the plastic buckling of column members within a sandwich plate core where one face of the sandwich is subject to an intense impulse, the problem addressed is one where lateral buckling takes place simultaneously as a compressive axial wave propagates down the member. The bucklewave problem is modeled as an infinitely long column (or wide plate) which is clamped against lateral deflection at the end where velocity is imposed and has a moving clamped condition coinciding with the front of the plastic compression wave. The model reveals that a column or plate suddenly compressed into the plastic range is dynamically stabilized against lateral buckling for lengths that are significantly longer than the corresponding length at which the member would buckle quasi-statically. This stabilization has significant implications for energy absorption under intense dynamic loading. The analysis method is benchmarked against a simpler, but mathematically analogous problem, for which closed form solutions are available: the dynamics of a guitar string lengthening at constant velocity.     

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.     

A comprehensive analysis of functionally graded sandwich plates: Part 2—Buckling and free vibration

The sinusoidal shear deformation plate theory, presented in the first part of this paper, is used to study the buckling and free vibration of the simply supported functionally graded sandwich plate. Effects of rotatory inertia are considered. The critical buckling load and the vibration natural frequency are investigated. Some available results for sandwich plates non-symmetric about the mid-plane can be retrieved from the present analysis. The influences of the transverse shear deformation, plate aspect ratio, side-to-thickness ratio and volume fraction distributions are studied. In addition, the effect of the core thickness, relative to the total thickness of the plate, on the critical buckling load and the eigenfrequencies is investigated.     

基于Layerwise离散层理论的复合材料夹层板屈曲分析

复合材料夹层结构由于面板和芯层力学特性差异较大,屈曲分析时要分层考虑各层的剪切变形.基于Reddy的Layerwise离散层理论,假设每一层变形服从一阶剪切变形理论,在统一的位移场描述下,推导建立了一种用于复合材料夹层结构屈曲分析的四节点四边形板单元,并采用混合插值方法对单元的剪切锁定进行了修正.分别对三种典型的夹层板结构进行线性屈曲有限元分析,并将计算结果与文献中已有结果进行了对比.结果表明:论文的分析方法能离散考虑各层的力学特性,将结构离散为多层时,计算结果与三维弹性理论或高阶板理论吻合;将结构等效为单层时,计算结果与基于一阶剪切变形理论的文献结果吻合,验证了单元的有效性.     

端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳．直杆撞击刚性平面或拉断卸载后将形成压缩波，因承载压缩载荷的长度增加可以引起失稳．冲击速度转换的压应力沿着杆件切线方向，该处弯矩和剪力为零；而众多文献设定的失稳段固支边界条件并不准确．基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件，得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5 倍．对于钢丝绳拉断形成的冲击失稳，载荷恒定而长度增加，可以产生高阶屈曲即在侧向出现多次曲折，并基于尼龙-橡胶带的模拟试验给出了定性说明．     

NONLINEAR BUCKLING BEHAVIOR OF DAMAGED COMPOSITE SANDWICH PLATES CONSIDERING THE EFFECT OF TEMPERATURE-DEPENDENT THERMAL AND MECHANICAL PROPERTIES

On the basis of the first-order shear deformation plate theory and the zig-zag deformation assumption, an incremental finite element formulation for nonlinear buckling analysis of the composite sandwich plate is deduced and the temperature-dependent thermal and mechanical properties of composite is considered. A finite element method for thermal or thermo-mechanical coupling nonlinear buckling analysis of the composite sandwich plate with an interfacial crack damage between face and core is also developed. Numerical results and discussions concerning some typical examples show that the effects of the variation of the thermal and mechanical properties with temperature, external compressive loading, size of the damage zone and ply angle of the faces on the thermal buckling behavior are significant. Project supported by the National Natural Science Foundation of China (No. 59975013).     

Thermal buckling and post-buckling response of imperfect temperature-dependent sandwich FGM plates resting on elastic foundation

Post-buckling behaviour of sandwich plates with functionally graded material (FGM) face sheets under uniform temperature rise loading is considered. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation, which acts in both compression and tension. The derivation of equations is based on the first-order shear deformation plate theory. Thermomechanical non-homogeneous properties of FGM layers vary smoothly by the distribution of power law across the thickness, and temperature dependency of material constituents is taken into account. Using the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect sandwich plates with FGM face sheets are derived. The boundary conditions for the plate are assumed to be simply supported in all edges. The governing equations are reduced to two coupled equation in terms of stress function and lateral deflection. Employing the single mode approach combined with Galerkin technique, an approximate closed-form solution is presented to calculate the critical buckling temperature and post-buckling equilibrium path of the plate. Presented numerical examples contain the influences of power law index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation coefficients.     

Thermoelastic buckling behavior of thick functionally graded rectangular plates

Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article. The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio, thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.     

Vibration and buckling of laminated sandwich plates having interfacial imperfections

The vibration and buckling characteristics of sandwich plates having laminated stiff layers are studied for different degrees of imperfections at the layer interfaces using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piece-wise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. The inter-laminar imperfections are represented by in-plane displacement jumps at the layer interfaces and characterized by a linear spring layer model. It is quite interesting to note that this plate model having all these refined features requires unknowns only at the reference plane. To have generality in the analysis, finite element technique is adopted and it is carried out with a new triangular element developed for this purpose, as any existing element cannot model this plate model. As there is no published result on imperfect sandwich plates, the problems of perfect sandwich plates and imperfect ordinary laminates are used for validation.