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。     

黏弹性层合圆柱壳的临界轴压分析

基于经典屈曲理论，研究了轴向受压黏弹性复合材料层合圆柱壳的临界屈曲载荷. 利用Boltzmann线性积分型本构关系描述铺设单层的各向异性黏弹性行为. 结合解析与数值 方法，由Donnell型屈曲控制方程以及边界条件的Laplace变换导出相空间的特征方程，根 据Laplace逆变换的极值定理，获得层合圆柱壳的瞬时弹性临界载荷与持久临界载荷. 针对 多组铺设方式，通过数值算例重点分析了临界载荷随铺设角的变化特征，两种临界载荷的峰 值点差异程度与铺设方式、几何参数以及材料类型的关系，得到了一些对黏弹性层合圆柱壳 的优化设计有参考价值的结论.     

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。     

多孔介质内黏弹性流体的热对流稳定性研究

基于修正的Darcy模型, 介绍了多孔介质内黏弹性流体热对流稳定性研究的现状和主要进展. 通过线性稳定性理论, 分析计算多孔介质几何形状(水平多孔介质层、多孔圆柱以及多孔方腔)、热边界条件(底部等温加热、底部等热流加热、底部对流换热以及顶部自由开口边界)、黏弹性流体的流动模型(Darcy-Jeffrey, Darcy-Brinkman-Oldroyd以及Darcy-Brinkman -Maxwell模型)、局部热非平衡效应以及旋转效应对黏弹性流体热对流失稳的临界Rayleigh数的影响. 利用弱非线性分析方法, 揭示失稳临界点附近热对流流动的分叉情况, 以及失稳临界点附近黏弹性流体换热Nusselt数的解析表达式. 采用数值模拟方法, 研究高Rayleigh数下黏弹性流体换热Nusselt数和流场的演化规律,分析各参数对黏弹性流体热对流失稳和对流换热速率的影响.主要结果:(1)流体的黏弹性能够促进振荡对流的发生;(2)旋转效应、流体与多孔介质间的传热能够抑制黏弹性流体的热对流失稳;(3)在临界Rayleigh数附近,静态对流分叉解是超临界稳定的, 而振荡对流分叉可能是超临界或者亚临界的,主要取决于流体的黏弹性参数、Prandtl数以及Darcy数;(4)随着Rayleigh数的增加,热对流的流场从单个涡胞逐渐演化为多个不规则单元涡胞, 最后发展为混沌状态.      

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。     

多孔介质内黏弹性流体的热对流稳定性研究

基于修正的Darcy模型,介绍了多孔介质内黏弹性流体热对流稳定性研究的现状和主要进展.通过线性稳定性理论,分析计算多孔介质几何形状(水平多孔介质层、多孔圆柱以及多孔方腔)、热边界条件(底部等温加热、底部等热流加热、底部对流换热以及顶部自由开口边界)、黏弹性流体的流动模型(Darcy-Jeffrey, DarcyBrinkman-Oldroyd以及Darcy-Brinkman-Maxwell模型)、局部热非平衡效应以及旋转效应对黏弹性流体热对流失稳的临界Rayleigh数的影响.利用弱非线性分析方法,揭示失稳临界点附近热对流流动的分叉情况,以及失稳临界点附近黏弹性流体换热Nusselt数的解析表达式.采用数值模拟方法,研究高Rayleigh数下黏弹性流体换热Nusselt数和流场的演化规律,分析各参数对黏弹性流体热对流失稳和对流换热速率的影响.主要结果:(1)流体的黏弹性能够促进振荡对流的发生;(2)旋转效应、流体与多孔介质间的传热能够抑制黏弹性流体的热对流失稳;(3)在临界Rayleigh数附近,静态对流分叉解是超临界稳定的,而振荡对流分叉可能是超临界或者亚临界的,主要取决于流体的黏弹性参数、Prandtl数以及Darcy数;(4)随着Rayleigh数的增加,热对流的流场从单个涡胞逐渐演化为多个不规则单元涡胞,最后发展为混沌状态.     

正交铺设层合板的蠕变屈曲分析

研究了正交铺设层合板的蠕变失稳问题。为了更好地模拟实际情况，在单层板的本构关系中，材料各主方向模量的松也时间均取不同值，并在建立控制方程时考虑了横向剪切变形的影响，通过理论分析，得到了粘弹性层合板的瞬时弹性临界载荷和持久临界载荷，并在算例中首次利用时间增量方法得到了有初始度层合板在长期受地的蠕变变表，计算结果表明了持久临界载荷对于粘弹性层合板的具体含义，从而使粘弹性层合板的为屈曲问题有了较为完整的     

用三维弹性力学方法研究圆板的稳定问题

用三维弹性力学方法研究任意边界条件圆板的轴对称稳定问题，利用Ｈ变换和Ｓｔｏｃｋｅｓ变换，导出位移函数及其偏导数的一种新型双重极数式，并由数学弹性定理论的基本方程和边界条件建立的特征方程，求得最小临界载荷的精确解，文末以简支圆板为例进行数字计算，结果表明：在弹性失稳范围内，三维弹性力学方法求得的临界载荷略低于经典理论的结果，对于薄板的弹性稳定问题，经典板理论有足够的精度。     

轴向压应力波下圆柱壳弹性动力失稳的判据与机理

基于动力失稳瞬间能量的转换和守恒,推导提出了受轴向力圆柱壳弹性动力失稳的判据和两个临界条件,由第一个临界条件导出的圆柱壳弹性动力失稳的控制方程、边界条件、屈曲变形连续与利用Hamilton原理的结果完全相同,但不足以确定包含在本问题中的两个特定特征参数（临界载荷参数和动力特征参数）,由第二个临界条件导出压缩波前的屈曲变形约束方程,基于控制方程有满足边界条件、变形连续条件和波前约束方程的非平凡解的条件,导出关于两个特征参数的一对特征方程,基于特征方程的解,精确地计算出临界载荷参数和动力特征参数的值以及动力失稳态态,由此建立了轴向力作用下圆桩壳弹性动力失稳的特征值分析方法。     

悬臂高梁在静动态载荷作用下侧向失稳的实验研究

本文进行了平头圆柱形弹体对铝合金悬臂高梁自由端正撞击引起侧向失稳的实验研究．通过多种不同尺寸梁的实验，研究了梁在静动态载荷下的侧向失稳临界载荷值及屈曲模态．最后给出一个在撞击载荷下，计算悬臂高梁侧向失稳临界冲击动能值的经验公式．     

Creep buckling and post-buckling analysis of the laminated piezoelectric viscoelastic functionally graded plates

The creep buckling and post-buckling of the laminated piezoelectric viscoelastic functionally graded material (FGM) plates are studied in this research. Considering the transverse shear deformation and geometric nonlinearity, the Von Karman geometric relation of the laminated piezoelectric viscoelastic FGM plates with initial deflection is established. And then nonlinear creep governing equations of the laminated piezoelectric viscoelastic FGM plates subjected to an in-plane compressive load are derived on the basis of the elastic piezoelectric theory and Boltzmann superposition principle. Applying the finite difference method and the Newmark scheme, the whole problem is solved by the iterative method. In numerical examples, the effects of geometric nonlinearity, transverse shear deformation, the applied electric load, the volume fraction and the geometric parameters on the creep buckling and post-buckling of laminated piezoelectric viscoelastic FGM plates with initial deflection are investigated.     

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。     

Axisymmetric static and dynamic buckling of laminated thick truncated conical cap

Axisymmetric buckling analysis is presented for moderately thick laminated shallow, truncated conical caps under transverse load. Buckling under uniformly distributed loads and ring loads applied statically or as step function loads is considered. Marguerre-type, first-order shear deformation shallow shell theory is formulated in terms of transverse deflection w, the rotation ψ of the normal to the mid-surface and the stress function Φ. The governing equations are solved by the orthogonal point collocation method. Truncated conical caps with a circular opening, which is either free or plugged by a rigid central mass, have been analysed for clamped and simple supports with movable and immovable edge conditions. Typical numerical results are presented illustrating the effect of various parameters.     

Post-buckling behaviour of graphite/epoxy stiffened panels with initial imperfections subjected to eccentric biaxial compression loading

The post-buckling behaviour of anisotropic stiffened panels with initial imperfections is investigated. Since buckling of the skin between the stiffeners often occurs first, a non-linear analysis is developed for symmetric panels under biaxial compression in order to obtain the out-of-plane panel deflection in the post-buckling range. The non-linear differential equations are expressed in terms of the out-of-plane displacement and the Airy function. They are solved with the Galerkin method for various boundary conditions by imposing an edge displacement control. The theoretical and experimental results obtained by the present analysis show that the transverse load can greatly influence the buckling loads and halfwave number. Since no experimental results have been found in the literature, several tests have been carried out on graphite/epoxy blade stiffened panels 900 mm long and 620 mm wide applying simultaneously biaxial compression loads with several combined ratios. An eccentricity results between longitudinal and transverse load, because the longitudinal compression is applied along the centroidal axes of the stiffened section while the transverse compression is applied to the skin panel. The correlation between the experimental and analytical results has been quite good; the experimental results demonstrate the influence of eccentricity of the transverse load on panel deflection in the pre- and post-buckling range.     

复合材料层合板蠕变屈曲与变形的优化问题

将瞬时弹性失稳荷载、持久临界荷载和后屈曲持久变形刚度作为复合材料层合板蠕变屈曲与变形的优化指标,对几组纤维铺设方式进行讨论,构造多目标优化模型,就纤维铺设角进行优化分析.考虑横向剪切变形效应,分别利用Lap lace变换和准弹性方法,导出了这三个优化指标的计算公式.     

ANALYSIS ON THE MAGNETO-ELASTIC-PLASTIC BUCKLING/SNAPPING OF CANTILEVER RECTANGULAR FERROMAGNETIC PLATES

An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented.Based on the expression of magnetic force from the variational principle of ferromagnetic plates,the buckling and bending theory of thin plates,the Mises yield criterion and the increment theory for plastic deformation,we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method.Along with the phenom- ena of buckling/snapping and bending,or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed,the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads,the plastic regions expanding with the magnitude of applied magnetic field,as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.     

基于新修正偶应力理论的Mindlin层合板稳定性分析

基于新的各向异性修正偶应力理论提出一个Mindlin复合材料层合板稳定性模型。该理论包含纤维和基体两个不同的材料长度尺度参数。不同于忽略横向剪切应力的修正偶应力Kirchhoff薄板理论,Mindlin层合板考虑横向剪切变形引入两个转角变量。进一步建立了只含一个材料细观参数的偶应力Mindlin层合板工程理论的稳定性模型。计算了正交铺设简支方板Mindlin层合板的临界载荷。计算结果表明该模型可以用于分析细观尺度层合板稳定性的尺寸效应。     

Thermally induced vibration and stability of laminated composite plates with temperature-dependent properties

This paper presents a study on the buckling and vibration of initially stressed composite plates with temperature-dependent material properties in thermal environments. The initial stress is taken to be a combination of a pure bending stress and an axial stress. The temperature distribution in the plate is assumed to be uniform and linear in the transverse direction. The governing equations including the transverse shear deformation effects are established using the variational method. The effects of various parameters on the buckling and vibration behaviors of laminated plates with respective temperature-dependent and temperature-independent material properties are investigated. The buckling load and natural frequency are sensitive to the thermal stresses and initial stresses. Numerical results reveal that temperature-dependent material properties should be considered in the buckling and vibration analysis for laminated plates under thermal conditions.     

Kármán-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis

Kármán-type nonlinear large deflection equations are derived occnrding to the Reddy’s higher-order shear deformation plate theory and used in the thermal postbuckling analysis The effects of initial geometric imperfections of the plate areincluded in the present study which also includes th thermal effects.Simply supported,symmetric cross-ply laminated plates subjected to uniform or nomuniform parabolictemperature distribution are considered. The analysis uses a mixed GalerkinGolerkinperlurbation technique to determine thermal buckling louds and postbucklingequilibrium paths.The effects played by transverse shear deformation plate aspeclraio, total number of plies thermal load ratio and initial geometric imperfections arealso studied.