非完善加筋圆柱壳在外压和热荷载共同作用下的后屈曲

基于壳体屈曲的边界层理论,本文给出有限长加筋圆柱壳在侧向外压和均布热荷载共同作用下的后屈曲分析。分析中同时考虑壳体非线性前屈曲变形,大挠度和初始几何缺陷的影响。肋条的处理采用“平均刚度”法。采用奇异摄动方法导得壳体屈曲载荷关系曲线和后屈曲平衡路径,并给出完善和非完善,纵向加筋或环向加筋圆柱壳数值算例。     

热-压电效应对轴压混合层合圆柱曲板后屈曲的影响

基于Karman-Donnell型非线性壳体方程，给出带压电作动器混合层合圆柱曲板在机械荷载、电荷载和热荷载作用下的后屈曲分析．假定温度场为均匀分布，电场仅有沿板厚方向的分量Ez，且假定材料性能常数与温度和电场的变化无关。将壳体屈曲的边界层理论推广到混合层合圆柱曲板受复合荷载作用的情况.相应的奇异摄动法用于确定圆柱曲板的屈曲荷载和后屈曲平衡路径.分析中同时考虑非线性前屈曲变形和初始几何缺陷的影响．数值算例给出完善和非完善，含整体覆盖或内埋压电作动器正交铺设层合圆柱曲板的后屈曲平衡路径。讨论了温度变化、控制电压、铺层方式、面内边界条件和初始几何缺陷等各种参数变化的影响。     

薄球壳在均布外压与温度耦合作用下的热屈曲研究

从张量方法推导出的轴对称薄球壳屈曲方程出发,推导出在均布外压与温度耦合作用下用位移表示的薄球壳热屈曲方程;应用虚功原理建立薄球壳屈曲最小势能泛函;进一步用Ritz(里兹)法分析了周边简支的半球壳的3种热屈曲问题.得到了: 1) 温度不超过屈曲临界温度值时,均布外压的临界载荷;2) 均布外压载荷为0时,屈曲临界温度值;3) 均布外压载荷不超过临界载荷时,屈曲临界温度值.     

考虑横向剪切的对称圆柱正交异性层合扁球壳的热屈曲

研究了对称层合圆柱正交异性扁球壳在温度场和均布压力联合作用下的热屈曲问题．考虑横向剪切的影响,应用修正迭代法获得了温度场影响下的临界荷载的解析表达式,讨论了剪切刚度和温度场对临界荷载的影响．     

中厚板的弹性屈曲和后屈曲

本文采用Reissner假定考虑横向剪切变形的影响,导出弹性矩形板大挠度方程.本文讨论考虑横向剪切变形的矩形板的弹性屈曲和后屈曲.采用文[8]提供的摄动方法,给出了完善和非完善中厚板的后屈曲平衡路径,并与经典薄板理论结果进行了比较.     

复合材料层合剪切圆柱曲板在侧压作用下的后屈曲

基于Reddy高阶剪切变形理论的Kármám-Donnell型非线性壳体方程,给出复合材料层合剪切圆柱曲板在侧压作用下的后屈曲分析。将壳体屈曲的边界层理论推广到复合材料层合剪切圆柱曲板受侧压作用的情况。相应的奇异摄动法,用于确定圆柱曲板的屈曲荷载和后屈曲平衡路径。分析中同时考虑非线性前屈曲变形和初始几何缺陷的影响。数值算例给出完善和非完善,中等厚度正交铺设层合圆柱曲板的后屈曲荷载-挠度曲线。讨论了横向剪切变形,曲板几何参数,铺层数,铺展方式和初始几何缺陷等各种参数变化的影响。     

功能梯度梁在热-机械荷载作用下的几何非线性分析

基于经典梁理论，运用虚功原理和变分法推导了均匀变温场与横向均布荷载联合作用的功能梯度梁的几何非线性控制方程.考虑端部不可移夹紧边界条件，运用打靶法求解了该两点边值问题.当横向均布荷载为0时，考察了功能梯度梁的热屈曲临界升温和屈曲平衡路径.当均匀变温与横向均布荷载都不为0时，考察了功能梯度梁的荷载 挠度曲线.数值结果表明:随材料体积分数指数增加，梁的有量纲热屈曲临界升温显著减小，后屈曲变形显著增加；变温对功能梯度梁的荷载 挠度曲线影响非常显著.发现了功能梯度梁的双稳态构形及其转换现象，梁的最终平衡位形不但与变温及荷载参数有关，还与加载历程有关.     

加肋圆柱壳在轴压作用下的屈曲和后屈曲

本文讨论完善和非完善的,纵向加肋和正交加肋圆柱壳在轴压作用下的屈曲和后屈曲性态.依据文[1]提供的圆柱薄壳屈曲的边界层理论及其分析方法,给出了加肋圆柱壳在轴压作用下的屈曲和后屈曲理论分析.本文同时讨论肋骨与壳板材料不同时对加肋圆柱壳屈曲和后屈曲性态的影响.     

湿热环境中复合材料层合圆柱薄壳屈曲和后屈曲

在宏-细观力学模型框架下,讨论湿热环境对复合材料层合圆柱薄壳在轴向压缩作用下屈曲和后屈曲行为的影响。基于细观力学模型复合材料性能与湿度和温度变化有关。壳体控制方程基于经典层合壳理论,并包括湿热效应。壳体屈曲的边界层理论被推广用于湿热环境的情况,相应的奇异摄动法用于确定层合圆柱薄壳的屈曲荷载和后屈曲平衡路径。分析中同时计及壳体非线性前屈曲变形和初始几何缺陷的影响。数值算例给出完善和非完善正交铺设层合圆柱薄壳在不同湿热环境中的后屈曲行为。讨论了温度和湿度,纤维体积比率,壳体几何参数,铺层数,铺层方式和初始几何缺陷等各种参数变化的影响。     

高阶剪切变形板理论Karman型方程及在热后屈曲分析中的应用

本文基于Ｒｅｄｄｙ高阶剪切变形板理论导出Ｋａｒｍａｎ型非线性大挠度方程并用于层合板热后屈曲分析，分析中计及板初始几何缺陷和热效应。给出了四边简支，对称正交铺设层合板在均匀或非均匀抛物型热分布作用下的后屈曲分析。采用摄动－Ｇａｌｅｒｋｉｎ混合法确定板的热屈曲载荷与热后屈曲平衡路径。同时讨论了横向剪切变形。采用摄动－Ｇａｌｅｒｋｉｎ混合法确定板的热屈曲载荷与热后屈曲平衡路径。同时讨论了横向剪切变形，板     

Thermoelastic stability analysis of laminated composite plates: An analytical approach

The paper presents Chebyshev series based analytical solutions for the postbuckling response of the moderately thick laminated composite rectangular plates with and without elastic foundations. The plate is assumed to be subjected to in-plane mechanical, thermal and thermomechanical loadings. In-plane mechanical loading consists of uniaxial, biaxial, shear loadings and their combinations. The temperature induced loading is due to either uniform temperature or a linearly varying temperature across the thickness. The mathematical formulation is based on higher order shear deformation theory (HSDT) and von-Karman nonlinear kinematics. The elastic foundation is modeled as shear deformable with cubic nonlinearity. The thermal and mechanical properties of the composites are assumed to be temperature dependent. The quadratic extrapolation technique is used for linearization and fast converging finite double Chebyshev series is used for spatial discretization of the governing nonlinear equations of equilibrium. The effects of plate parameters and foundation parameters on buckling and postbuckling response of the plate are presented.     

Bending of thick functionally graded plates resting on Winkler–Pasternak elastic foundations

The static response of simply supported functionally graded plates (FGP) subjected to a transverse uniform load (UL) or a sinusoidally distributed load (SL) and resting on an elastic foundation is examined by using a new hyperbolic displacement model. The present theory exactly satisfies the stress boundary conditions on the top and bottom surfaces of the plate. No transverse shear correction factors are needed, because a correct representation of the transverse shear strain is given. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second parameter is zero. The equilibrium equations of a functionally graded plate are given based on the hyperbolic shear deformation theory of plates presented. The effects of stiffness and gradient index of the foundation on the mechanical responses of the plates are discussed. It is established that the elastic foundations significantly affect the mechanical behavior of thick functionally graded plates. The numerical results presented in the paper can serve as benchmarks for future analyses of thick functionally graded plates on elastic foundations.     

三边夹紧一边自由的矩形厚板的弯曲

利用厚板的Reissner理论中的广义简支边概念[1]得到了三边夹紧一边自由受均布横向载荷作用的矩形厚板的精确解.研究和考察了板的厚度对弯曲的影响及薄板弯曲的Kirchhoff理论的适用范围.     

Development of a higher order finite element on a Winkler foundation

Analyzing thick plates as a construction component has been of interest to structural engineering research for several decades. In particular, thick plates resting on elastic foundations are more specific. Mindlin's plate theory for thick plate analysis and the Winkler theory for elastic foundation analyses have wide applications. The current research considers analysis of isotropic plates on a Winkler foundation according to Mindlin's plate theory. The analysis uses a higher order plate element to avoid shear locking phenomena in the plate. The main features of this element are representation of real displacement functions of the plate perfect and shear locking do not occur at the plates modeled with this element. Derivation of the equations for finite element formulation for thick plate theory uses fourth-order displacement shape functions. A computer program using the finite element method, coded in C++, analyzes the plates resting on an elastic foundation. The analysis involves a 17-noded finite element. The study's graphs and tables assist engineers' designs of thick plates resting on elastic foundations. The study concludes with the computer-coded program, which allows effective use for the shear locking-free analysis of thick Mindlin plates resting on elastic foundations.     

Compressive and thermal postbuckling behaviors of laminated plates with piezoelectric fiber reinforced composite actuators

This paper studied compressive postbuckling under thermal environments and thermal postbuckling due to a uniform temperature rise for a shear deformable laminated plate with piezoelectric fiber reinforced composite (PFRC) actuators based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The material properties are assumed to be temperature-dependent and the initial geometric imperfection of the plate is considered. The compressive and thermal postbuckling behaviors of perfect, imperfect, symmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded PFRC actuators are conducted under different sets of thermal and electric loading conditions. The results reveal that, the applied voltage usually has a small effect on the postbuckling load–deflection relationship of the plate with PFRC actuators in the compressive buckling case, whereas the effect of applied voltage is more pronounced for the plate with PFRC actuators, compared to the results of the same plate with monolithic piezoelectric actuators.     

Analysis of functionally graded plates using higher order shear deformation theory

This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.     

关于简支厚板与薄板的关系

厚板的数学理论是建立在与薄板不同的力学假定的基础上的。本文分析了厚板与薄板之间静力学方面的关系。对于任意的简支多边形板,得到了厚板解通过薄板解的显式表达式,从而证明了:Reissner模型的厚板解与薄板解具有相同的剪力,但弯矩、转角、挠度有差别;而washizu模型的厚板解则与薄板解不仅剪力相同,连弯矩与转角亦相同,只是挠度有差别。     

Effect of random system properties on bending response of thermo-mechanically loaded laminated composite plates

In this paper, effect of random variation in system properties on bending response of geometrically linear laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modeled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behavior of the composite plate. A C⁰ finite element method in conjunction with the first order perturbation technique procedure developed earlier by authors for the plate subjected to lateral loading is employed to obtain the second order response statistics (mean and variance) of the transverse deflection of the plate. Typical numerical results for the second order statistics of the transverse central deflection of geometrically linear composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and linearly varying temperature distribution are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The performance of the stochastic laminated composite model is demonstrated through comparison of mean transverse central deflection with those results available in literature and standard deviation of the deflection with an independent Monte Carlo simulation.     

Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory

In this article, an analytical approach for buckling analysis of thick functionally graded rectangular plates is presented. The equilibrium and stability equations are derived according to the higher-order shear deformation plate theory. Introducing an analytical method, the coupled governing stability equations of functionally graded plate are converted into two uncoupled partial differential equations in terms of transverse displacement and a new function, called boundary layer function. Using Levy-type solution these equations are solved for the functionally graded rectangular plate with two opposite edges simply supported under different types of loading conditions. The excellent accuracy of the present analytical solution is confirmed by making some comparisons of the present results with those available in the literature. Furthermore, the effects of power of functionally graded material, plate thickness, aspect ratio, loading types and boundary conditions on the critical buckling load of the functionally graded rectangular plate are studied and discussed in details. The critical buckling loads of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be used as benchmark.     

Calculation of rigidly clamped circular plates in the statement of the problem on contact interaction in a two-layer package

The use of a mechanicomathematical model of bending of thick transversely isotropic plates is illustrated, where the plate is divided in an arbitrary number of equally thick conditional layers. This model allows one to approximately reduce the problem of determination of stresses and displacements in the thick plate to a corresponding contact problem for a bent pack age of layers. The axisymmetric bending of a rigidly clamped package consisting of two plates rigidly fastened together is considered. The results of numerical calculations are presented, which are compared with those obtained within the framework of a refined bending model of plates (with account of transverse compression and shear) and of the Timoshenko model, as well as in the statement of the three-dimensional theory of elasticity. The accuracy of satisfying the boundary conditions in each model is analyzed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 93–108, January–February, 2007.