复杂载荷下加筋圆柱壳非线性冲击屈曲研究

将加筋圆柱壳离散成为由圆柱壳和加强筋组成的壳体-肋骨系统,假设环向加筋与壳体在接触处刚性连接,由Hamilton变分原理推导出加筋圆柱壳结构的运动方程,以研究加筋圆柱壳在水下冲击载荷和静水压力以及动水压力组成的复杂载荷联合作用下的非线性屈曲行为。借助增量数值(在时域采用4阶Runge-Kutta方法)的方法来分析了加筋圆柱壳的非线性屈曲行为,经过算例分析验证了材料因素和初始缺陷对结构屈曲的重要影响。     

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。     

高阶剪切变形板理论K■rm■n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，板长宽比，铺层数以及初始几何缺陷等各种参数变化的影响．     

考虑损伤效应的正交各向异性板的弹塑性后屈曲分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程．基于经典非线性板理论,得到了考虑损伤效应的正交各向异性板的增量型非线性平衡方程,且采用有限差分法和迭代法进行求解．数值算例中,讨论了损伤演化、初始缺陷对正交各向异性板弹塑性后屈曲行为的影响．数值结果显示了弹塑性后屈曲与弹性后屈曲的不同,并且损伤和损伤演化对板的弹塑性后屈曲的影响不可忽略．     

加筋碟形薄壳的塑性屈曲分析

本文采用非线性前屈曲一致理论分析均布外压下加筋碟形薄壳的塑性屈曲问题，建立了这类壳体的能量表达式和屈曲方程，给出了简明的计算格式，数值分析结果表明，所导出的算法具有较好的精度，计算过程也简单方便。     

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。     

复合材料叠层板的非线性动力稳定性

研究复合材料叠层板的非线性动力稳定性,分析中考虑大挠度和初始几何缺陷的存在,得到了不同边界条件和不同铺设方法叠层板在荷载作用下的突变失稳模型及其屈曲临界条件．     

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。     

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     

中心集中载荷作用下波纹圆板的变形应力和稳定性研究

本文用迴转扁壳大挠度理论研究波纹圆板在中心集中力作用下的变形、应力和稳定性,利用牛顿-样条函数法求解了浅正弦波纹圆板的非线性壳方程,获得了屈曲前和屈曲后解答,并对一些特定波形的波纹板给出了由电子计算机得到的数值结果。     

Optimization of the static and dynamic characteristics of plates with isogrid stiffeners

In this paper, the orientation angles of stiffeners arranged in the form of isogrid configuration over a flat plate are selected to optimize the static and dynamic characteristics of these plates/stiffeners assemblies. The static characteristics are optimized by maximizing the critical buckling loads of the isogrid plate, while the dynamic characteristics are optimized by maximizing multiple natural frequencies of the stiffened plate.

A finite element model is developed to describe the statics and dynamics of Mindlin plates which are stiffened with arbitrarily oriented stiffeners. The model is used as a basis for optimizing separately or simultaneously the critical buckling loads and natural frequencies of the plates per unit volume of the plates/stiffeners assemblies.

Numerical examples are presented to demonstrate the utility of the developed model and optimization procedures. The presented approach can be invaluable in the design of plates with isogrid stiffeners for various vibration and noise control applications.     

Thermal buckling analysis of point-supported laminated composite plates in unilateral contact

This paper deals with the thermal buckling analysis of point-supported thin laminated composite plates. The analysis is performed for rhombic and rectangular plates and two cases of bilateral and unilateral buckling. In the unilateral buckling, it is assumed that the plate is in contact with a rigid surface and lateral deflection is forced to be only in one direction. The element-free Galerkin (EFG) method is employed to discretize equilibrium equations. Point supports are modeled in the form of distinct restrained circular surfaces through developing a numerical procedure based on the Lagrange multiplier technique. The unilateral behavior of the plate is incorporated in the analysis by using the penalty method and the Heaviside contact function. The final system of nonlinear algebraic equations is solved iteratively. Two types of point support arrangements are considered and the effect of different parameters such as number of point supports, plate aspect ratio and lamination scheme on the buckling coefficient of composite plates is investigated.     

Analytical solutions of refined plate theory for bending,buckling and vibration analyses of thick plates

Analytical solutions for bending, buckling, and vibration analyses of thick rectangular plates with various boundary conditions are presented using two variable refined plate theory. The theory accounts for parabolic variation of transverse shear stress through the thickness of the plate without using shear correction factor. In addition, it contains only two unknowns and has strong similarities with the classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. Equations of motion are derived from Hamilton’s principle. Closed-form solutions of deflection, buckling load, and natural frequency are obtained for rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are presented to verify the validity of present solutions. It is found that the deflection, stress, buckling load, and natural frequency obtained by the present theory match well with those obtained by the first-order and third-order shear deformation theories.     

关于一阶剪切板的Kármán型精化理论

依据Mindlin_Reissner理论 ,着重研究一阶剪切板的K rm n型精化理论 ,并推导出仅以挠度和应力函数为未知变量的广义K rm n型大挠度方程 ,适用于复合材料上复合构造剪切板的非线性分析·　在当前板的精化理论中 ,消去的两个转角以隐含形式作用于板的整体变形·　这一工程理论适用于各种计及横向剪切复合材料板、正交各向异性中厚板和夹层板等的线性和非线性分析·　容易发现 ,针对具体的工程应用 ,由该方程可直接获得相应的退化形式 ,并且与文献所载的一致·     

Elastic stability of all edges simply supported,stepped and stiffened rectangular plate under Biaxial loading

In this paper using finite difference method the lower bound buckling load for simply supported (a) stepped and stiffened rectangular thin plate (b) linear and non-linear variation of thickness (c) uniformly distributed compressive forces in both directions (d) uniformly distributed compressive force in y direction and non-uniform distribution of compressive force in x-direction is discussed. The thin plate is divided into 900 rectangular meshes. The partial derivatives are approximated using central difference formula. Eight hundred and forty one equations are formed and using the program developed and the least eigenvalue is obtained. The buckling coefficients are calculated for different types of stepped and non prismatic plates and the results are presented in tables and graphs for ready use by designers. Buckling factors for some cases are presented in the form of three separate tables and compared with the values obtained by Xiang, Wei and Wang. The results are in close agreement.     

Elastic stability of all edges simply supported,stepped and stiffened rectangular plate under uniaxial loading

In this paper using finite difference method the lower bound buckling load for simply supported stepped and stiffened rectangular plate with uniformly distributed compressive forces in one direction is discussed. The plate is divided into 400 rectangular meshes. The partial derivatives are approximated using central difference formula. Three hundred and sixty-one equations are formed and using MATLAB the least eigenvalue is obtained. The buckling coefficients are calculated for different types of stepped plates and the results are presented in tables and graphs for ready use by designers. Two separate tables are presented in comparison with the exact buckling factor for stepped rectangular plate by Xiang, Wei and Wang. The results give a close agreement.     

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.     

具有初挠度的柔韧圆板的振动问题

本文推导出具有初挠度柔韧圆板的振动方程,在相平面上讨论了运动稳定性.用Galerkin法和Lindstedt-Poincaré摄动法求得具有初挠度圆板非线性振动的周期解,讨论了初挠度对柔韧圆板的动力特性的影响.     

Buckling mode localization in rib-stiffened plates with misplaced stiffeners – a finite strip approach

Buckling mode localization in rib-stiffened plates with randomly misplaced stiffeners is studied in this paper. A method of finite strip is employed to establish the equations of equilibrium for the rib-stiffened plates under axial compressive load. The equations of equilibrium are then expressed in the form of transfer matrices. Localization factors, which characterize the average exponential rates of growth or decay of amplitudes of deflection, are determined using the method of transfer matrix. The results obtained from a finite strip formulation agreed very well with those obtained from a previous study using an analytical approach. The method of finite strip presented in this study is suitable for studying the localization phenomenon in buckling modes of rib-stiffened plates, especially those with nonuniform cross sections.