功能梯度斜板的屈曲分析

研究面内荷载作用下功能梯度斜板的屈曲问题.基于经典板理论,假设材料性质为板厚度方向坐标的幂函数,不考虑温度的影响,推导功能梯度板在纵向荷载作用下的平衡微分方程,运用坐标转换关系,建立斜坐标系下功能梯度斜板的屈曲微分方程.采用微分求积法,离散屈曲微分方程,结合边界条件,给出功能梯度斜板在两对边受有均布压力作用下临界屈曲荷载的无量纲数值解.在此基础上,讨论板的几何外形尺寸、夹角、梯度指标以及中面变形等因素对临界屈曲荷载的影响.结果表明:功能梯度板的临界屈曲荷载变化介于相应的均质各向同性板的临界屈曲荷载变化之间;功能梯度材料板的临界屈曲荷载变化随板的相对几何外形尺寸宽长比b/a的减小而减小,随梯度指标κ和夹角θ的增加而减小;中面变形对夹角较小和梯度指标较高的板有较大影响.     

变厚度多孔梯度材料圆板的热后屈曲分析

为分析多孔梯度材料圆板在非均匀温度场中的热后屈曲响应,基于经典板理论和物理中面概念建立了梯度多孔材料圆板在热载荷作用下的控制微分方程,其中假设厚度变化沿半径为二次抛物线型且板在其厚度上具有对称和非对称的非均匀孔隙率分布。采用打靶法数值求解了问题的屈曲和后屈曲响应,给出了均匀升温和热传导下的梯度多孔非线性变厚度圆板后屈曲平衡路径。结果显示：变厚度系数、孔隙率系数、孔隙分布方式以及温度场对板的临界载荷和后屈曲平衡路径均有影响;在不同温度场中孔隙率系数越大,屈曲时的临界载荷越小;孔隙率对称分布下的临界载荷大于非对称情况下的。     

陶瓷/金属非保守FGM斜板的颤振分析

研究了陶瓷/金属非保守功能梯度材料（FGM）斜板的颤振问题。以薄板理论为基础,假定材料的等效物性参数为沿厚度方向体积分数的幂律变化,在斜坐标系下建立了非保守FGM斜板的运动微分方程。运用微分求积法,对四边固支边界条件下陶瓷/金属非保守FGM斜板的量纲一复频率进行了数值计算,分析了FGM斜板的梯度指标、夹角和长宽比的变化对非保守FGM斜板稳定性的影响。结果表明,非保守FGM斜板的临界颤振荷载随梯度指标和夹角的增大而减小,随长宽比的增大而增大。     

纤维增强FGM梁的自由振动和临界屈曲载荷分析

基于经典梁理论（CBT）研究轴向力作用下纤维增强功能梯度材料（FGM）梁的横向自由振动和临界屈曲载荷问题。首先考虑由混合律模型来表征纤维增强FGM梁的材料属性,其次利用Hamilton原理推导轴向力作用下纤维增强FGM梁横向自由振动和临界屈曲载荷的控制微分方程,并应用微分变换法（DTM）对控制微分方程及边界条件进行变换,计算了纤维增强FGM梁在固定-固定（C-C）、固定-简支（C-S）和简支-简支（S-S）3种边界条件下横向自由振动的无量纲固有频率和无量纲临界屈曲载荷。退化为各向同性梁和FGM梁,并与已有文献结果进行对比,验证了本文方法的有效性。最后讨论在不同边界条件下纤维增强FGM梁的刚度比、纤维体积分数和无量纲压载荷对无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。     

壳体屈曲分析中关于能力减弱系数的剖析

工程中通常采用有限元中的线性屈曲方法和非线性屈曲方法来求解壳体的屈曲载荷。对于复杂结构(如钢安全壳),若直接采用非线性屈曲方法求解,除计算工作量大外,还不容易得到符合实际要求的临界载荷。因此,工程中常通过线弹性方法来获得符合实际要求的临界载荷。介绍了壳体屈曲的线弹性理论解,然后利用ANSYS软件求解圆柱壳受轴向和侧向外压的屈曲载荷,并与理论解进行了对比;最后通过对比前人的试验结果与线弹性理论得到的上临界值来剖析"能力减弱系数"的含义和合理性。结果表明:采用线弹性方法来求解壳体屈曲问题是可行的,但必须进一步考虑"能力减弱系数"、"安全系数"和"塑性折减系数"后才能得到工程上所需的临界屈曲载荷值。     

局部受损预载结构屈曲强度和后屈曲承载能力评估和预报

项目负责人:沈惠申所在单位:上海交通大学项目批准号:59975058项目简介本课题主要涉及结构非线性稳定理论及其应用。以研究复合材料层合剪切板壳结构在复杂环境和复杂荷载作用下的屈曲强度和后屈曲承载能力为主要目标。复合材料层合板壳结构通常承受机械荷载和热荷载的共同作用,而预加热荷载或机械荷载往往会降低板壳结构的屈曲荷载（或临界温度）和后屈曲/热后屈曲承载能力。复合材料的力学性能对于外部环境有着很大的依赖性。外部环境的两种效应可以造成很大的内应变,从而影响屈曲荷载。这两种效应是吸湿效应和热效应。水     

交接环形耐压壳屈曲特性试验与数值研究

研究了不锈钢交接环形耐压壳在均匀外压作用下的屈曲性能。使用的交接环形耐压壳的截面半径为70.5 mm,壁厚为1.319 mm,圆周旋转半径为134 mm。制作了6个交接壳模型,并对其进行几何测量、静水外力试验和数值计算,在此基础上对交接环形耐压壳屈曲行为进行分析,研究了交接角度和环肋参数对屈曲的影响规律。结果表明,交接角度对交接环壳屈曲载荷没有影响,环肋的宽度和厚度达到一定阈值时,临界屈曲载荷值保持不变且接近于交接单元的屈曲载荷。     

薄壁金半球壳镀金沉积法制造技术研究

通过对薄壁金半球壳的结构工艺性分析,采用了在黄铜胎上沉积金层的工艺方法来制造薄壁金半球壳,获得的半径为2mm和4mm,厚度为0.05mm的纯金半球壳体,工艺实现过程相对简单,制造成本较低.为薄壁壳体的制造提供一种新的技术途径.     

球形封头开孔接管结构屈曲特性研究

针对外压作用下球形封头开孔接管结构,采用有限元非线性屈曲分析方法,探讨不同结构参数对其临界失稳压力Pcr的影响.研究结果表明,当球壳主体参数径厚比一定时,临界失稳压力削弱系数K随开孔率增大而下降,随接管与封头厚度比增大而增大.接管与封头厚度比较小时,计算模型失稳位置位于接管;接管与封头厚度比增至一定值时,计算模型失稳位...     

波纹蒙皮结构屈曲性能研究

对两种加强槽的波纹蒙皮结构的屈曲性能进行了分析,讨论了加强槽的半径(宽度),加强槽深度,加强槽个数对临界屈曲载荷的影响,并对加强槽槽间距以及加工可行性对加强槽各个参数的取值约束进行了分析。分析结果表明,临界屈曲载荷随加强槽深度增加而增加。当加强槽深度一定时,存在一个加强槽半径(宽度)临界曲线,当处于该临界曲线左侧时,临界屈曲载荷随半径增加而增加,反之减小。当加强槽半径和深度一定时,存在一个加强槽个数的临界曲面,当处于该曲面下侧时,临界屈曲载荷随加强槽个数增加而增加。     

Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells

Non-linear buckling analyses of imperfect functionally graded truncated conical shells with simply supported boundary conditions and subjected to an axial compressive load have been presented in this work. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The non-linear prebuckling deformations and initial geometric imperfections of an FGM truncated conical shell are both taken into account. The fundamental relations, modified Donnell type non-linear stability and compatibility equations of an imperfect FGM truncated conical shell are obtained and are solved by superposition and Galerkin methods, and the upper and lower critical axial loads has been found analytically. The numerical illustrations concern the non-linear buckling response of FGM truncated conical shells with different values of truncated conical shell parameters, initial imperfections and compositional profiles. Comparing the results of this study with those in the literature validates the present analysis.     

Postbuckling of symmetrically laminated, moderately thick, axisymmetric shallow spherical shells

The paper deals with the buckling and postbuckling behaviour of cylindrically orthotropic, axisymmetric laminated, moderately thick shallow spherical shells under uniformly distributed normal loading. Considering the effects of transverse shear, the governing equations of equilibrium for the shells are derived and expressed in terms of normal deflection , slope qf and stress function gy. An iterative Chebyshev series solution technique is employed for the buckling and postbuckling analyses. Critical loads are estimated and the effects of boundary conditions, material properties, shell parameter, base radius to thickness ratio and number of layers on the postbuckling behaviour are shown.     

Theory and comparison of the effect of composite and shape memory alloy stiffeners on stability of composite shells and plates

The effects of composite and shape memory alloy stiffeners on stability of composite cylindrical shells and rectangular plates subjected to a compressive load are compared. The governing equations for reinforced cylindrical shells are developed based on the Love first approximation theory and smeared stiffeners technique. It is shown that composite stiffeners are more efficient in cylindrical shells, while shape memory alloy stiffeners may be preferable in plates or in long shallow shells. It is also proven that shape memory alloy stiffeners increase the upper and lower buckling loads, i.e. the linear buckling load and the minimum postbuckling load-carrying capacity of cylindrical shells modeled as single-degree-of-freedom systems by the same amount.     

Buckling of shallow spherical shells including the effects of transverse shear deformation

The large deflection equation of a shallow spherical shell under uniformly distributed transverse loads is established in this paper with consideration of effects of transverse shear deformation on flexural deformation. Using an updated iteration method, an analytical solution for nonlinear stability of a shallow spherical shell is obtained. Formulae for estimating the critical buckling loads are presented for two types of boundary conditions. Discussions on the influences of the geometric and physical parameters on the critical buckling loads are given.     

Dynamic buckling of suddenly loaded imperfect hybrid FGM cylindrical shells with temperature-dependent material properties under thermo-electro-mechanical loads

Only static buckling of the hybrid functionally graded material (FGM) cylindrical shells has been investigated so far. In the present paper, dynamic buckling of imperfect FGM cylindrical shells with integrated surface-bonded sensor and actuator layers subjected to some complex combinations of thermo-electro-mechanical loads is investigated. The general form of Green's strain tensor in curvilinear coordinates and a high-order shell theory proposed earlier by the author are used. The complicated nonlinear governing equations are solved using the finite-element method. Buckling load is detected by a modified Budiansky's criterion proposed earlier by the author. Effects of temperature dependency of material properties, volume fraction index, load combination, and initial geometric imperfections on thermo-electro-mechanical post-buckling behavior are evaluated. Results reveal that the volume fraction index, temperature gradient, layer sequence, and the adaptive feedback control somewhat may affect the buckling load.     

Buckling analysis of FGM plates under uniform,linear and non-linear in-plane loading

The paper investigates the buckling responses of functionally graded material (FGM) plate subjected to uniform, linear, and non-linear in-plane loads. New nonlinear in-plane load models are proposed based on trigonometric and exponential function. Non-dimensional critical buckling loads are evaluated using non-polynomial based higher order shear deformation theory. Navier’s method, which assures minimum numerical error, is employed to get an accurate explicit solution. The equilibrium conditions are determined utilizing the principle of virtual displacements and material property are graded in the thickness direction using simple Voigt model or exponential law. The present formulation is accurate and efficient in analyzing the behavior of thin, thick and moderately thick FGM plate for buckling analysis. It is found that with the help of displacement-buckling load curve, critical buckling load can be derived and maximum displacement due to the instability of inplane load can be obtained. Also, the randomness in the values of transverse displacement due to inplane load increases as the extent of uniformity of the load on the plate is disturbed. Furthermore, the parametric varying studies are performed to analyse the effect of span-to-thickness ratio, volume fraction exponent, aspect ratio, the shape parameter for non-uniform inplane load, and non-dimensional load parameter on the non-dimensional deflections, stresses, and critical buckling load for FGM plates.

     

Rigid-plastic collapse of compression-bent shallow shells

Limit analysis solutions are given for simply supported shallow spherical shells under combined external loading. The effect of transverse shear on collapse loads is examined in the paper. Lower bound and exact load interaction curves at collapse are given for several shell configurations. The shell material is assumed rigid-plastic and yields according to the von Mises criterion. The results indicate that the lower bound approach gives acceptable results when extremely shallow shells are considered. It is also shown that the reduction of collapse loads due to transverse shear is of the same order as found for circular plates.     

Elastoplastic dynamic instability of long circular cylindrical shells under pure bending

This paper presents a numerical study which is concerned with the prediction of the response and instabilities in long circular cylindrical shells under dynamic pure bending. Of particular interest is the response of such shells, bent into the plastic range of the material, and the various instability characteristics of the shells under dynamic bending (sudden step load). It was found that the major deformation characteristic of the shells is essentially similar to that observed in the static bending when the applied moment is much smaller than the critical dynamic moment. However, when the applied moment is close to the critical dynamic moment, the ovalization of the shell cross-section was found to be localized over a length of several shell diameters in the central region, even though the response of the shell curvature was shown to be still stable in this case. When the applied moment reaches the critical dynamic moment, the response of the shell curvature was shown significantly increasing with time and the shell buckled catastrophically. For thicker shells, it was found that the development of localized ovalization of the shell cross-section is the major factor that causes shell dynamic instability. For thinner shells, however, besides the localized ovalization, the bifurcation induced by short wavelength ripples on the compressed side of the shell was also observed in the initial buckling patterns. After the bifurcation, the initial buckling pattern was replaced by the final postbuckling mode characterized by a localized sharp cupping in the centre of the shell.     

Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells

In this paper, an analytical solution is provided for the postbuckling behaviour of moderately thick plates and shallow shells made of functionally graded materials (FGMs) under edge compressive loads and a temperature field. The material properties of the functionally graded shells are assumed to vary continuously through the thickness of the shell, according to a power law distribution of the volume fraction of the constituents. The fundamental equations for moderately thick rectangular shallow shells of FGM are obtained using the von Karman theory for large transverse deflection and high-order shear deformation theory for moderately thick plates. The solution is obtained in terms of mixed Fourier series and the obtained results are compared with those of the Reissner–Mindlin's theory for moderately thick plates and the classical theory ignoring transverse shear deformation. The effect of material properties, boundary conditions and thermomechanical loading on the buckling behaviour and the associated stress field are determined and discussed. The results reveal that thermomechanical coupling effects and the boundary conditions play a major role in dictating the response of the functionally graded plates and shells under the action of edge compressive loads.