轴压柱壳弹塑性稳定性分析的通用方程推导

针对由于轴压引起的壳体弹塑性屈曲而导致的材料在成型和制造过程中的失效力学行为，选择适用于轴压的屈曲模态函数，利用能量法确定了屈曲参数满足的一般非线性方程组，给出了求解不含缺陷或含缺陷的几何线性或非线性弹塑性的临界失衡平衡位形曲线的方法。     

含口盖复合材料圆柱壳轴压屈曲性能分析

对完整复合材料圆柱壳进行了轴向压缩破坏试验,得到了圆柱壳的载荷-应变曲线和破坏载荷,试验结果表明:在轴压载荷作用下,圆柱壳的破坏形式为屈曲破坏。结合ANSYS有限元软件对复合材料圆柱壳进行屈曲分析,有限元计算结果与试验结果一致,验证了模型和计算方法的有效性。利用所建立的模型,对圆柱壳的铺层顺序进行改进设计,分析了铺层角度对开口圆柱壳屈曲载荷的影响。在开口处加装复合材料口盖进行补强,计算了不同口盖铺层方式下的柱壳屈曲强度。计算结果表明:优化复合材料叠层顺序可提升结构的屈曲载荷,开口后圆柱壳的轴向屈曲载荷大幅降低,加装口盖可使开口圆柱壳的轴向稳定性得到有效的增强。提出了一种提高含口盖的复合材料圆柱壳轴向屈曲强度的改进设计方法,为复合材料壳体的稳定性设计提供参考。     

有初始缺陷的FGM圆柱壳的非线性动力学分析

研究了有初始几何缺陷的FGM圆柱壳在面内载荷与横向载荷共同作用下的非线性动力学行为。材料组分的体积分数沿厚度方向呈幂律分布。基于Reddy的三阶剪切变形理论,运用Hamilton原理,推导出了FGM圆柱壳振动的非线性偏微分方程;利用Galerkin法离散控制方程,将偏微分方程离转化为常微分方程。为了准确地描述圆柱壳的非线性动力学行为,考虑到了对称模态。通过Runge-Kutta法进行数值仿真,研究了系统的非线性动态响应,并得到了分岔图、最大Lyapunov指数、相图和时间历程图。通过对比有2种不同类型缺陷的数值结果分析了缺陷类型和面内载荷对系统非线性动态响应的影响。     

柱壳纯弯曲内时弹塑性屈曲分析和计算

首次将内时理论应用于屈曲问题，由具有非保守性质的内时虚功变分方程，研究了柱壳在纯弯曲下的塑性屈曲响应。结果显示了卡门－钱学森关于屈由“跳跃理论”的性质，证实了湘利关于塑性屈曲临界载荷不唯一的提法，表明了塑性屈曲破坏是一个相继屈曲的过程。     

分布轴对称缺陷对薄壁圆柱壳屈曲可靠性影响

为了分析分布轴对称缺陷参量对薄壁圆柱壳屈曲可靠性的影响,根据Budiansky临界解答,建立了具有初始分布轴对称缺陷薄壁圆柱壳体的等效安全余量.利用改进一次二阶矩方法,研究了分布轴对称初始缺陷对薄壁圆柱壳体屈曲安全问题,以可靠度的概念分析了结构屈曲敏感度的问题,分析了基于结构可靠度的薄壁结构屈曲强度评定方法,提出了基于结构可靠度的缺陷敏感度的分析方法,通过结构可靠度指标的变化能够间接地反映结构对缺陷的敏感性.研究表明,基于结构可靠度的不完整薄壁圆柱壳屈曲安全评定方法是可行的,提出的等效安全余量的方法,为复杂安全余量建立和简化结构安全评定提供了参考.     

功能梯度材料圆（环）板的屈曲分析

基于经典板理论，推导了功能梯度材料圆形板在边界面内均布压力作用下的轴对称屈曲方程．假设功能梯度材料性质沿板厚度方向按成分含量百分比的幂指数形式连续变化，用打靶法求解所得方程，得到了功能梯度材料圆(环)板的临界屈曲载荷，并分析了材料的梯度性质、内外半径比以及边界条件对板临界载荷的影响．     

均匀轴压圆柱薄壳的稳定性分析

采用解析法、线性和非线性有限元法对均匀轴压圆薄壳的稳定问题进行了分析,就本算例而言,三种方法所得的初始屈曲荷载是近似相同的。非线性有限元分析显示,在后屈曲阶段的荷载位移曲线上形成了一段近似水平的曲线,与之对应的是一近似常量的后屈曲承载力通过对以往实验数据的统计分析,得到了计算屈曲力的经验公式,其结果经与非线性有限元法的分析结果比较,初步发现试验得到的圆柱壳的后屈曲应力而非其初试屈曲应力,从而得到了     

圆柱壳在静水压力作用下的弹塑性稳定

本文推导出大挠度圆柱壳在静水压力作用下弹塑性稳定问题增量形式的基本方程,并采用伽辽金配点法分析了两端简支圆柱壳的算例,所得计算结果与已有文献和实验结果基本一致。     

梯度功能材料轴承的热弹性分析

针对梯度功能材料圆柱壳的轴对称热弹性响应和球壳的球对称热弹性响应提出了简单而精确的解。类似于复合材料层合结构的研究，将梯度功能材料圆柱壳或球壳沿厚度分为若干层，各层视为均匀材料，从而导出温度解、位移解和应力解。只要层数足够大，其解将收敛于精确解。算例检验了解的收敛性，讨论了分层数的选取以及材料和结构参数对热弹性响应的影响。所述方法对非均匀材料结构的分析具有借鉴作用。     

生物骨圆柱壳的蠕变屈曲分析

将生物胫骨考虑为纤维增强的粘弹性复合材料圆柱壳,并进行了蠕变屈曲分析.采用广义Maxwell模型,提出了胫骨的粘弹性复合材料圆柱壳力学模型,得到了受轴向载荷作用粘弹性圆柱壳的蠕变屈曲控制方程.通过Laplace变换,将控制方程转换到相空间,在相空间中得到临界荷载的表达式;经过Laplace逆变换,得到了随时间变化的屈曲荷载曲线.最后依据具体的人胫骨粘性系数,对人胫骨轴压屈曲压力进行计算和分析比较,得到了蠕变屈曲临界载荷曲线,给出了蠕变屈曲荷载随胫骨长度及时间的变化曲线.研究结果表明:将胫骨考虑为纤维增强的粘弹性复合材料圆柱壳其瞬时临界荷载值、持久临界荷载值均小于将该胫骨考虑为功能梯度圆柱壳的屈曲荷载.     

轴向脉冲载荷冲击下弹性圆柱壳动态屈曲中的竹节现象

本文针对弹性圆柱壳在轴向脉冲载荷冲击下动态局部屈曲问题,提出一种新的方法,即哈密顿体系方法.通过构造哈密顿体系,在辛空间中将临界载荷和动态屈曲模态归结为辛本征值和本征解问题.发现圆柱壳屈曲的临界载荷被分为两类,其分别对应圆柱壳压缩屈曲和弯曲屈曲.辛本征解反映了局部的压缩屈曲模态和横向的弯曲屈曲模态.在物理上表现出壳体的压缩型竹节屈曲现象和弯曲型竹节屈曲现象.同时数值结果揭示了临界载荷和屈曲模态的规律及影响因素.     

双轴载荷作用下柱壳的塑性屈曲

采用各向异性刚线性硬化模型研究了柱壳的塑性屈曲问题，当把本构方程的起算点设置在线硬化的起始位置时，本构方程具有线性形式，基此建立了柱壳屈曲的基本方程，并用它求解了四边简支柱壳在双轴载荷作用下的屈曲问题，在弱各项异性情况下获得了最小屈曲载荷的解析表达式．     

Stability of perfect and imperfect cylindrical shells under axial compression and torsion

Stability analyses of perfect and imperfect cylindrical shells under axial compression and torsion were presented. Finite element method for the stability analysis of perfect cylindrical shells was put forward through comparing critical loads and the first buckling modes with those obtained through theoretical analysis. Two typical initial defects, non-circularity and uneven thickness distribution, were studied. Critical loads decline with the increase of non-circularity, which exist in imperfect cylindrical shells under both axial compression and torsion. Non-circularity defect has no effect on the first buckling mode when cylindrical shell is under torsion. Unfortunately, it has a completely different buckling mode when cylindrical shell is under axial compression. Critical loads decline with the increase of thickness defect amplitude, which exist in imperfect cylindrical shells under both axial compression and torsion, too. A greater wave number is conducive to the stability of cylindrical shells. The first buckling mode of imperfect cylindrical shells under torsion maintains its original shape, but it changes with wave number when the cylindrical shell is under axial compression.     

轴压下大型薄壁圆柱壳的稳定性研究

承受轴向和周边径向压力的大型薄壁钢柱壳结构的稳定性分析是一个十分复杂的问题.根据理想壳体结构的屈曲平衡方程得出的临界应力,结合德国和我国的设计规范,通过有限单元法研究了初始缺陷、环向加劲肋间距、大开孔对薄壁圆柱壳稳定性的影响.结果表明:初始缺陷可使薄壁柱壳的极限屈曲应力降低至理想壳体临界应力的1/4以下;环向加劲肋间距的减小能够使得壳体极限屈曲应力显著增加,进而大大地提高了壳体的轴向承载力;大开孔的存在严重削弱了壳体的整体稳定性.上述结论对于薄壁柱壳的稳定性分析具有一定的理论意义和实用价值.     

含损伤复合材料圆柱壳非线性动力响应及屈曲

为分析损伤对复合材料圆柱壳结构动力性能的影响,该文以一阶剪切变形理论为基础,由Hamilton原理推导出包含横向剪切变形以及初始几何缺陷的圆柱壳的非线性动力方程.复合材料圆柱壳上的初始几何变形以初始几何缺陷的方式描述并引入方程,针对基体破坏子层进行刚度折减,并求得脱层损伤区域的等效刚度矩阵.采用半解析法求解方程,并根据求得的位移响应情况,由B-R准则判定屈曲,确定屈曲临界载荷;分析初始几何变形、伴随脱层及子层基体破坏等损伤形式对复合材料圆柱壳非线性动力响应及屈曲的综合影响.     

Method of lines for temperature field of functionally graded materials

The finite element method (FEM) and the boundary element method (BEM) are often adopted. Howev er, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the method of lines (MOL) is introduced to solve the temperature field of FGM. The basic idea of the method is to semi-discretize the governing equation into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs. The functions of thermal properties are directly embodied in these equations and these properties are not discretized in the domain. Thus, difficulty of FEM and BEM is overcome by the method. As a numerical example, the temperature field of a plane problem is analyzed for FGMs through varying thermal conductivity coefficient by the MOL.     

Method of lines for temperature field of functionally graded materials

The finite element method (FEM) and the boundary element method (BEM) are often adopted. However, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the method of lines (MOL) is introduced to solve the temperature field of FGM. The basic idea of the method is to semi-discretize the governing equation into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs. The functions of thermal properties are directly embodied in these equations and these properties are not discretized in the domain. Thus, difficulty of FEM and BEM is overcome by the method. As a numerical example, the temperature field of a plane problem is analyzed for FGMs through varying thermal conductivity coefficient by the MOL. Foundation item: Project (90305023 and 59731020) supported by the National Natural Science Foundation of China     

弹性地基中变厚度圆柱壳的轴对称弯曲

圆柱壳是工程中常用的一种壳体结构(构件),但对于弹性地基中变厚度圆柱壳的研究却较少.在等截面圆柱壳初参数解的基础上,利用阶梯折算法和传递矩阵法,研究了弹性地基中沿轴向任意变厚度圆柱壳的轴对称弯曲问题,所得公式具有简捷、统一的特点,适合计算机编程.文末给出了算例.结果表明利用传递矩阵法分析变厚度圆柱壳是非常有效的.对沿轴向任意变厚度圆柱壳,可得到满意的计算结果;对阶梯型圆柱壳,可得到准确计算结果.这种分析方法还可以进一步推广到环向加肋的圆柱壳和变基床系数的弹性地基中圆柱壳的轴对称弯曲分析.     

Optimal design of functionally graded Pm PV/CNT nanocomposite cylindrical tube for purpose of torque transmission

Carbon nanotube(CNT)/polymer nanocomposites have vast application in industry because of their light mass and high strength. In this work, a cylindrical tube which is made up of functionally graded(FG) PmP V/CNT nanocomposite, is optimally designed for the purpose of torque transmission. The main confining parameters of a rotating shaft in torque transmission process are mass of the shaft, critical speed of rotation and critical buckling torque. It is required to solve a multi-objective optimization problem(MOP) to consider these three targets simultaneously in the process of design. The three-objective optimization problem for this case is defined and solved using a hybrid method of FEM and modified non-dominated sorting genetic algorithm(NSGA-II), by coupling two softwares, MATLAB and ABAQUS. Optimization process provides a set of non-dominated optimal design vectors. Then, two methods, nearest to ideal point(NIP) and technique for ordering preferences by similarity to ideal solution(TOPSIS), are employed to choose trade-off optimum design vectors. Optimum parameters that are obtained from this work are compared with the results of previous studies for similar cylindrical tubes made from composite or a hybrid of aluminum and composite that more than 20% improvement is observed in all of the objective functions.