Nonlinear deformation and stability of supported oval cylindrical shells under torsion and bending with internal pressure

A problem of geometrically nonlinear deformation and stability of supported cylindrical shells with the oval cross-section contour is solved by the finite element method. The nonlinear deformation and stability of shells under combined loading by bending, torsion moments, transverse force and internal pressure are analyzed. The critical loads and buckling modes of shells are determined. The influence of deformation nonlinearity and shell ovality on critical loads is clarified.     

Analysis of nonlinear deformation and stability of reinforced elliptic cylindrical shells under bending with internal pressure

A finite element statement of solving problems on stability of reinforced elliptic cylindrical shells taking into account momentness and nonlinearity of their subcritical stress strain state is presented. The explicit expressions for displacements of noncircular cylindrical shell elements as rigid bodies are determined by integrating the equations obtained by equating the components of linear strains to zero. These expressions were used to construct the form functions for an efficient quadrilateral finite element of natural curvature. An efficient numerical algorithm of nonlinear deformation and stability of shells was developed. The stability of reinforced elliptic cylindrical shells under combined loading by bending moment, transverse boundary force and internal pressure is analyzed. We also examine how the critical loads are affected by the strain nonlinearity and ellipticity of shell deformation at the subcritical stage.     

Research on Nonlinear Deformation and Stability of an Advanced Aircraft Fuselage Composite Section under Pure Bending

The finite element algorithm developed by the authors has been used for solving the strength and stability problems of shells. The effect of deformation nonlinearity, stiffness of stringer set, shell thickness on critical loads has been determined.     

复合材料壳体的应力和稳定性分析

一、引言 在现有的文献中,复合材料壳体的稳定性计算,大都采用环元针对轴对称分布载荷的轴对称旋转壳进行的。但是在实际结构中有大量的非轴对称壳体,壳壁大都是变厚度,实际载荷也大多是非轴对称分布,并且往往还有由温度改变而产生的热应力,或称它为“热载”。为了解决这些更为广泛的实际问题,开展了这项研究工作。     

几何非线性样条单元

 <正>结构的有限变形与稳定性分析具有重要意义。有限元法的应用,促进了几何非线性研究工作的开展。本文在线性样条单元C’〕的基础上提出一种几何非线性样条板壳单元,壳体的应变位移关系采用Von一K巨rmon方案,以分片样条Hermite插值构造单元的位移模式。对于弱非线性问题,采用修正的Newton一Raphson法解非线性方程组。对于极值点失稳情况,以固定弧长法追踪屈曲路径,并用曲线拟合的方法确定结构的临界载荷值。     

Nonlinear deformation and stability of discretely reinforced elliptical cylindrical shells under transverse bending and internal pressure

A finite element formulation of solving the stability problems for the discretely reinforced noncircular cylindrical shells is presented taking into account that their subcritical stress strain state is instantaneous and nonlinear. The author-developed finite elements for a natural-curved shell and the beam elements of reinforcements are used. A numerical algorithm to study the nonlinear deformation and stability of shells was developed. The stability of a stringer-stiffened cylindrical shell with an elliptical cross-sectional contour under transverse bending and internal pressure is examined. We also investigate the effect of internal pressure, ellipticity and nonlinearity of deformation, as well as of reinforcement discreteness and heterogeneity.     

转动壳体外压屈曲的有限元分析

由于转动离心力的影响,壳体的屈曲临界压力随转速的提高而升高。本文推导了转动壳体线性屈曲的有限元公式,并用DMAP语言编制相应的程序修改MSC/NASTRAN的解题步骤考虑离心力完成了分析。还利用MSC/NASTRAN的几何非线性分析功能完成了有初始几何缺陷转动壳体的有限元分析,计算后屈曲的载荷—变形曲线,得出不同转速下的缺陷敏感度曲线。     

Aeroelastic stability analysis of heated flexible panel subjected to an oblique shock

The critical conditions for aeroelastic stability and the stability boundaries of a flexible two-dimensional heated panel subjected to an impinging oblique shock are considered using theoretical analysis and numerical computations, respectively. The von-Karman large deflection theory of isotropic flat plates is used to account for the geometrical nonlinearity of the heated panel, and local first-order piston theory is employed in the region before and after shock waves to estimate the aerodynamic pressure. The coupled partial differential governing equations, according to the Hamilton principle, are established with thermal effect based on quasi-steady thermal stress theory. The Galerkin discrete method is employed to truncate the partial differential equations into a set of ordinary differential equations, which are then solved by the fourth-order Runge-Kutta numerical integration method. Lyapunov indirect method is applied to evaluate the stability of the heated panel. The results show that a new aeroelastic instability (distinct from regular panel flutter) arises from the complex interaction of the incident and reflected wave system with the panel flexural modes and thermal loads. What’s more, stability of the panel is reduced in the presence of the oblique shock. In other words, the heated panel becomes aeroelastically unstable at relatively small flight aerodynamic pressure.     

Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel

In the present article, the linear and the nonlinear deformation behaviour of functionally graded (FG) spherical shell panel are examined under thermomechanical load. The temperature-dependent effective material properties of FG shell panel are evaluated using Voigt’s micro-mechanical rule in conjunction with power-law distribution. The nonlinear mathematical model of the FG shell panel is developed based on higher-order shear deformation theory and Green-Lagrange type geometrical nonlinearity. The desired nonlinear governing equation of the FG shell panel is computed using the variational principle. The model is discretised through suitable nonlinear finite element steps and solved using direct iterative method. The convergence and the val-idation behaviour of the present numerical model are performed to show the efficacy of the model. The effect of different parameters on the nonlinear deformation behaviour of FG spherical shell panel is highlighted by solving numerous examples.     

基于广义力的旋翼振动载荷计算

为描述挥舞、摆振铰和变距轴承的运动引入了三个刚体运动自由度 ,旋翼桨叶通过 5节点15自由度有限单元离散 ,计入了桨叶刚性运动与非线性弹性变形之间的动力学耦合效应。利用曲线坐标系下的本构方程 ,对经典的中等变形梁理论进行了重新的推导。另外 ,采用了Leishman Beddoes非定常和动态失速模型 ,入流由自由尾迹分析获得。导出的旋翼桨叶非线性时变常微分方程以广义力的形式给出。桨叶截面载荷和运动方程在位形空间中同时求解。由本文分析得出的桨叶振动载荷与SA349/ 2小羚羊直升机飞行测试数据吻合程度很好。     

Nonlinear Deformation and Stability of Discrete-Reinforced Elliptical Cylindrical Composite Shells under Torsion and Internal Pressure

The problem of strength and stability of shells under torsion and internal pressure was solved. It was found out the influence of the internal pressure, ellipticity and nonlinearity of deformation on the critical buckling load of the shell.     

带气弹稳定性约束的复合材料浆叶减振优化设计

研究以降低直升机旋翼激振力为目标的复合材料桨叶结构动力学减振优化设计 ,分析了桨叶结构特性及桨尖后掠角等参数对N次 /转旋翼桨毂振动载荷的影响。在建立的桨叶二维结构特性有限元分析方程中 ,计入了桨叶剖面翘曲变形的影响 ,并利用哈密尔顿原理推导了旋翼桨叶的一维非线性运动微分方程。以桨毂交变载荷为目标函数 ,直接以复合材料桨叶典型剖面构造节点数据、铺层设计参数和桨尖后掠角等为设计变量 ,引入桨叶挥舞惯量、固有频率和气弹稳定性约束 ,进行旋翼的动力学优化设计 ,并结合 3片桨叶旋翼的设计进行了算例分析 ,优化结果使 3次/转的桨毂载荷降低了 2 4 .9%～ 33%。     

复合材料叠层板壳材料非线性有限元分析

 本文采用通用于复合材料叠层厚、薄板壳的Heferosis三维退化曲壳元,利用Hill屈服准则和层状模型法,研制了针对金属基复合材料叠层板壳进行弹塑性分析的超参元程序。算例结果表明,叠层板壳分析方法和所编程序是可靠的,精度良好。     

基于流固耦合的斜激波冲击作用下曲壁板气动弹性分析

采用自主发展的双向流固耦合求解器,研究了斜激波冲击作用下曲壁板的气动弹性响应特性。曲壁板的几何非线性大变形运动方程采用有限差分法求解,流体控制方程基于有限体积法求解,双向流固耦合采用交错迭代算法。计算结果表明:当动压小于临界颤振动压时,曲壁板表现出静平衡状态,且随着动压的增大,壁板变形的非对称性越明显。当动压大于临界颤振动压时,壁板振动位移先增大后减小,最终达到稳定颤振状态,且该极限环颤振并不关于初始位置正负对称的。同时,随着动压的增大,壁板颤振的正向峰谷值、负向峰谷值和振幅均逐渐增大,颤振频率则逐渐减小。壁板振动响应规律并不随着壁板弯曲高度的改变而单调递增或递减,较小的弯曲高度可以降低壁板颤振临界动压值,但是当弯曲高度进一步增大后,由于气动非线性特性增强,准周期无规则运动状态被激发了出来,临界颤振动压迅速升高。     

传递矩阵-直接积分法及其应用

本文提出了借传递矩阵法建立“特征盘”的运动方程,然后借直接积分法求解,用以求转子-支承系统的临界转速、振型、不平衡响应、及稳定性分析的方法。导出了在考虑其本身的转动惯量、质量、剪切应力影响下的轴段传递矩阵。以实例说明了借传递矩阵法建立“特征”微分方程组的过程。计算与实测了一个模型转子-支承系统的不平衡响应、临界转速及振型,二者基本吻合。     

电场及双向压缩下含压电层的对称层合圆柱壳体的动力稳定性

 应用一阶剪切变形理论, 分析了简支边界有限长含压电层的对称层合圆柱壳及壳块在谐变电场及双向周期荷载作用下的动力稳定性问题, 并用模态展开的方法得出一阶动力不稳定区。选择几种模态为例说明材料的压电性、壳体几何参数和加载形式对不稳定区的影响。结果表明此类压电复合结构的动力不稳定区主要由结构自身刚度及外载所决定, 而受外加电场及压电效应影响很小。     

固体药柱的大变形分析

采用物质描述法，选择初始构形作为参考构形，导出以Ｋｉｒｃｈｈｏｆｆ应力和Ｇｒｅｅｎ应变表示的粘弹性大变形本构关系和有限元方程，利用ＴｏｔａｌＬａｇｒａｎｇｉａｎ增量法进行求解，取得了满意的结果。     

A closed-form nonlinear model for spatial Timoshenko beam flexure hinge with circular cross-section

Beam flexure hinges can achieve accurate motion and force control through the elastic deformation. This paper presents a nonlinear model for uniform and circular cross-section spatial beam flexure hinges which are commonly employed in compliant parallel mechanisms. The proposed beam model takes shear deformations into consideration and hence is applicable to both slender and thick beam flexure hinges. Starting from the first principles, the nonlinear strain measure is derived using beam kinematics and expressed in terms of translational displacements and rotational angles. Second-order approximation is employed in order to make the nonlinear strain within acceptable accuracy. The natural boundary conditions and nonlinear governing equations are derived in terms of rotational Euler angles and subsequently solved for combined end loads. The resulting end load-displacement model, which is compact and closed-form, is proved to be accurate for both slender and thick beam flexure using nonlinear finite element analysis. This beam model can provide designers with more design insight of the spatial beam flexure and thus will benefit the structural design and optimization of compliant manipulators.     

非线性波流场和波流载荷的数值模拟

本文用数值模拟的方法研究了大尺度物体上所受的非线性波与水流的共同作用力。非线性水波与水流相互作用场的计算采用有限差分法,引入坐标变换获得了固定计算域,用松弛迭代法求解差分方程。波流联合作用力的计算用时间步进法,每一时刻采用简单格林函数的边界元法求解。入射势采用以上波流场的计算结果,开边界选取离物体足够远,其上的速度势为入射势。     

常开空心轴裂纹转子系统的动力学特性

研究了常开空心轴裂纹转子系统的动力学特性.考虑裂纹单元截面中性轴的时变特性,推导了裂纹转子的刚度矩阵,考虑重力及不平衡激励,采用有限元法建立了常开空心轴裂纹转子系统的动力学方程.采用谐波平衡法对方程进行求解,给出了不同裂纹深度下的三维幅频图,表明在临界转速和亚临界转速处均有峰值出现;分析了裂纹深度、裂纹位置对该系统的临界转速的影响,表明位于跨中靠近惯性量较大圆盘的深裂纹对常开空心轴裂纹转子系统的影响大,临界转速下降快;计算了该系统在亚临界转速时的非线性振动响应,结果表明:亚临界转速下常开空心轴裂纹转子系统会发生超谐共振现象.所提出的空心轴裂纹的建模方法为航空发动机转子系统裂纹故障的非线性动力学分析提供了理论指导.