一种内压膨胀系统的动态响应分析

论文采用LS-DYNA非线性动力学有限元程序,对一种曲边柱壳-多体内压膨胀系统在均布内压作用下的动态膨胀过程进行了数值分析,获得了曲边柱壳动态响应规律.文中分析了各种因素对曲边柱壳的变形模式及其应力、应变变化规律的影响；模拟了曲边柱壳在内部压力和外围变形体共同作用下的耦合变形运动过程.模拟计算结果与试验现象基本一致.     

一种几何大变形下的非线性气动弹性求解方法

非线性气动弹性的时域求解中, 涉及到非线性的流体动力学(CFD)和非线性的结构动力学(CSD)耦合问题. 基于Co-rotational理论, 推导了三维壳单元几何非线性下的切线刚阵和内力公式, 针对推进过程中的能量守恒, 引入预估-校正推进格式, 发展了一种近似能量守恒的非线性动态响应算法; 基于1/2时间步的交错耦合格式, 结合带有几何守恒律的双时间推进求解雷诺平均N-S方程的求解器, 发展了非线性气动弹性求解的高精度耦合格式. 通过结构几何大变形下的静力和动力分析验证了所发展的结构非线性求解器, 并通过AGARD445.6机翼的非线性气动弹性响应分析, 说明了所发展耦合求解方法的实用性.      

弹性连杆机构的非线性动力学特性分析

本文应用动力学虚功原理建立了计入几何非线性时弹性连杆机构一般形式的动力学有限元模型，该模型是具有周期性的时变非线性微分方程，针对方程的这一特点，文中给出了一种高效的闭式迭代求解方法。最后通过实例研究了几何非线性对弹性连杆机构动特性的影响，并通过实验研究验证了本文建模及求解方法的正确性。本文的研究结果对弹性机构的动态设计有指导意义。     

索网天线的参变量变分及非线性有限元方法

针对大型周边桁架式索网天线由拉索拉压模量不同引起的本构非线性和结构大变形引起的几何非线性问题,给出了基于参变量变分原理的几何非线性有限元方法. 首先针对含预应力索单元拉压模量不同分段描述的本构关系,通过引入参变量,导出了基于参变量及其互补方程的统一描述形式,避免了传统算法需要根据当前变形对索单元张紧/松弛状态的预测,提高了算法收敛性. 然后利用拉格朗日应变描述索网天线结构大变形问题,结合几何非线性有限元法,建立了基于参变量的非线性平衡方程和线性互补方程;并给出了牛顿-拉斐逊迭代法与莱姆算法相结合的求解算法. 数值算例验证了本文提出的算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于大型索网天线结构的高精度变形分析和预测.      

THE PARAMETRIC VARATIONAL PRINCIPLE AND NON-LINEAR FINITE ELEMENT METHOD FOR ANALYSIS OF ASTROMESH ANTENNA STRUCTURES

针对大型周边桁架式索网天线由拉索拉压模量不同引起的本构非线性和结构大变形引起的几何非线性问题,给出了基于参变量变分原理的几何非线性有限元方法. 首先针对含预应力索单元拉压模量不同分段描述的本构关系,通过引入参变量,导出了基于参变量及其互补方程的统一描述形式,避免了传统算法需要根据当前变形对索单元张紧/松弛状态的预测,提高了算法收敛性. 然后利用拉格朗日应变描述索网天线结构大变形问题,结合几何非线性有限元法,建立了基于参变量的非线性平衡方程和线性互补方程;并给出了牛顿-拉斐逊迭代法与莱姆算法相结合的求解算法. 数值算例验证了本文提出的算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于大型索网天线结构的高精度变形分析和预测.     

有初始几何缺陷陷的壳体弹塑性大变形分析

本文在等温小变形弹塑性内时本构方程偏量形式的基础上，导出了适用于大位移、大动、小应变分析的弹塑性内时本构方程，进一步推导出了带有初始几何缺陷的非线性弹塑性问题的有限元方程，可用于分析缺陷对结构非线性塑性反应的影响，也可用于带缺陷的非线性问题求解及稳定性分析。     

弹性曲梁在机械和热载荷共同作用下的几何非线性模型及其数值解

基于Euler-Bernoulli梁的几何非线性理论,建立了弹性曲梁在任意分布机械载荷和热载荷共同作用下的几何非线性静平衡控制方程。该模型不仅计及了轴线伸长,同时也精确地考虑了梁的初始曲率对变形的影响以及轴向变形与弯曲变形之间的相互耦合效应。应用打靶法数值求解了半圆形曲梁在横向均匀升温作用下的非线性弯曲问题,数值比较了轴向伸长对曲梁变形的影响。     

有初始几何缺陷的壳体弹塑性大变形分析

本文在等温小变形弹塑性内时本构方程偏量形式的基础上，导出了适用于大位移、大转动、小应变分析的弹塑性内时本构方程，进一步推导出了带有初始几何缺陷的非线性弹塑性问题的有限元方程，可用于分析缺陷对结构非线性弹塑性反应的影响，也可用于带缺陷的非线性问题求解及稳定性分析．     

带初始几何缺陷FGM固支圆柱壳的非线性动力学分析

本文主要研究了带初始几何缺陷的功能梯度固支圆柱壳在不同体积分数下的非线性动力学行为。假定该功能梯度圆柱壳材料的组分是沿厚度的方向呈梯度几何变化的。运用经典板壳理论、von-Karman几何非线性应变位移关系以及Hamilton原理,推导出两端固支FGM圆柱壳的偏微分非线性运动控制方程。本文考虑了圆柱壳的对称模态,利用Galerkin法对上述非线性动力学方程进行截断,得到常微分形式的非线性动力学方程。主要运用Runge-Kutta法进行数值仿真,并且画出了其最大lyapunov指数图,主要研究了面内载荷对振动响应的影响,并对比了不同体积分数对系统非线性动力学的影响。     

轴向约束梁柱在火灾引起温度沿截面不均匀分布条件下的大变形分析

火灾升温引起钢材强度和刚度降低,对温度沿截面分布不均匀的构件还将产生热弯曲,火灾下结构分析同时涉及几何非线性和材料非线性,无法求得解析解,只能通过数值方法求解.本文基于轴线可伸长梁理论,用勒让德多项式作为基函数逼近梁柱轴向和横向变形,根据平衡方程误差平方和最小的条件确定多项式系数的方法,分析了轴向约束钢柱在火灾引起的沿截面线性分布温度场下的受力和变形性能.考虑了温度梯度、轴向约束刚度比、荷载比、构件长度等参数的影响和升温条件下钢材的弹塑性性能的影响,该方法结果与解析结果和有限元分析结果吻合.研究表明,随着荷载比的增大构件的临界温度迅速降低,轴向约束刚度、温度梯度和构件长度仅影响构件的变形,对构件的临界温度影响较小.     

Static and dynamic buckling modes of a cylindrical shell under external pressure

We consider the problem of static and dynamic buckling modes of thin shells under external hydrostatic pressure. If the statement of the problem uses the linearized equations of motion obtained in the moderately large bending theory of shells according to the classical or refined model, then part of terms related to the external load in these equations are assumed to be conservative, and the other terms are assumed to be nonconservative. In this connection, we study four statements of the elastic stability problem for a cylindrical shell with hinged faces. The first of them is the statement of the static boundary value problem in the sense of Euler, where the action of external pressure is assumed to be conservative. The second statement is used to study small vibrations near the static equilibrium by a dynamic method for the same conservative load. The third and fourth statements of the problem correspond to the action of a nonconservative load and are similar to the first and second statements, respectively. They use the linearized equations of equilibrium and motion constructed earlier in a consistent version on the basis of a Timoshenko type model and allowing one to reveal all classical and nonclassical shell buckling modes.     

Studies of nonlinear deformation and stability of stiffened oval cylindrical shells under combined loading by bending moment and boundary transverse force

The finite-element statement of stability problems for stiffened oval cylindrical shells is presented with the moments and the nonlinearity of their subcritical stress-strain state taken into account. Explicit expressions for the displacements of elements of noncircular cylindrical shells as solids are obtained by integration of the equations derived by equating the linear deformation components with zero. These expressions are used to construct the shape functions of the effective quadrangular finite element of natural curvature, and an efficient algorithm for studying the shell nonlinear deformation and stability is developed. The stability of stiffened oval cylindrical shells is studied in the case of combined loading by a boundary transverse force and a bending moment. The influence of the shell ovality and the deformation nonlinearity on the shell stability is investigated.     

Analysis for the thermoelastic bending of a functionally graded material cylindrical shell

An analytic study for thermoelastic bending of a functionally graded material (FGM) cylindrical shell subjected to a uniform transverse mechanical load and non-uniform thermal loads is presented. Based on the classical linear shell theory, the equations with the radial deflection and horizontal displacement are derived out. An arbitrary material property of the FGM cylindrical shell is assumed to vary through the thickness of the cylindrical shell, and exact solution of the problem is obtained by using an analytic method. For the FGM cylindrical shell with fixed and simply supported boundary conditions, the effects of mechanical load, thermal load and the power law exponent on the deformation of the FGM cylindrical shell are analyzed and discussed.     

线载荷作用下圆柱壳环向弯曲变形的研究

通过引入单三角级数形式的位移函数, 求解了法向任意分布载荷作用下对 边简支时圆柱壳的环向弯曲问题, 把线载荷近似为微元矩形区的分布载荷, 推导出了线 载荷作用下圆柱壳的环向弯曲变形计算式, 并给出了线载荷为均布和线性变化时的具体解. 计算表明, 该种边界约束条件下圆柱壳的环向弯曲变形位移分布场的理论计算结果与有限元 分析结果基本吻合.     

基于混合变量的脱层壳屈曲分析

提出一种分析脱层圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于一阶剪切理论，通过定义广义位移变量和对应的广义力变量，建立壳的改进的混合变量能量泛函；然后引入条形单元，对混合变量在环向进行离散，从而导出超级壳单元的混合变量能量泛函，由变分原理得到控制方程，采用传递函数方法得到其形式解；最后，将含环向贯穿脱层的复合材料层合壳作为超级壳单元的组合体，得到脱层壳的屈曲方程。给出了脱层大小和深度以及脱层壳边界条件对屈曲载荷的影响。     

轴向压应力波下圆柱壳弹性动力失稳的判据与机理

基于动力失稳瞬间能量的转换和守恒,推导提出了受轴向力圆柱壳弹性动力失稳的判据和两个临界条件,由第一个临界条件导出的圆柱壳弹性动力失稳的控制方程、边界条件、屈曲变形连续与利用Hamilton原理的结果完全相同,但不足以确定包含在本问题中的两个特定特征参数（临界载荷参数和动力特征参数）,由第二个临界条件导出压缩波前的屈曲变形约束方程,基于控制方程有满足边界条件、变形连续条件和波前约束方程的非平凡解的条件,导出关于两个特征参数的一对特征方程,基于特征方程的解,精确地计算出临界载荷参数和动力特征参数的值以及动力失稳态态,由此建立了轴向力作用下圆桩壳弹性动力失稳的特征值分析方法。     

厚壁圆柱壳的弹性静力分析

本文研究了考虑横向剪切影响的弹性厚壁圆柱壳的静力问题。利用变分原理得到平衡微分方程组和相应的边界条件。将平衡方程组归并成一个高阶微分方程,用数值法求出它的特征根,得到问题的解。     

Dynamics of Articulated Structures. Part I. Theory

ABSTRACT

A finite element based method is developed for geometrically nonlinear dynamic analysis of spatial articulated structures; i.e., structures in which kinematic connections permit large relative displacement between components that undergo small elastic deformation. Vibration and static correction modes are used to account for linear elastic deformation of components. Kinematic constraints between components are used to define boundary conditions for vibration analysis and loads for static correction mode analysis. Constraint equations between flexible bodies are derived in a systematic way and a Lagrange multiplier formulation is used to generate the coupled large displacement-small deformation equations of motion. A lumped mass finite element structural analysis formulation is used to generate deformation modes. An intermediate-processor is used to calculate time-independent terms in the equations of motion and to generate input data for a large-scale dynamic analysis code that includes coupled effects of geometric nonlinearity and elastic deformation. Examples are presented and the effects of deformation mode selection on dynamic prediction are analyzed in Part II of the paper.     

Study of nonlinear deformation and stability of reinforced shells under combined loading by a bending moment and a transverse boundary force

We present a finite-element statement for the solution of stability problems for reinforced elliptic cylindrical shells with moment properties and nonlinearity in their precritical stressstrain state taken into account. Integrating the equations obtained by equating the linear strain components with zero, we find explicit expressions for the displacements of elements of noncircular cylindrical shells as rigid bodies. Using these expressions, we construct the shape functions of a fourangle finite element of natural curvature and develop an effective algorithm for studying nonlinear deformation and stability of shells. We study the stability of reinforced elliptic cylindrical shells under combined loading by a transverse boundary force and a bending moment and investigate how the ellipticity of the shells and the nonlinearity of deformation at the precritical stage affect the shell stability.     

超音速气流中受热曲壁板的非线性颤振特性

基于von Karman 大变形理论及带有曲率修正的一阶活塞理论, 用Galerkin方法建立了超音速气流中受热二维曲壁板的非线性气动弹性运动方程; 采用牛顿迭代法计算得到由静气动载荷和热载荷引起的静气动弹性变形; 根据李雅谱诺夫间接法分析了壁板初始曲率与温升对颤振边界的影响; 对二维曲壁板的非线性气动弹性方程组进行数值积分求解,分析了动压参数对受热二维曲壁板分岔特性的影响, 给出了典型状态下曲壁板非线性颤振响应的时程图与相图. 分析结果表明对小初始曲率的曲壁板, 温升对其静气动弹性变形影响较大, 且随着温升的增加其颤振临界动压急剧减小; 对具有较大初始曲率的曲壁板, 温升对其静气动弹性变形的影响较弱, 且随着温升的增加颤振临界动压基本保持不变. 初始几何曲率与气动热效应使得曲壁板具有复杂的动力学特性, 不再像平壁板一样, 经过倍周期分岔进入混沌, 而会出现由静变形状态直接进入混沌运动的现象, 且在混沌运动区域中还会出现静态稳定点或谐波运动, 在大曲率情况下, 曲壁板不会产生混沌运动, 而是幅值在一定范围内的极限带振荡.