关于几种新的极分解计算方法

对变形梯度极分解的计算方法进行了分析,给出极分解计算的四种新方法：（１）增量叠加法;（２）基于伸长张量不变量（近似）计算法;（３）确定主转动轴计算法;（４）坐标变换法．增量叠加极分解计算方法将为建立以伸长张量为应变度量的大变形大转动有限元分析方法提供基础．本文还给出了伸长张量物质时间导数的简洁表达式     

基于Updated Lagrangian法的三维粘弹性大变形问题的有限元分析

本文基于Updated Lagrangian增量迭加方法,采用以现时Kirchhoff应力增量和现时Green应变增量表示的虚功方程和Kirchhoff应力张量-Green应变张量的积分本构关系,导出粘弹性大变形的虚功方程。依此采用二十节点三维立方等参数元编制相应的计算程序。三个算例结果与以往一维、二维的计算结果完全符合。     

聚合物熔体三维挤出胀大的数值模拟

采用有限元方法分析K-BKZ本构方程描述的聚合物熔体的三维挤出胀大.对于本构方程中偏应力张量的计算,首先给出质点的运动轨迹,分段求出局部的变形梯度张量,再求出整体的变形梯度、Cauchy-Green应变张量和 Finger应变张量,沿轨迹采用分段高斯积分计算应力.把应力作为方程的右端项,给出迭代方法,求解非线性方程组.并根据自由面处的边界条件,迭代得出出口处自由面的最终位置.对轴对称流道和矩形流道进行分析计算,并把结果与二维分析和实验结果进行了比较,显示方法是可行的.     

非线性有限分析中的应变近似

本文论证了非线性有限元分析中,若干与应变近似有关的问题,其中包括四种应变张量的条件等值性,提出了简化壳体应变分量的新途径,比较了近似应变、应力和结构反力的不同求法,评述了采用不同简化应变的大变形平衡方程。     

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．     

材料力学中索的张力与变形

推导张紧索在铅直分布力作用下的平衡方程，求得其精确解，说明索张力的水平分量为常量．给出索的应力、变形、应变能等表达式．分析了水平悬索的张力与变形，并通过数值结果进行了说明．     

有初始几何缺陷的壳体弹塑性大变形分析

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、小应变分析的弹塑性内时本构方程。并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。文中给出的算例表明本方法是可行有效的。     

自旋张量的绝对表示及其在有限变形理论中的应用

基于对一类线性张量方程的一般解法,导出了任一对称张量所对应的自旋张量的绝对表示。该结果可以很自然地用于研究左和右伸长张量的自旋并研讨在连续介质力学中常见到的各种转动率张量间的关系。一个重要的公式,即Hill意义下广义应变的共轭应力和Cauchy应力之间的关系,从功共轭原理建立了起来。尤其是详细讨论了对数应变的时间变率及相应的共轭应力。无疑,上述结果对有限变形条件下本构理论的研究是颇为重要的。     

论弹性体最小余能原理的变分条件

众所周知,弹性体变形状态时的应力张量σ_(ij)、应变张量e_(ij)和位移u_i必需满足下列五个条件,即(1) 静力平衡方程     

增量型各向异性损伤理论与数值分析

考虑到目前各向异性损伤理论存在一些不足,该文在增量型各向异性损伤理论的框架下,引入二阶对称张量,构造四阶对称有效损伤张量,建立了有效应力方程．类似于塑性流动分析方法,定义了增量弹性应力．应变关系．利用von Mises塑性屈服准则,并考虑各向异性损伤效应,推导出四阶对称的弹．塑性变形损伤刚度张量,其对称性反映了材料的固有特性．根据物体的变形和现时损伤状态,构造了材料损伤演化方程,方程中各项具有明确的物理意义．通过对A12024-T3金属薄板单向拉伸的有限元分析,确定了损伤演化参数,验证了损伤演化方程的正确性．此外还对含孔口薄板做有限元模拟,讨论了反力—位移曲线的变化规律以及它所揭示变形性质,给出了损伤场的分布规律。     

用复变量表示的环壳几何非线性方程及其摄动解

本文从小应变,中小转动问题的弹性薄壳一般方程出发,导出用复未知函数表示的非线性的环壳轴对称变形的基本方程,并用摄动方法分別求解了整环壳和开口环壳问题.所得到的结果与其他作者用数值方法得到的结果吻合很好。     

GENERALIZATION OF KIRCHHOFF KINETIC ANALOGY TO THIN ELASTIC SHELLS 1)

将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应, 在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法. 在直法线假设下,在弹性中面上构筑空间正交轴系, 此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度. 沿两个坐标线的弯扭度表达了弹性薄壳的变形和位形,证明了弯扭度之间以及弯扭度与中面切矢间的相容关系. 用Euler角和Lam$\acute{e}$系数表达了非完整约束和中面位形的微分方程,用弯扭度和Lam$\acute{e}$系数表达了应变和应力以及内力及其本构方程.导出了用分布内力集度表达的弹性薄壳在变形后位形上的平衡偏微分方程组,方程的形式与刚体动力学的Euler方程和弹性细杆的Kirchhoff方程具有相似性,实现了Kirchhoff动力学比拟对弹性薄壳的推广.总结了弹性薄壳静力学和刚体动力学以及弹性细杆静力学在概念上的比拟关系.最后给出了一个算例. 为研究弹性薄壳的变形和运动提供新的建模方法和研究思路.也可进一步推广到弹性薄壳动力学.     

Kirchhoff动力学比拟对弹性薄壳的推广

将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应, 在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法. 在直法线假设下,在弹性中面上构筑空间正交轴系, 此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度. 沿两个坐标线的弯扭度表达了弹性薄壳的变形和位形,证明了弯扭度之间以及弯扭度与中面切矢间的相容关系. 用Euler角和Lam$\acute{e}$系数表达了非完整约束和中面位形的微分方程,用弯扭度和Lam$\acute{e}$系数表达了应变和应力以及内力及其本构方程.导出了用分布内力集度表达的弹性薄壳在变形后位形上的平衡偏微分方程组,方程的形式与刚体动力学的Euler方程和弹性细杆的Kirchhoff方程具有相似性,实现了Kirchhoff动力学比拟对弹性薄壳的推广.总结了弹性薄壳静力学和刚体动力学以及弹性细杆静力学在概念上的比拟关系.最后给出了一个算例. 为研究弹性薄壳的变形和运动提供新的建模方法和研究思路.也可进一步推广到弹性薄壳动力学.      

Nonlinear deformation and buckling of elastic inhomogeneous shells under thermomechanical loads

The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finite-element scheme. The method is justified numerically. Results of practical importance are obtained in analyzing poorely studied classes of inhomogeneous shells. These results provide an insight into the nonlinear deformation and buckling of shells under various combinations of thermomechanical loads     

On the incremental equations in non-linear elasticity — I. Membrane theory

A new formulation of the equations of membrane theory in non-linear elasticity is described. It is based on the consistent use of certain conjugate variables averaged through the (undeformed) thickness of the thin shell which the membrane approximates. The deformation gradient is taken as the basic measure of deformation, and its average value as the membrane measure of deformation. It is shown that the average elastic strain energy can be regarded as a function of the average deformation gradient to within an error which is of the second order in a certain small parameter. Moreover, to the same order, the average strain energy is a potential function for the average nominal stress. This means that the averages of the conjugate variables (nominal stress and deformation gradient) are also conjugate.In terms of the average conjugate variables, the membrane equilibrium equations are obtained by averaging from the equilibrium equations of the full three-dimensional theory. Discussion of the order of magnitude of the errors involved in the membrane approximation is a feature of the analysis.The corresponding incremental equations are also derived as a prelude to their application in certain bifurcation problems. One such problem is examined in the companion paper (Part II) in which results for thick shells and membranes are compared.     

载流圆锥薄壳的磁弹性应力与变形分析

在建立旋转壳体的非线性磁弹性运动方程的基础上,研究了电磁场和机械载荷联合作用下载流圆锥薄壳的磁弹性效应．通过算例,得到了载流圆锥薄壳的位移及应力与通电电流强度之间的关系．解决了圆锥薄壳顶点处的奇异性问题,给出了轴对称条件下的数值解．计算结果表明：改变通电电流强度,可以改变载流圆锥薄壳的应力与变形状态,达到控制圆锥薄壳的受力与变形的目的．     

Stress Concentration Near Openings in Composite Shells

The results of studying the stress–strain distribution in composite shells with curvilinear openings are reported. Nonclassical generalizing formulations and methods for solution of linear and nonlinear problems are stated. Numerical results obtained for thin and nonthin shells are analyzed with regard for features of the deformation of composites     

Describing the elastoplastic deformation of layered shells under axisymmetric loading with allowance for the third invariant of the stress deviator

A method for numerical analysis of the elastoplastic stress–strain state of thin layered shells of revolution under axisymmetric loading is proposed. Constitutive equations describing the elastoplastic deformation of isotropic materials with allowance for the stress mode are used. Numerical results are presented     

Approximate theories for wave propagation and vibrations in elastic rings and helical coils of small pitch

From the equations of linear elasticity, three levels of approximate theories are derived for in-plane deformation and motion of thin, circular rings. The accuracy of each theory is determined by comparison with harmonic wave solutions of the elasticity solution. Boundary conditions for uniqueness are established. The results may also be applied to helical coils of small pitch and to cylindrical shells when the equations are converted to plane strain.     

Creep buckling of axially compressed circular cylindrical shells of a zirconium alloy: Experiment and computer simulation

Experiments were performed to study the deformation and buckling of axially compressed circular cylindrical shells of Zr2.5Nb zirconium alloy under creep conditions. Computer simulation using the MSC.Marc 2012 software was conducted by step-by-step integration of the equations of quasistatic deformation of thin shells using Norton’s law of steady creep. The results of the experiment and computer simulation show that the buckling modes are a combination of axisymmetric bulges located near one end or both ends of the shell and axisymmetric buckling modes with the formation of three or four waves in the circumferential direction. A comparison is made of the time dependences of the axial strain of the shells obtained in the experiment and by computer simulation. It is shown that for large axial compressive stresses, these dependences are in satisfactory agreement. For lower values of these stresses, the difference between the theoretical and experimental dependences is greater.