首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到18条相似文献,搜索用时 196 毫秒
1.
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  相似文献   

2.
变形梯度张量极分解中转动张量的直接表示及其应用   总被引:1,自引:0,他引:1  
本文通过变分途径建立了变形梯度张量的极分解和加法分解之间的联系.采用工程界通常采用的变形梯度张量的加法分解形式,得到了三维空间中极分解的转动张量和伸长张量的直接表示,即实现了转动和变形的分离.由这些直接表示,可以得到各种有用的近似表示.  相似文献   

3.
对变形樟度极分解的计算方法进行了分析,给出了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。增加叠加极分解计算方法将为建立以伸长张量为变应度量的大变形大转动有限分析方法提供基础。本文还给出了伸长张量物质时间导数的简洁表达式。  相似文献   

4.
伸缩张量率的抽象表示   总被引:2,自引:0,他引:2  
本文用“主轴内蕴法”给出右-左伸缩张量 U 和 V 的时间导数 U 和 V 的抽象表示。文中引进所谓“分离技巧”,使能有效地应用张量函数的标准表示。V 的表达式是新的。还给出U 和 V 的两个新关系式。  相似文献   

5.
偏心环空层流螺旋流速度的近似解析解   总被引:1,自引:0,他引:1  
本文分析计算了石油钻井工程偏心环空中内管转动的螺旋流动。将偏心环空的三维流动简化为环空薄层内的二维流动,从黎曼空间曲面张量表达的动量方程出发,求得了偏心环空层流螺旋流动速度的近似解析解,用此方程的同心环空表达式与精确解比较,精度较高。  相似文献   

6.
自旋张量的绝对表示及其在有限变形理论中的应用   总被引:1,自引:0,他引:1  
王文标  段祝平 《力学学报》1990,22(5):566-573
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。  相似文献   

7.
本文用旋转张量表示绕定点转动的刚体的角速度。给出计算刚体绕体轴系列、固定轴系列或体轴与固定轴交叉出现的一系列转动时其合成运动的角速度的统一公式。  相似文献   

8.
本文基于Cauchy平均转动的新近成果,给出一种变形和应变的近似分析方法,在此基础上讨论了Green应变的近似表达式及其误差计,这些近似表达式在求解非线性力学问题中是常采用的,文中关于Green应变常用近表达式的误差估计是严格基于小应变-中等或大转动变形的明确定义而获得的。  相似文献   

9.
基于绝对节点坐标的多柔体系统动力学高效计算方法   总被引:4,自引:0,他引:4  
刘铖  田强  胡海岩 《力学学报》2010,42(6):1197-1205
绝对节点坐标法已经被广泛应用于柔性多体系统的动力学研究之中, 但是其计算效率问题尚未得到很好的解决. 基于绝对节点坐标方法计算弹性力及其对广义坐标的偏导数矩阵(Jacobi矩阵), 通常是基于第二类Piola-Kirchhoff应力张量来完成, 计算效率不高.根据虚功原理并采用第一类Piola-Kirchhoff应力张量的方法直接推导得到了弹性力及其Jacobi矩阵的解析表达式. 基于不同方法所得的数值算例结果对比研究表明, 该方法可使计算效率大大提高.   相似文献   

10.
依据弹塑性耦合问题的不同类型,应用广义正交原理,在应变空间上推导出已知宏、细观形变规律情况下两种不同形式的弹塑性耦合张量理论表达式及其显形式。该两类弹塑性耦合张量作为宏、细观的对耦形式可应用于体胞模型的损伤力学理论分析与数值计算。  相似文献   

11.
In this paper, the polar decomposition of a deformation gradient tensor is analyzed in detail. The four new methods for polar decomposition computation are given: (1) the iterated method, (2) the principal invariant's method, (3) the principal rotation axis's method, (4) the coordinate transformation's method. The iterated method makes it possible to establish the nonlinear finite element method based on polar decomposition. Furthermore, the material time derivatives of the stretch tensor and the rotation tensor are obtained by explicit and simple expressions. The authors gratefully acknowledge the support rendered by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangxi of China in 1998.  相似文献   

12.
An explicit expression of the derivative of the square root of a tensor is provided, by using the expressions of the derivatives of the eigenvalues and eigenvectors of a symmetric tensor. Starting from this result, the derivatives of the right and left stretch tensor U, V and of the rotation R with respect to the deformation gradient F, are calculated. Expressions for the material time derivatives of U, V and R are also given. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

13.
Through a variational approach, an explicit connection between the additive and the polar decompositions of deformation gradient has been established. An exact formula for determining the rotation tensor in polar decomposition is obtained. The formula is fundamental in continuum mechanics and can be used to separate the rotation and the pure strain in deformation, by which various approximate expressions can be easily obtained.  相似文献   

14.
The local rigid-body component of continuum deformation is typically characterized by the rotation tensor, obtained from the polar decomposition of the deformation gradient. Beyond its well-known merits, the polar rotation tensor also has a lesser known dynamical inconsistency: it does not satisfy the fundamental superposition principle of rigid-body rotations over adjacent time intervals. As a consequence, the polar rotation diverts from the observed mean material rotation of fibers in fluids, and introduces a purely kinematic memory effect into computed material rotation. Here we derive a generalized polar decomposition for linear processes that yields a unique, dynamically consistent rotation component, the dynamic rotation tensor, for the deformation gradient. The left dynamic stretch tensor is objective, and shares the principal strain values and axes with its classic polar counterpart. Unlike its classic polar counterpart, however, the dynamic stretch tensor evolves in time without spin. The dynamic rotation tensor further decomposes into a spatially constant mean rotation tensor and a dynamically consistent relative rotation tensor that is objective for planar deformations. We also obtain simple expressions for dynamic analogues of Cauchy's mean rotation angle that characterize a deforming body objectively.  相似文献   

15.
Derivatives and Rates of the Stretch and Rotation Tensors   总被引:2,自引:0,他引:2  
General expressions for the derivatives and rates of the stretch and rotation tensors with respect to the deformation gradient are derived. They are both specialized to some of the formulas already available in the literature and used to derive some new ones, in three and two dimensions. Essential ingredients of the treatment are basic elements of differential calculus for tensor valued functions of tensors and recently derived results on the solution of the tensor equation A X + XA= H in the unknown X. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

16.
An explicit representation for the rotation tensor which contains the lower powers of deformation gradient is proposed and used to evaluate the angle and axis of the rotation tensor. Some related equations about the rotation tensor are established. Through the approximate analysis, the relation between the S-R decomposition and the polar decomposition is examined. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

17.
Based on the general solution given to a kind of linear tensor equations, the spin of a symmetric tensor is derived in an invariant form. The result is applied to find the spins of the left and the right stretch tensors and the relation among different rotation rate tensors has been discussed. According to work conjugacy, the relations between Cauchy stress and the stresses conjugate to Hill's generalized strains are obtained. Particularly, the logarithmic strain, its time rate and the conjugate stress have been discussed in detail. These results are important in modeling the constitutive relations for finite deformations in continuum mechanics. The project is supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences (No. 87-52).  相似文献   

18.
To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Pade-type approximation is denned. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Pade-type approximation are explicitly given.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号