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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
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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
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传统键基近场动力学模型存在泊松比限制的问题,为了解决这一问题发展了态基近场动力学模型。其中非常规态的近场动力学模型通过定义非局部的变形梯度将近场力和传统应力关联起来,方便使用传统本构,但是态基近场动力学计算效率低于键基近场动力学。结合态基模型和键基模型的优势,提出键基对应模型,定义了基于键的变形梯度,参考连续介质力学中变形梯度的极分解过程,将键的变形分为转动部分和伸长部分。从而进一步定义了应变,通过物理方程求应力,进而计算键传递的近场力。键基对应模型解决了键基近场动力学的泊松比限制问题,也不需要进行近场动力学微观材料常数的计算。数值算例和理论推导证明了键变形梯度定义以及近场力计算方式的正确性。 相似文献
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考虑旋转对自引力球壳的影响,借助MATHEMATICA符号计算软件求解了Navier方程,得到了自引力旋转球壳的弹性力学解析解,给出了应变和应力张量的解析表达式,并分析了应变和应力张量的性质,得到了在球壳或球体内主应力最大的位置,即在极角θ≈49°和θ≈131°处,或在纬度41°S和41°N处。 相似文献
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阐述了四元数的张量概念,并利用四元数乘法的结构张量建立了各种四元数分量矩阵与四元数张量的关系。从而使四元数运算归结为一般的张量运算. 相似文献
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一种简单高效的任意四边形薄板单元赵振峰,陈万吉(大连理工大学,116024)关键词有限元法,薄板,应变张量不变量/拟协调元1引言为了克服薄板弯曲单元中C1连续性要求带来的困难,本文采用一个新的方法构造了一类四边形薄板单元.文中将单元的能量积分分解为两... 相似文献
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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
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
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The present paper generalizes the method for solving the derivatives of sym- metric isotropic tensor-valued functions proposed by Dui and Chen(2004)to a subclass of nonsymmetric tensor functions satisfying the commutative condition.This subclass of tensor functions is more general than those investigated by the existing methods.In the case of three distinct eigenvalues,the commutativity makes it possible to introduce two scalar functions,which will be used to construct the general nonsymmetric tensor func- tions and their derivatives.In the cases of repeated eigenvalues,the results are acquired by taking limits. 相似文献
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A linear bi-spatial tensor equation which contains many often encountered equations as particular cases is thoroughly studied. Explicit solutions are obtained. No conditions on eigenvalues of coefficient tensors are imposed. 相似文献
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THELINEARBI-SPATIALTENSOREQUATIONφ_(ij)A ̄iXB ̄j=CChenYuming(陈玉明),XiaoHeng(肖衡),LiJianbo(李建波)(DepartmentofAppliedMathematics,Hun... 相似文献
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Huang Yong-nian 《应用数学和力学(英文版)》1992,13(12):1115-1120
In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous
linear differential equations with constant coefficients and the n th-order homogeneous linear differential equation with
constant coefficients. In fact, we give the general formula for calculating the elements of the matrix exp [At]. We also give the results when the characteristic equation has the repeated roots. The present method is simpler and better
than, the other methods. 相似文献
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An anisotropic elastic-damage model for initially-isotropic materials is presented. The model is based on a pseudo-logarithmic
second-order damage tensor rate. To derive the complete expression of the tangent stiffness entering the rate constitutive
law, various tensor operations and derivatives of tensor functions must be developed. Such derivations have been performed
in compact form. Some useful tensor derivatives and a table of tensor algebra operations are given in Appendix. This note
should interest engineering researchers involved in the development of constitutive models through tensor formalism.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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黄永念 《应用数学和力学(英文版)》1992,13(12):1115-1120
In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the n th-order homogeneous linear differential equation with constant coefficients. In fact, we give the general formula for calculating the elements of the matrix exp[At]. We also give the results when the characteristic equation has the repeated roots. The present method is simpler and better than the other methods. 相似文献
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It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on quantifying the relationship between the true stress and applied stress. In this paper, we derive an explicit relationship among applied stress tensor, material-fabric tensor, and force-fabric tensor; and we propose a relationship between the true stress tensor and the applied stress tensor. The validity of this derived relationship is examined by using the discrete element simulation results for granular material under biaxial and triaxial loading conditions. 相似文献
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Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor. 相似文献
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Bounds on the Effective Anisotropic Elastic Constants 总被引:2,自引:0,他引:2
Hill [12] showed that it was possible to construct bounds on the effective isotropic elastic coefficients of a material with
triclinic or greater symmetry. Hill noted that the triclinic symmetry coefficients appearing in the bounds could be specialized
to those of a greater symmetry, yielding the effective isotropic elastic coefficients for a material with any elastic symmetry.
It is shown here that it is possible to construct bounds on the effective elastic constants of a material with any anisotropic
elastic symmetry in terms of triclinic symmetry elastic coefficients. Similarly, it is then possible to specialize the triclinic
symmetry coefficients appearing in the bounds to those of a greater symmetry. Specific bounds are given for the effective
elastic coefficients of cubic, hexagonal, tetragonal and trigonal symmetries in terms of the elastic coefficients of triclinic
symmetry. These results are obtained by combining the approach of Hill [12] with a representation of the stress-strain relations
due, in principle, to Kelvin [25,26] but recast in the structure of contemporary linear algebra.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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A method of averaging the data on the anisotropic elastic constants of a material is presented. The anisotropic elastic constants are represented by the elasticity tensor which is expressed as a second rank tensor in a space of six dimensions. The method consists of averaging eigenbases of different measurements of the elasticity tensor, then averaging the eigenvalues referred to the average eigenbasis. The eigenvalues and eigenvectors are obtained by using a representation of the stress-strain relations due, in principle, to Kelvin [17, 18]. The formulas for the representation of the averaged elasticity tensor are simple and concise. The applications of these formulas are illustrated using previously reported data, and are contrasted with the traditional analysis of the same data by Hearmon [9]. An interesting result that emerges from this analysis is a method dealing with variable composition anisotropic elastic materials whose elastic constants depend upon the particular composition. In the case of porous isotropic materials, for example, it is customary to regress the Young's modulus against porosity. The results of this paper suggest a structure or paradigm for extending to anisotropic materials this empirical method of regressing elastic constant data against composition or porosity. 相似文献