On the convergence of the rayleigh quotient iteration for the computation of the characteristic roots and vectors. II

Archive for Rational Mechanics and Analysis -     

非线性自由振动的迭代响应法

构造了一个考虑横向振动和板面内运动的三节点几何非线性等参环形板单元,采用迭代求响应的方法,研究了中心附有刚性质量块的非线性轴对称自由振动的频率,与已有的结果比较表明,本文的方法得到更为精确的数值结果。     

A computer model of the two-roll mill for generalised Newtonian flow

We investigate the flow of a generalised Newtonian liquid between two contra-rotating cylinders of equal size — the so called two-roll mill problem. A finite element method is used to obtain solutions for the case of a Carreau model and for a power law model. Consideration is given to the influence of shearthinning on the flow pattern around the cylinders. Results are presented for different speeds of rotation of the cylinders and for various values of fluid parameters. A comparison is made with the analytical solution of Jeffrey.     

基于逆迭代法的结构动力缩聚技术

有限元模型的动力缩聚法已被广泛地应用到大阶系统的特征分析、试验－分析模型的相关分析等领域中。本文从逆迭代法出发,导出了一种有限元模型动力缩聚迭代方法。该方法具有三个显著的优点：其一是收敛速度远远超过现有的动力缩聚迭代法;若干是该迭代法收敛的可以从理论上得到保证,其三是由于没有必要的在每次迭代中都去计算降阶系数的刚度矩阵、质量矩阵和特征问题,因而可减少计算工作量,尤其在主自由度数较大的情况下。     

一类加权全局迭代参数卡尔曼滤波算法

结合参数卡尔曼滤波算法和全局迭代推广卡尔曼滤波算法本文提出了加权全局迭代参数卡尔曼滤波算法。参数卡尔曼滤波算法可避免系统参数和状态变量之间的非线性耦合 ,同时通过带有目标函数的全局迭代算法保证能够获取到稳定、收敛的识别结果。分别针对线性结构模型和随动强化双线性结构模型进行了仿真参数识别。结果显示 ,不加权的全局迭代参数卡尔曼滤波算法对线性系统是有效的 ,而对非线性系统必须使用加权的全局迭代参数卡尔曼滤波算法。当信噪比较大 ,迭代无法得到收敛的结果时 ,目标函数保证了较好识别结果的获得     

Monotonicity principle in the rayleigh problem for an isothermally incompressible fluid

The convection of an isothermally incompressible fluid in a horizontal layer with free undeformable boundaries kept at a constant temperature is considered. Under the fairly common assumptions of the temperature dependence of the specific volume, it is shown that the monotonicity principle holds and that the spectrum of critical Rayleigh numbers is countable and prime. Models with linear and quadratic temperature dependences of the specific volume are given as examples. The results on the spectrum of the critical Rayleigh numbers are also valid for some other boundary conditions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 35–42, September–October, 2007.     

On a generalised viscosity equation for polymer solutions

Based on the AFVS concept, a simple equation to predict the viscosity behaviour of polymer solutions is proposed in the following form $$(\ln \eta _r )^{ - 1} = \frac{\alpha }{{\tilde c}} + \delta .$$ This has been verified by comparison with experimental data. The equation appears to have a far more general validity as it appears to correlate the data for a large variety of binary systems including suspensions, liquid mixtures etc.     

An anisotropic elastoplastic constitutive formulation generalised for orthotropic materials

This paper presents a finite strain constitutive model to predict a complex elastoplastic deformation behaviour that involves very high pressures and shockwaves in orthotropic materials using an anisotropic Hill’s yield criterion by means of the evolving structural tensors. The yield surface of this hyperelastic–plastic constitutive model is aligned uniquely within the principal stress space due to the combination of Mandel stress tensor and a new generalised orthotropic pressure. The formulation is developed in the isoclinic configuration and allows for a unique treatment for elastic and plastic orthotropy. An isotropic hardening is adopted to define the evolution of plastic orthotropy. The important feature of the proposed hyperelastic–plastic constitutive model is the introduction of anisotropic effect in the Mie–Gruneisen equation of state (EOS). The formulation is further combined with Grady spall failure model to predict spall failure in the materials. The proposed constitutive model is implemented as a new material model in the Lawrence Livermore National Laboratory (LLNL)-DYNA3D code of UTHM’s version, named Material Type 92 (Mat92). The combination of the proposed stress tensor decomposition and the Mie–Gruneisen EOS requires some modifications in the code to reflect the formulation of the generalised orthotropic pressure. The validation approach is also presented in this paper for guidance purpose. The \({\varvec{\psi }}\) tensor used to define the alignment of the adopted yield surface is first validated. This is continued with an internal validation related to elastic isotropic, elastic orthotropic and elastic–plastic orthotropic of the proposed formulation before a comparison against range of plate impact test data at 234, 450 and \({\mathrm {895\,ms}}^{\mathrm {-1}}\) impact velocities is performed. A good agreement is obtained in each test.     

广义特征值问题的并行EBE向量迭代法

本文利用ＥＢＥ策略和共轭梯度法，将广义特征值问题向量迭代法中各步的计算在单元级上进行，避免了总刚度和总质量矩阵的组集，大大节省了存储量。由此建立的ＥＢＥ向量迭代法尤其适宜于并行处理。数值算例结果表明无论是串行、还是并行计算，这类ＥＢＥ向量迭代法都能有效提高计算速度。     

A combined programming and iteration algorithm for finite element analysis of three-dimensional contact problems

Comparing with two-dimensional contact problems, three-dimensional frictional contact problems are more difficult to deal with, because of the unknown slip direction of the tangential force and enormous computing time. In order to overcome these difficulties, a combined PQP (Parametric Quadratic Programming) and iteration method is derived in this paper. The iteration algorithm, which alleviates the difficulty of unknown slip direction, is used along with the PQP method to cut down computing costs. Numerical example is given to demonstrate the validity of the present algorithm. The project supported by the Machinary and Electronics Ministry of China     

Size effects in generalised continuum crystal plasticity for two-phase laminates

The solutions of a boundary value problem are explored for various classes of generalised crystal plasticity models including Cosserat, strain gradient and micromorphic crystal plasticity. The considered microstructure consists of a two-phase laminate containing a purely elastic and an elasto-plastic phase undergoing single or double slip. The local distributions of plastic slip, lattice rotation and stresses are derived when the microstructure is subjected to simple shear. The arising size effects are characterised by the overall extra back stress component resulting from the action of higher order stresses, a characteristic length l_c describing the size-dependent domain of material response, and by the corresponding scaling law lⁿ as a function of microstructural length scale, l. Explicit relations for these quantities are derived and compared for the different models. The conditions at the interface between the elastic and elasto-plastic phases are shown to play a major role in the solution. A range of material parameters is shown to exist for which the Cosserat and micromorphic approaches exhibit the same behaviour. The models display in general significantly different asymptotic regimes for small microstructural length scales. Scaling power laws with the exponent continuously ranging from 0 to −2 are obtained depending on the values of the material parameters. The unusual exponent value −2 is obtained for the strain gradient plasticity model, denoted “curl H^p” in this work. These results provide guidelines for the identification of higher order material parameters of crystal plasticity models from experimental data, such as precipitate size effects in precipitate strengthened alloys.     

Integrability of the generalised Hill problem

Nonlinear Dynamics - We consider a certain two-parameter generalisation of the planar Hill lunar problem. We prove that for nonzero values of these parameters the system is not integrable in the...     

相对差商算法性能的统计研究

本文通过服从一致分布随机算例的均匀抽样方式，对离散变量优化问题的相对差商算法进行了数值实验，按启发式算法的性能评价指标对数值实验结果进行了统计分析，为评价相对差商算法的实际性能提供了统计依据