An adaptive updating full-Newton step interior-point algorithm with modified Newton direction

We adopt the self-adaptive strategy to update the barrier parameter of a feasible primal-dual interior-point algorithm. We obtain two adaptive updating methods, namely, cheap updates and sharp updates. We compare the effectiveness of the short updates with the adaptive update methods on some benchmark problems. The numerical results show that the sharp updates method is superior to short updates and cheap updates methods.     

Determination of dynamic properties of flax fibres reinforced laminate using vibration measurements

Experimental and numerical methods to identify the linear viscoelastic properties of flax fibre reinforced polymer (FFRP) composite are presented in this study. The method relies on the evolution of storage modulus and loss factor as observed through the frequency response. Free-free symmetrically guided beams were excited in the dynamic range of 10 Hz to 4 kHz with a swept sine excitation focused around their first modes. A fractional derivative Zener model has been identified to predict the complex moduli. A modified ply constitutive law has been then implemented in a classical laminates theory calculation (CLT) routine. Overall, the Zener model fitted the experimental results well. The storage modulus was not frequency dependant, while the loss factor increased with frequency and reached a maximum value for a fibre orientation of 70°. The damping of FFRP was, respectively, 5 and 2 times higher than for equivalent carbon and glass fibres reinforced epoxy composites.     

The force–moments on a deforming body introduced impulsively into an inviscid incompressible fluid with uniform vorticity

This paper is concerned with the derivation of dynamical equations for freely deforming bodies with more than six degrees of freedom which are immersed in an inviscid incompressible fluid. Following Proudman's pioneering work for a sphere our method is applied to a fluid with uniform vorticity but otherwise arbitrary non-uniform strain-rate at the instant after the body has been impulsively introduced into the fluid. The rotational disturbance field is consequently zero thus enabling the generalised force–moments of arbitrary order to be determined from a Laplace problem through the use of Green's theorem and generalised Kirchhoff potentials. An infinite system of equations is obtained each which contains an inertial term, given by the rate of change of the generalised Kelvin Impulse, a generalised lift, a deformation-induced surface momentum flux and a surface kinetic energy. The assumption of an impulsive start places no constraint on the use of our force–moment formulae in irrotational flow but they can only be applied at the starting instant in rotational flow or, when the strain-rate is weak, for early times in the body's motion. Nonetheless, the start conditions for the rotational case can be created experimentally and be applied to initially free tumbling bodies when they start to deform. This newly identified equation system provides the foundation for new analytical and numerical approaches to the macroscopic modelling of freely deforming bodies and bubbly two-phase flow. In particular, the equations show that the added masses are not sufficient to characterise the body's geometry and that independent geometric constants are also required, here referred to as the added Kirchhoff energies. Finally, the zero- and first-order force–moment equations are used to derive the force and torque that apply to bodies with six degrees of freedom and their analytic forms are shown to agree with independent results for arbitrarily shaped deforming bodies in both rotational and irrotational flows.     

LIE SYMMETRY ANALYSIS AND PAINLEVE ANALYSIS OF THE NEW （2＋1）-DIMENSIONAL KdV EQUATION

Lie point symmetries associated with the new （2＋1）-dimensional KdV equation ut ＋ 3uxuy ＋ uxxy = 0 are investigated. Some similarity reductions are derived by solving the corresponding characteristic equations. Painlevé analysis for this equation is also presented and the soliton solution is obtained directly from the Bǎcklund transformation.     

非线性多值算子扰动的映射定理

本文讨论非线性多值算子的非紧扰动的映射定理,并给出非线性泛函方程ｚ∈Ｔ（ｘ）＋Ｆ（ｘ）可解性的最新结果,其中Ｔ是多值算子且（Ｔ＋１/ｎＩ）^－１是１－集压缩,而Ｆ是１－集压缩或γ－凝聚．所得的结果改善了［５,８,１２］中的主要结果     

纳米锐钛矿相变的原位XRD研究

钛氧化物具有3种物相：锐钛矿、板钛矿和金红石，其中，锐钛矿和板钛矿为室温稳定相．在温度较高的条件下会向热力学更稳定的金红石相转变。锐钛矿向金红石的相变是热力学亚稳定相向稳定相的转变，由于这种相变过程不存在平衡温度．分析研究其相变过程无论从理论方面还是从实际应用方面均具有重要的意义。     

Calculation for path-domain independentJ integral with elasto-viscoplastic consistent tangent operator concept-based boundary element methods

This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals. The project supported by National Natural Science Foundation of China (9713008) and Zhejiang Natural Science Foundation Special Funds No. RC.9601     

可逆的渐近非扩张型半群的遍历定理

本文在Ｈｉｌｂｅｒｔ空间中证明了右可逆的连续渐近非扩张型半群的遍历保核收缩存在定理，并讨论了可控的连续渐近非扩张型半群的遍历收敛定理     

Hölder continuity for a class of X-elliptic equations with singular lower order term

The regularity for a class of X-elliptic equations with lower order term
Lu＋vu=-∑i,j=1 mXj^＊（aij（x）Xiu）＋vu=μ
is studied, where X = {X1,..., Xm} is a family of locally Lipschitz continuous vector fields, v is in certain Morrey type space and μ a nonnegative Radon measure. The HSlder continuity of the solution is proved when μ satisfies suitable growth condition, and a converse result on the estimate of μ is obtained when u is in certain HSlder class.     

左截断数据下非参数回归模型的复合分位数回归估计

利用局部多项式方法研究了误差具有异方差结构的非参数回归模型,在左截断数据下构造了回归函数的复合分位数回归估计,并得到了该估计的渐近正态性结果,最后通过模拟,在服从一些非正态分布的误差下,得到该估计比局部线性估计更有效.