A Second-Order Solution of Saint-Venant's Problem for a Piezoelectric Circular Bar Using Signorini's Perturbation Method

We study electromechanical deformations of a homogeneous transversely isotropic piezoelectric prismatic circular bar loaded only at the end faces. The constitutive relations for the material of the bar are taken to be quadratic in the displacement gradients and the electric field. It is found that the two end faces of the bar when twisted with no electric charge applied to them will exhibit a difference in the electric potential. Thus the piezoelectric cylinder could be used to measure the torque or the angular twist. This revised version was published online in August 2006 with corrections to the Cover Date.     

一种确定均匀动脉壁面切应力的非线性方法

从Ling和Atabek提出的``局部流'理论出发，提出一种利用测量血液黏度、管轴上 的血流速度、压力和管径波形计算均匀动脉管壁切应力的非线性方法. 将这种方法与柳兆荣 等提出的利用测量血液黏度、管轴上的血流速度和平均管径计算切应力的线性方法比较，结 果表明，当管壁脉动幅度较小时，两种方法计算的压力梯度、流速剖面和管壁切应力差别较 小；而当管壁脉动幅度增大时，两种方法计算的压力梯度、流速剖面和管壁切应力差别增大. 对于小幅脉动均匀动脉，用线性方法计算管壁切应力有较高的精度；而对于大变形 均匀动脉，则需要考虑非线性因素对管壁切应力的影响. 由于作为输入量的血液黏度、轴心 血流速度、压力波形和管径波形可在活体上通过无损伤或微损伤的检测方法得到， 所提出的计算切应力的方法为在体或离体研究切应力与动脉重建的关系提供了方法学基础.     

强非线性动力系统周期解分析

给出一类强非线性动力系统周期解存在性，唯一性和稳定性的简易差别法以及周期解的摄动法。本差别法把问题归结为干扰力在相应的未扰系统振动周期上的功函数及其导数的讨论，其限制条件比现有结果弱。本摄动法可以认为是经典Ｌｉｎｄｓｔｅｄｔ－Ｐｏｉｎｃａｒｅ（Ｌ－Ｐ）法在强非线性振动系统的推广。它与Ｌ－Ｐ法的主要区别在于假设系统的振动频率为相角的非线性函数。     

Approximate solutions and scalarization in set-valued optimization

Abstract

Certain notions of approximate weak efficient solutions are considered for a set-valued optimization problem based on vector and set criteria approaches. For approximate solutions based on the vector approach, a characterization is provided in terms of an extended Gerstewitz’s function. For the set approach case, two notions of approximate weak efficient solutions are introduced using a lower and an upper quasi order relations for sets and further compactness and stability aspects are discussed for these approximate solutions. Existence and scalarization using a generalized Gerstewitz’s function are also established for approximate solutions, based on the lower set order relation.     

计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。     

二次特征矩阵表示的特征值有界性分析

采用二次特征矩阵近似表示精确有限元和精确动态子结构分析中得出的超越或非线性动态刚度阵，并证明了在满足一定条件的前提下，二次特征阵给出的特征值是精确刚度阵特征值的上界或下界。     

Generalized Forchheimer Equation for Two-Phase Flow Based on Hybrid Mixture Theory

In this paper, we derive a Forchheimer-type equation for two-phase flow through an isotropic porous medium using hybrid mixture theory. Hybrid mixture theory consists of classical mixture theory applied to a multiphase system with volume averaged equations. It applies to media in which the characteristic length of each phase is small relative to the extent of the mixture. The derivation of a Forchheimer equation for single phase flow has been obtained elsewhere. These results are extended to include multiphase swelling materials which have nonnegligible interfacial thermodynamic properties.     

Rheology/morphology/flow conditions relationships for polymethylmethacrylate/rubber blend

Viscoelastic behavior, phase morphology and flow conditions relationships in polymer/rubber blends have been investigated. The importance of such correlations is illustrated on polymethylmethacrylate (PMMA)/rubber blends subjected to different flow conditions both under small and large deformations. In small-amplitude oscillatory shear (the morphology does not change during the flow) the elastic modulus G of the concentrated blends shows a secondary plateau, G _p , in the low frequency region. This solid-like behavior appears for rubber particle contents beyond the percolation threshold concentration (15%). Morphological observations revealed that for concentrations higher than 15%, the particles are dispersed in a three-dimensional network-type structure.In capillary flow it was found that the network-type structure was destroyed and replaced by an alignment of particles in the flow direction. This morphological modification resulted in a decrease in both viscosity and post-extrusion swell of the blends. Morphological observations revealed that the ordered structure in the flow direction was concentrated only in the skin region of the extrudate, where the shear stress is higher than the secondary plateau, G _p . A simple kinetic mechanism is proposed to explain the observed morphology.Similarly, steady shear measurements performed in the cone-and-plate geometry revealed alignment of particles in the flow direction for shear stress values higher than G_p.Presented in part at the Symposium Recent Developments in Structured Continua Montréal (Canada) 26–28 May 1993 and at the 45th Canadian Chemical Engineering Conference, Quebec, October 15–18 (1995)     

A decoupled modal form Duffing equation for an orthotropic laminate in a clamped boundary condition with thermal diffusion

The non-linear thermo-elasticity response of an orthotropic laminate in a clamped boundary condition is analyzed by means of the method of weighted residuals for its behaviors subject to thermal and mechanical loading. The equation of motion for the laminate's deflection is obtained in the form of a decoupled modal form Duffing equation, without Berger's approximation. The thermal field, with both the in-plane and transverse temperature variations, is incorporated in both a steady-state and transient state. The formulation indicates that a transverse thermal field with a temperature rise produces a load onto the laminate, while the in-plane temperature variation affects the system frequency and stability. We demonstrate the numerical results of the modal response of an isotropic laminate for the thermal buckling and vibration.