A Measuring System for Bulk and Shear Characterization of Polymers

This paper describes a novel measuring system for investigating the influence of pressure and temperature on the mechanical properties of time-dependent polymer materials. The system can measure the volume and the shear relaxation moduli of solid polymer specimens simultaneously subjected to temperatures from −50 to +120°C with a precision of ±0.01°C, and pressures from atmospheric to 500 MPa with a precision of ±0.1 MPa. The paper demonstrates the measuring capabilities of the apparatus. For poly(vinyl) acetate (PVAc) are presented sample measurements of the shear relaxation modulus as function of time, pressure and temperature; specific volume; the bulk creep compliance; the coefficient of thermal expansion; the bulk modulus; and the pressure drop experiments which simulate conditions to which a material is exposed during the injection molding process. The shear moduli may be measured in the range from 1 to 4,000 MPa with the relative error of 3%.The error of volumetric measurements is 0.05%, which corresponds to 0.00005 cm³/g. In all cases results are shown as measured, no additional smoothing or filtering was employed. This paper is dedicated to Professor Nicholas W. Tschoegl on the occasion of his 87th birthday, for his contributions to the field of time-dependent bulk properties of polymeric materials.     

基于基面力概念的一种新型余能原理有限元方法

在高玉臣(2003)提出的单元柔度矩阵表达式的基础上,基于基面力的概念,利用余能原理和Lagrange乘子法推导出以基面力为基本未知量的余能原理有限元支配方程张量表达式和节点位移表达式,编制出相应的有限元程序,通过对一些典型的弹性理论问题的计算分析,数值解与理论解相吻合。研究表明,这种方法简单而有效,是有限元方法的一种新思路,具有较好的应用前景。     

Research on viscoelastic behavior of semi-crystalline polymers using instrumented indentation

In this study, the viscoelastic behavior of a polyamide 12 (PA12) polymer was evaluated using instrumented indentation technology based on a rheological model. The creep compliance and retardation spectra were obtained to analyze the viscoelastic response during the holding stage according to the rheological model under different preloading conditions. The results showed that the viscoelastic responses were independent of the indentation depth or load under step loading conditions. However, the creep compliance increases, and the peak intensity of the retardation spectrum decreases with a decrease in the preloading rate owing to the structural relaxation observed during the preloading stage under ramp loading conditions. Furthermore, softening dispersion can be completed during the loading stage under continuous stiffness measurement (CSM) conditions. As the preloading strain rate changes, the peak of the retardation spectrum gradually decreases until it disappears completely. Moreover, studies on indentation creep using the CSM method are challenging because of the complicated viscoelastic response observed during the preloading stage.     

The relaxation of polymers with linear flexible chains of uniform length

The analysis of dynamic mechanical data indicates that linear flexible polymer chains of uniform length follow a scaling relation during their relaxation, having a linear viscoelastic relaxation spectrum of the formH() = n ₁ G _N ⁰ × (/ _max) ⁿ¹ for _max. Data are well represented with a scaling exponent of about 0.22 for polystyrene and 0.42 for polybutadiene. The plateau modulusG _N ⁰ is a material-specific constant and the longest relaxation time depends on the molecular weight in the expected way. At high frequencies, the scaling behavior is masked by the transition to the glassy response. Surprisingly, this transition seems to follow a Chambon-Winter spectrumH() = C^–n2, which was previously adopted for describing other liquid/solid transitions. The analysis shows that the Rouse spectrum is most suitable for low molecular-weight polymersM M _c , and that the de Gennes-Doi-Edwards spectrum clearly predicts terminal relaxation, but deviates from the observed behavior in the plateau region.Dedicated to Prof. Richard S. Stein on the occasion of his 65th birthday.On sabbatical leave from the University of Linz, Austria.     

Truss topology optimization under uncertain nodal locations with proportional topology optimization method

This paper presents an approach to solving truss topology optimization problem with small uncertainty in the locations of the structural nodes. The nodal locations in the truss are assumed to be random, and the probabilistic method is used here to deal with the uncertainty. The objective of the optimization problem is to minimize the mean compliance of the truss structure under nodal location uncertainty. It is a well-acknowledged barrier to compute the inverse of the structural stiffness matrix which involves variations in the optimization problem. In this paper, based on Neumann series expansion, this optimization problem can be recast into a simpler deterministic structural optimization problem. In order to avoid the sensitivity calculations for the objective function, the proportional topology optimization method which shows comparable e?ciency and accuracy with gradient-based method is used. The numerical examples demonstrate the effectiveness and high e?ciency of the proposed approach, and further illustrate that the optimal truss topology can be dramatically impacted by nodal location uncertainties.     

The anisotropic and angularly inhomogeneous elastic wedge under a monomial load distribution

In this study, the generally anisotropic and angularly inhomogeneous wedge under a monomial type of distributed loading of order n of, the radial coordinate r at its external faces is considered. At first, using variable separable relations in the equilibrium equations, the strain–stress relations and the strain compatibility equation, a differential system of equations, is constructed. Decoupling this system, an ordinary differential equation is derived and the stress and displacement fields may be determined. The proposed procedure is also applied to the elastostatic problem of an isotropic and angularly inhomogeneous wedge. The special cases of loading of order n=−1 and n=−2, where the self-similarity approach is not valid, are examined and the stress and displacements fields are derived. Applications are presented for the cases of an angularly inhomogeneous wedge and in the case of a bi-material isotropic wedge.     

纤维金属板层分层尺寸的测量方法研究

导出了纤维金属胶接层板双面裂纹搭接剪切（ＤＣＬＳ）试样分层尺寸和柔度之间的线性关系式，提出了ＤＣＬＳ试样分层尺寸的柔度测量法，并与用光测法测得的分层尺寸进行了对比。结果表明，用柔度法测定ＤＣＬＳ试样的分层尺寸，不仅测量结果准确，而且简单易行，避免了光测法的诸多麻烦和精度低的缺点。     

配置柔顺机构空间机器人双臂捕获卫星操作力学模拟及基于神经网络的全阶滑模避撞柔顺控制

讨论了空间机器人双臂捕获卫星操作过程避免关节冲击破坏的避撞柔顺控制问题. 为此在关节电机与机械臂之间设计了一种旋转 型串联弹性执行器(rotatory series elastic actuator, RSEA)--柔顺机构,其作用在于:(1) 通过其内置弹簧的拉伸或压缩变形来吸收捕获操作过程中被捕获卫星对空间机器人关节产生的冲击能量;(2) 可以利用合理设计的与之配合的避撞柔顺控制策略来保证关节冲击力矩受限在安全范围. 首先,利用第二类Lagrange方程分别建 立了捕获操作前含柔顺机构双臂空间机器人的开环分系统动力学模型与目标卫星的分系统动力学模型;之后,基于系统动量 守恒关系、闭链系统位置与速度几何约束关系,获得了捕获操作后空间机器人与被捕获卫星闭链混合体系统综合动力学方程; 最后,基于RBF神经网络提出了一种捕获操作后两者混合体系统镇定运动的全阶终端滑模避撞柔顺控制方案. 所提方案结合柔 顺机构在有效吸收、缓冲被捕获卫星冲击能量的同时,还在冲击能量过大时适时开、关空间机器人关节驱动器,以避免关节驱 动器过载、破坏;此外,还通过最小权值范数法分配了机械臂各关节力矩,以保证双臂协调操作. Lyapunov稳定性理论证明了 系统的全局稳定性,系统计算机数值仿真也验证了上述避撞柔顺控制策略的有效性.      

TORSIONAL VIBRATIONS OF RIGID CIRCULAR PLATE ON TRANSVERSELY ISOTROPIC SATURATED SOIL

An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established. By appropriate transform, the dual integral equations were converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficient, the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly. Selected examples were presented to analyse the influence of saturated soil's anisotropy on the foundation's vibrations.