中心集中力作用下圆薄板的固有频率—载荷特征关系

本文讨论了中心集中静载作用下圆薄板在非线性弯曲静平衡构形附近的微幅自由振动,其静平衡问题采用问题的精确解在此基础上,用伽辽金法获得了其最低固有频率——载荷特征关系.所得结果可供这类谐振弹性元件设计中参考.     

基于运动约束解过约束并联机构变形协调方程

提出利用运动约束关系来间接求解过约束并联机构变形协调方程．首先介绍了该方法的原理，接着分别针对平面和空间过约束并联机构，详述该方法的解决步骤，结果验证了该方法的正确性，从中还可看出该方法在求解复杂过约束并联机构时非常简洁，最后介绍了采用该方法解决多度过约束问题．     

损伤弹性材料的有效模量及本构关系

考虑了微裂纹之间的相互作用，利用随机熔断丝网络（Ｒａｎｄｏｍｆｕｓｅｎｅｔｗｏｒｋ）作为模型，模拟了脆性材料在外载荷作用下，其有效模量随损伤的演变行为，并考察了系统含损伤的本构关系。发现在损伤初期，有效模量和损伤具有线性下降关系；而在后期，由于损伤局部化，有效模量迅速下降，提出了一个有效模量随损伤变化的非线性关系。讨论了利用网络模型来研究材料含损伤本构关系的可行性和优越性。     

Identification de la relation de dispersion dans les barresIdentification of the dispersion relation in rods

Dispersion and attenuation of longitudinal waves in elastic or weakly viscoelastic rods are measured by analysing the resonant frequencies present in the strain spectrum due to an unknown loading. The method takes the finite measuring time of the test into account. It is applied to an aluminium bar, in which the dispersion relation is identified very accurately at frequencies up to 60 kHz. To cite this article: R. Othman et al., C. R. Mecanique 330 (2002) 849–855.     

Parameter identification for viscoelastic materials

Starting from the general stress-strain relation for a linear Boltzmann-Volterra material, which is in agreement with the principle of inertia, a new identification procedure is proposed. Instead of running one long-range relaxation experiment, following asingle suitably specified deformation history, material characterization is done using the data ofn short relaxation experiments followingn different deformation histories. To interpret these data a direct non-iterative algorithm has been developed. Compared with other methods, for example curve fitting by using Gauss' method, this direct method is numerically stable and allows a simple direct evaluation of the error due to the scattering of experimental data. The method has been applied to the determination of the relaxation times of an unsaturated polyester material.     

The mirror relations and nonlinear viscoelasticity of polymer melts

An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namelyS ₁₂ () = – a ( – 1) (a = 0 for 1,a = 1 for 1) for the mirroring of the viscosities,S ₁₂ () = – a (–k ²/) (a = 0 for k, a = 1 for k) for the mirroring of the first normal-stress coefficients, and for the third relation. Here denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value ofk is used.     

A differential constitutive equation for polymer melts

A modification of the Giesekus constitutive equation is derived by incorporating (approximately, via the Peterlin approximation) the finite extensibility of polymer molecules into dumbbell kinetic theory along with the anisotropic hydrodynamic drag suggested by Giesekus. The constitutive equation that is obtained retains much of the simplicity of Giesekus' constitutive equation, but it involves terms that are cubic in the stress as well as those that are quadratic. It is shown that the constitutive equation quantitatively describes the steady elongational viscosity of the IUPAC polymer melt A (including the strain softening of the melt), but it cannot describe the elongational and shear viscosities simultaneously. It is also shown that the constitutive equation satisfies the Lodge-Meissner relation for shear strains less than unity.     

铝-锂合金动态扭转实验研究

利用霍普金森扭杆（Torsional Split-Hopkinson Bar）技术对三种不同成份或状态的铝-锂合金材料的动态应力-应变-应变率关系进行了实验测定。应变率范围由1300s-1到2600s-1,研究表明随着应变率的提高,三种不同成份或状态的铝-锂合金材料的韧性和强度都有不同程度的提高。对剪切带的初步观察发现,随应变率的增加,剪切带有变窄的趋势。     

开采沉陷工程岩体本构关系研究

传统开采沉陷理论存在对采动岩体本构关系研究不够的问题, 本文在运用现代工程地质学理论和现代数学力学理论相结合, 对采动岩体本构关系进行深入研究的基础上, 提出了用“黑箱”问题“灰箱”化的全息反分析法, 确定采动工程岩体本构关系及其有关参数。实例分析表明, 对于复杂岩体结构的开采沉陷问题, 能够取得满意的结果。     

On kinetics of hysteresis

An initiation criterion and a kinetic relation describing hysteresis in shape memory alloys consistent with non-equilibrium thermodynamics are proposed. The initiation of phase transition begins always at zero driving force, defined as the negative derivative of free energy with respect to the volume fraction of high strain phase. The kinetic relation is obtained from the dissipation potential which is proportional to the magnitude of the volume fraction rate times the newly formed volume fraction. The proposed theory turns out to be rate-independent, but history dependent, and can describe all features of hysteresis loops observed in experiments.