夹层结构杆在弹性基础上的弹塑性变形

对位于弹性基底上的、具有可压缩非线性芯子的3层弹塑性杆的弯曲问题进行了研究．研究分析了由2个受力层和1个芯子层组成的3层构件的力学响应．解决了位于弹性基底上的3层杆弯曲的复杂问题．对所给出的弹性解法进行了收敛性检验,以保证该弹性解是可以接受的．计算结果表明,材料的塑性和物理非线性对位于弹性基底上的夹层结构杆的变形影响很大．     

Polyconvex potentials,invertible deformations,and thermodynamically consistent formulation of the nonlinear elasticity equations

It is shown that the nonstationary finite-deformation thermoelasticity equations in Lagrangian and Eulerian coordinates can be written in a thermodynamically consistent Godunov canonical form satisfying the Friedrichs hyperbolicity conditions, provided that the elastic potential is a convex function of entropy and of the minors of the elastic deformation Jacobian matrix. In other words, the elastic potential is assumed to be polyconvex in the sense of Ball. It is well known that Ball’s approach to proving the existence and invertibility of stationary elastic deformations assumes that the elastic potential essentially depends on the second-order minors of the Jacobian matrix (i.e., on the cofactor matrix). However, elastic potentials constructed as approximations of rheological laws for actual materials generally do not satisfy this requirement. Instead, they may depend, for example, only on the first-order minors (i.e., the matrix elements) and on the Jacobian determinant. A method for constructing and regularizing polyconvex elastic potentials is proposed that does not require an explicit dependence on the cofactor matrix. It guarantees that the elastic deformations are quasiisometries and preserves the Lame constants of the elastic material.     

需求弹性、抗衡势力与价格歧视

构建完全信息动态博弈模型,考察下游市场需求弹性、零售商抗衡势力对中间产品价格歧视的影响问题。结果表明,低弹性市场中零售商抗衡势力会削弱价格歧视,且改善低弹性市场消费者福利,而高弹性市场中零售商抗衡势力会增强价格歧视,且损害低弹性市场消费者福利。而高弹性市场消费者福利的变化则依赖于零售商的抗衡势力强度,只有当抗衡势力较强时,高弹性市场消费者福利才能够得到改善。     

Bilateral estimates for solutions of boundary value problems in Kirchhoff plates

Dirichlet boundary value problems are studied for thin elastic plates on an elastic foundation within Kirchhoff's classical model. The aim is to construct dual problems that make it possible to obtain bilateral error estimates for approximate solutions. In the absence of an elastic foundation, the dual functionals are maximized on function sets whose elements satisfy certain differential restrictions. The theory is illustrated by means of a numerical example.     

Discussion of Different Model Approaches for the Flow Behavior of Ice

Ice of Antarctic ice shelves is assumed to behave on long-term as an incompressible viscous fluid, which is dominated on short time scales by the elastic response. Hence, a viscoelastic material model is required. The thermodynamic pressure is treated differently in elastic and viscous models. For small deformations, the elastic isometric stress for ν → 0.5 gives similar results to those solving for pressure in an incompressible laminar flow model. A viscous model, in which the thermodynamic pressure is approximated by an elastic isometric stress, can be easily extended to viscoelasticity. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Critical states of thin-wall conical gyroscopes elastically attached to a rotating platform

The analysis of effects of emergence of critical states of rigid and elastic thin-wall conical shell frustums hinged or elastically attached by their smaller edges to a rotating platform is performed on the basis of hybrid differential equations. The cases of simple and compound rotations of the carrying platform are considered. It is established that in the case of simple rotation the peculiarities of the critical state onset for the rigid and elastic shells are determined by relationships between their axial inertia moments, whereas in compound rotation the first frequencies of precession resonant vibrations of elastic shells do not depend on elastic pliability of the ties between the shell and the platform.     

The vibrations and stability of a prestressed plate on an elastic foundation

The free vibrations of a transversely isotropic prestressed linear elastic half-space, localized close to a free surface, are considered. The free vibrations of a prestressed transversely isotropic infinite plate, lying on an elastic foundation, are also considered. The dispersion equation is analysed as a function of the wave numbers, the elastic properties of the foundation and of the plate and the values of the prestresses. The investigation is confined to cases when the initial stresses are less than the critical values, while the elastic waves do not penetrate into the depth of the foundation but are localized close to the free surface. The stability of the half-space and the plate on an elastic foundation is also considered. When analysing the vibrations and the stability of the plate, the results in the three-dimensional formulation of the problem are compared with the results of the two–dimensional Kirchhoff–Love and Timoshenko–Reissner models.     

Anisotropy of elasticity of a composite with irregularly oriented anisometric filler particles

The effects of orientation and shape of filler particles on the elastic properties of composites have been analyzed. The elastic constants of a composite with irregularly oriented filler particles were calculated by using the method of orientational averaging of the properties of a representative structural element. The elastic constants of the structural element were found according to a known generalized Eshelby solution for a finite concentration of ellipsoidal inclusions. The diagrams of elasticity anisotropy for a transversely isotropic structural element and an orthotropic composite with irregularly oriented inclusions are presented. A quantitative estimate for the degree of anisotropy of elastic properties of composites is suggested. Data on the influence of shape anisometry of inclusions on the anisotropy coefficient of filled composites are also reported.     

Effect of the Rounding Radius of Supports on the Accuracy of Determining the Interlayer Shear Modulus of Reinforced Plastics from Short-Beam Bending Tests

The accuracy of determining the elastic constants of reinforced plastics is estimated based on bending tests of short beams using the results of a numerical experiment with known elastic constants of the specimen material. Several combination variants for the initial values of the shear modulus and support radius are considered. It is shown that the calculation error of the shear modulus is considerably higher than that of the elastic modulus A decrease in the shear modulus increases the accuracy of its determination. The radius of supports affects this accuracy insignificantly.     

Low-frequency acoustic characteristics of biological tissues

The laws of propagation of elastic waves of different types in biological tissues in the acoustic frequency range have been theoretically and experimentally investigated. The contributions of the imaginary and real components of the complex modulus of elasticity to the elastic wave velocity are analyzed. It is shown that in soft tissues, low-frequency elastic disturbances are propagated chiefly by shear (transverse) waves. The geometric dispersion of the elastic wave velocity has been investigated in experiments on gel model systems; the results of the measurements are in agreement with the theoretical dispersion curve.     

弹性半空间地基上四边自由矩形板稳态振动的解析解

采用双重Fourier变换,分析得到弹性半空间地基受竖向稳态荷载作用下的积分变换解．与四边自由矩形板的振动解析解相结合,得出弹性半空间地基上四边自由矩形板稳态振动的解析解．还给出算例及参数影响分析．     

Effect of hydrostatic pressure on mechanical properties of plastics

The effect of hydrostatic pressure on the elastic and strength properties of plastics is investigated. Hydrostatic pressure is found to raise the modulus of elasticity, the tensile strength, and the elastic limit. Approximate equations for calculating the strength and elastic properties under various amounts of hydrostatic presure are proposed.Mekhanika polimerov, Vol. 1, No. 1, pp. 65–75, 1965     

The three-dimensional contact problem for a wedge-shaped valve

The three-dimensional contact problem for an elastic wedge-shaped valve, situated in a wedge-shaped cavity in an elastic space, is investigated. A regular asymptotic method is used to solve the integral equation of this problem. The method is effective for a contact area relatively far from the edge of the wedge-shaped cavity. Calculations are carried out. The solutions of the three-dimensional auxiliary problems on the equilibrium of an elastic wedge-shaped cavity and an elastic wedge are based on well-known Green's functions, constructed using Fourier and Kontorovich–Lebedev integral transformations.     

含椭圆形夹杂的压电体平面应变问题

利用复变函数理论,对在无限远处均匀应力和电位移载荷作用下的含有椭圆形弹性夹杂的横观各向同性压电材料,作了力电分析．在该文有限元结果和前人相关理论解的基础上,提了出一个可接受的认为弹性夹杂体内的应力场为常应力场的假设．在采用了不导通电边界条件之后,获得了以复势形式表示的压电基体的和弹性夹杂体内部的应力场解．     

Small amplitude, free longitudinal vibrations of a load on a finitely deformed stress-softening spring with limiting extensibility

A constitutive theory for a general class of incompressible, isotropic stress-softening, limited elastic rubberlike materials is introduced. The model is applied to study the small amplitude, free longitudinal vibrational frequency of a load about a suspended static equilibrium stretch of a finitely deformed, stress-softening spring with limiting extensibility. A number of physical results, including bounds on the frequency, are reported. It is proved, for example, that the normalized vibrational frequency for the ideally elastic neo-Hookean oscillator is a lower bound for the normalized frequency of every incompressible, isotropic stress-softening, limited elastic oscillator within the general class. All results are illustrated for the special limited elastic Gent and the purely elastic Demiray biomaterial models, both with stress-softening characterized by a Zú?iga–Beatty front factor damage function. The results for both stress-softening models are compared with experimental data for several gum rubbers and thoracic aortic tissue provided by others; and, overall, it is found that the stress-softening, limited elastic Gent model best characterizes the data.     

Problems of the concentration of elastic stresses near defects in spherically multilayered media

A spherically multilayered medium, whose elastic parameters change abruptly on the spherical surfaces, with defects in the form of cracks or thin rigid inclusions, is considered. The method of solving problems of the stress concentration near such defects is based on the introduction of linear combinations of the displacements and stresses as the fundamental unknowns. This enables the difficulties related to the presence of an arbitrary number of layers to be effectively overcome. The method is described initially for an unbounded elastic medium and defects of spherical form, situated on the surfaces where the elastic parameters change (interphase defects) and a way of extending this to the case of an elastic medium of finite dimensions, defects of other forms and not situated on these surfaces, is indicated. The method is described in detail as it applies to the case of a two-layer medium with an interphase crack when a torsion centre at the origin of coordinates acts on the medium. The problem is reduced to an integral equation, an effective method of solving it is given, and a formula is obtained for the stress intensity factor.     

经济弹性函数的几何解释

弹性函数是研究当自变量有微弱变化时 ,函数的相对变化率 .本文构造一条初始弹性直线 ,弹性函数就是函数的切线斜率与初始弹性直线斜率之比 ;也是函数在弹性支点的微分与初始弹性直线在弹性支点的增量之比 .     

两对边简支中间有任意多个单向弹性线支矩形板横向振动的一个解析解法*

本文给出了两对边简支另两对边任意支承的中间有任意多个单向弹性线支矩形板横向振动的一个新的解析解法、将弹性线支反力看作是作用于板上的待求外力,求得了含有来知的弹性线支反力的两对边简支矩形板的运动方程的解析解;利用弹性线支反力与板横向位移之间的线性关系导出频率方程;频率方程及振型函数的表述均与已有方法不同.     

多变量样条元法分析弹性地基板的弯曲,振动与稳定问题

本文应用双三次乘积型二元B样条函数来构造弹性地基板的位移、弯矩和扭矩等多种场函数，由混合变分原理导出多变量样条无法方程．文中，对弹性地基板的弯曲、振动与稳定问题作了分析与计算．由于，本文方法设定了各自独立的场函数，因此，所算得的场未知量如位移、弯矩和扭矩值的精度均比较高。