Gap detection in the spectrum of an elastic periodic waveguide with a free surface

A three-dimensional periodic elastic waveguide is constructed whose continuous spectrum (the frequencies that admit propagating waves) contains a gap, i.e., an interval that has its ends in the continuous spectrum but contains at most a discrete spectrum. The waveguide consists of an infinite chain of massive bodies connected by short thin links, and its surface is assumed to be free. The method for detecting a gap also applies to plane problems, including scalar ones. Periodic elastic waveguides with different shapes or contrasting properties are indicated in which a gap can also be detected.     

质量、价格对顾客满意度的影响

关于质量、价格对顾客满意度的影响,尽管许多学者已经取得了显著的成就,但是这些研究都是基于定性分析,本部分转变研究角度,利用数学方法,分析质量、价格对顾客满意度的影响,给出顾客满意度和质量、价格的函数关系式;提出顾客满意度关于质量的弹性概念和顾客满意度关于价格的弹性概念,这样就可以从量化的角度来研究不同水平的质量或者不同价格对顾客满意度的影响及其非线性关系.     

商品的总收益弹性与需求弹性守恒定理及其应用

本文介绍和证明了同一商品的总收益弹性与需求弹性守恒定理［１］及其推论，获得了一个重要公式，即ＥＲ±Ｅｄ＝１（ＥＲ即商品的总收益弹性，Ｅｄ即需求弹性）并以市场上常见的商品为例，列举了这一公式在经济预测决策方面的种种应用。     

ON THE RECOVERY OF A CURVE ISOMETRICALLY IMMERSED IN E~n

It is known from classical differential geometry that one can reconstruct a curve with (n - 1) prescribed curvature functions, if these functions can be differentiated a certain number of times in the usual sense and if the first (n - 2) functions are strictly positive. It is established here that this result still holds under the assumption that the curvature functions belong to some Sobolev spaces, by using the notion of derivative in the distributional sense. It is also shown that the mapping which associates with such prescribed curvature functions the reconstructed curve is of class C∞.     

在轧机机架产生双表面贯穿裂纹下的断裂强度分析

某钢厂的2030平整轧机机架上发现有R=60mm的双表面张开型圆裂纹，为了安全生产，必须给出断裂力学强度评价。但是，要获得这种裂纹的应力强度因子，还没有理论解，文章应用弹性论并结合三维光弹性法和有限元法得到了K2值，二个方法所取得的值不仅吻合而且获得了机架在设计载荷下工作裂纹是稳定和不扩展的结论，此结论对生产现场有极大指导意义。     

Emission of dislocations from grain boundaries by grain boundary dissociation

In this article, we examine the conditions that favour the emission of Shockley partial dislocations (SPDs) that standoff from a grain boundary (GB) plane by a few lattice parameters as part of the atomic structure of some GBs. To do so, we consider GBs to be formed by the operation of arrays of intrinsic grain boundary dislocations (GBDs) that create the tilt and twist misorientation, and the lattice mismatch between the two crystal grains adjoining the GB. The conditions to be considered that favour SPDs are the following: (1) Frank’s rule, (2) the proper sequential arrangement of partial dislocations to bound an intrinsic stacking fault and (3) the equilibrium stand-off distance (ESD). We apply an isotropic elasticity analysis to compute the ESD, in the absence of an applied stress, for SPDs emerging from asymmetric tilt GBs in two FCC metals, Cu and Al. The ESD is shown to be dependent on the glide plane orientation relative to the GB plane and on the position of the glide planes, relative to the position of the GBDs. An applied stress increases the ESD up to a critical stress that removes the SPDs without limit from the GB. We examine the effect of the stacking fault energy on the ESD and critical stress. The critical stress is effectively linearly dependent on the stacking fault energy. Finally, we present results of atomistic simulations of asymmetric tilt Σ11[1?0?1]{4?1?4}||{2?5?2} GBs in Cu bicrystal models subject to shock loading that behave in a manner similar to the elasticity predictions. The atomistic simulations reveal additional behaviour associated with elastic incompatibility between the two grains in the bicrystal models.     

An anisotropic thin crystal deformed by an inclined dislocation

The elastic field around a dislocation piercing obliquely an anisotropic thin crystal is obtained by combining the classical solution applicable to an infinite anisotropic crystal with an analysis using the concept of continuous dislocation density. Numerical applications are presented for inclined dislocations in Ni₃Al and Ni.     

A degenerating Cahn–Hilliard system coupled with complete damage processes

In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described by a degenerating Cahn–Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a degenerating quasi-static balance equation for the displacement field. All these equations are highly nonlinearly coupled. Because of the doubly degenerating character of the system, the doubly nonlinear differential inclusion and the nonsmooth domain, the structure of the model is very complex from an analytical point of view.A novel approach is introduced for proving existence of weak solutions for such degenerating coupled system. To this end, we first establish a suitable notion of weak solutions, which consists of weak formulations of the diffusion and the momentum balance equation, a variational inequality for the damage process and a total energy inequality. To show existence of weak solutions, several new ideas come into play. Various results on shrinking sets and its corresponding local Sobolev spaces are used. It turns out that, for instance, on open sets which shrink in time a quite satisfying analysis in Sobolev spaces is possible. The presented analysis can handle highly nonsmooth regions where complete damage takes place. To mention only one difficulty, infinitely many completely damaged regions which are not connected with the Dirichlet boundary may occur in arbitrary small time intervals.     

An efficient algebraic multigrid method for quadratic discretizations of linear elasticity problems on some typical anisotropic meshes in three dimensions

The quality of the mesh used in the finite element discretizations will affect the efficiency of solving the discreted linear systems. The usual algebraic solvers except multigrid method do not consider the effect of the grid geometry and the mesh quality on their convergence rates. In this paper, we consider the hierarchical quadratic discretizations of three‐dimensional linear elasticity problems on some anisotropic hexahedral meshes and present a new two‐level method, which is weakly independent of the size of the resulting problems by using a special local block Gauss–Seidel smoother, that is LBGS_v iteration when used for vertex nodes or LBGS_m iteration for midside nodes. Moreover, we obtain the efficient algebraic multigrid (AMG) methods by applying DAMG (AMG based on distance matrix) or DAMG‐PCG (PCG with DAMG as a preconditioner) to the solution of the coarse level equation. The resulting AMG methods are then applied to a practical example as a long beam. The numerical results verify the efficiency and robustness of the proposed AMG algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

Interfacial Properties of Aqueous Nonionic Fluorocarbon Surfactant Solutions

The equilibrium, dynamic surface tensions, and surface dilatational elasticity of aqueous solutions of nonionic fluorocarbon surfactant are reported. The critical micellar concentration, CMC (0.023 mM) and equilibrium surface tension (24.6 m N . m^?1) at CMC were measured by Wilhelmy plate method for aqueous solution of C₈F₁₇SO₂N(C₃H₇)(C₂H₄O)_nH (n=20), abbreviated as EF122A. The surface tension decay is slower for C₈F₁₇SO₂N(C₃H₇)(C₂H₄O)_nH (n=10) system, abbreviated as EF122B compared to the EF122A system over short time region, which indicates the slow transport of the surfactant molecules to the surface. The relaxation time for surface tension decay is estimated by fitting a series of exponentials to the dynamic surface tension data and it decreases with temperature for EF122A. Slow exchange of monomers between bulk and interface is reflected in the high elasticity value of the air‐liquid interface for EF122B compared with EF122A within measured frequency window (0.125–1.25 Hz).