Failure prediction of hybrid composite using Arcan's device and Drucker-Prager model

Hybrid composites are promising materials due the possibility of combining the properties of different fiber types with those of the polymeric matrix. The higher number of phases involved in this kind of material and the hydrostatic component of polymer behavior make it unfeasible to use classic models for failure prediction, like the Von Mises or Treska models. In this study, a modified Arcan's device was applied for mechanical characterization of a polymeric blend matrix composite reinforced with randomly oriented continuous fibers (a clutch disc) to generate combined loading conditions. Experimental results were applied in the Von Mises and Drucker-Prager theoretical models for failure prediction. Additionally, scanning electron microscopy (SEM) was applied to analyze the fracture surface. The failure envelope provided by the Drucker-Prager model fit the experimental results, making it a promising tool for predicting the behavior of this type of hybrid composite.     

Series solutions of unsteady MHD flows above a rotating disk

The series solutions of unsteady flows of a viscous incompressible electrically conducting fluid caused by an impulsively rotating infinite disk are given by means of an analytic technique, namely the homotopy analysis method. Using a set of new similarity transformations, we transfer the Navier–Stokes equations into a pair of nonlinear partial differential equations. The convergent series solutions are obtained, which are uniformly valid for all dimensionless time 0 ≤ τ < ∞ in the whole spatial region 0 ≤ η < ∞. To the best of our knowledge, such kind of series solutions have never been reported. The effect of magnetic number on the velocity is investigated.     

On sofic actions and equivalence relations

The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes? Embedding Problem, and prove the equivalence of these two definitions. We introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic. We also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic.     

A semi-finite algebra associated to a subfactor planar algebra

We canonically associate to any planar algebra two type II_∞ factors M_±. The subfactors constructed previously by the authors in Guionnet et al. (2010) [6] are isomorphic to compressions of M_± to finite projections. We show that each M_± is isomorphic to an amalgamated free product of type I von Neumann algebras with amalgamation over a fixed discrete type I von Neumann subalgebra. In the finite-depth case, existing results in the literature imply that M₊≅M₋ is the amplification a free group factor on a finite number of generators. As an application, we show that the factors Mj constructed in Guionnet et al. (in press) [6] are isomorphic to interpolated free group factors L(F(rj)), rj=1+2δ−2j(δ−1)I, where δ² is the index of the planar algebra and I is its global index. Other applications include computations of laws of Jones-Wenzl projections.     

On the double commutant of Cowen-Douglas operators

Let T be a Cowen-Douglas operator. In this paper, we study the von Neumann algebra V^?(T) consisting of operators commuting with both T and T^? from a geometric viewpoint. We identify operators in V^?(T) with connection-preserving bundle maps on E(T), the holomorphic Hermitian vector bundle associated to T. By studying such bundle maps, the structure of V^?(T) as well as information on reducing subspaces of T can be determined.     

基于能量辨识的非线性静电-结构系统的自由度缩减建模方法

给出了一种基于系统能量函数辨识的静电致动微薄板系统自由度缩减建模方法.从Von Karman应变-位移关系式出发,推导出以广义模态坐标为变量的系统动能、应变能以及电容函数的函数表达式.为了将应变能以及电容函数写成广义模态坐标的多变量多项式形式,利用一系列经静态非线性结构有限元计算的结果,拟合得到多变量多项式的未知系数.由Lagrangian方程获得原系统的自由度缩减模型.利用该模型对器件的静/动态特性进行仿真,其计算费用很低.与有限元结果比较,验证了建模方法的正确性.     

The spectral method and numerical continuation algorithm for the von Kármán problem with postbuckling behaviour of solutions

In this paper a spectral method and a numerical continuation algorithm for solving eigenvalue problems for the rectangular von Kármán plate with different boundary conditions (simply supported, partially or totally clamped) and physical parameters are introduced. The solution of these problems has a postbuckling behaviour. The spectral method is based on a variational principle (Galerkin’s approach) with a choice of global basis functions which are combinations of trigonometric functions. Convergence results of this method are proved and the rate of convergence is estimated. The discretized nonlinear model is treated by Newton’s iterative scheme and numerical continuation. Branches of eigenfunctions found by the algorithm are traced. Numerical results of solving the problems for polygonal and ferroconcrete plates are presented. Communicated by A. Zhou.     

Continuity and generators of dynamical semigroups for infinite Bose systems

For a class of quasifree quantum dynamical semigroups on the algebra of the canonical commutation relations (CCR) we give sufficient conditions for these semigroups to extend to ultraweakly continuous semigroups of normal operators on the von Neumann algebra associated with a representation of the CCR. Then the explicit form of the generators of the extended semigroups is calculated.