Bending and buckling of a class of nonlinear fiber composite rods

An investigation of the mechanics of bending and buckling is carried out for a class of nonlinear fiber composite rods composed of embedded unidirectional fibers parallel to the rod axis. The specific class of composite considered is one in which the fibers interact with the matrix through a nonlinear Needleman-type cohesive zone [Needleman, A., 1987. A continuum model for void nucleation by inclusion debonding. ASME J. Appl. Mech. 54, 525-531; Needleman, A., 1992. Micromechanical modelling of interfacial decohesion. Ultramicroscopy 40, 203-214]. The primary decohesive mechanism active in bending and buckling of these composite rods is shear slip along the fiber-matrix interfaces allowing the use of a previously developed constitutive relation for antiplane shear response [Levy, A.J., 2000b. The fiber composite with nonlinear interface—part II: antiplane shear. ASME J. Appl. Mech. 67, 733-739]. The formulation requires the specification of a potential interface force-slip law that is assumed to permit interface failure in shear.Four cases of the bending and shearing of beams (concentrated or uniform load on a cantilever or a simply supported beam) are analyzed, each of which exhibits qualitatively distinct response. For certain values of interface parameters, the beam deflection or its gradient at a fixed location can change discontinuously with load. Furthermore, for interface parameter values within a certain range, singular surfaces will exist in uniformly loaded beams where there is a non-uniform distribution of shear stress along the beam length. These singular surfaces divide the beam into regions of maximal and minimal fiber slip and propagate with a rate that varies inversely as the square of the applied load. For other parameter values, singular surfaces will not exist and fiber slip will be diffuse.For the class of nonlinear composite considered, bifurcation and imperfection buckling of pinned-pinned columns is analyzed. For bifurcation buckling, a nonlinear eigenvalue problem is derived and the solution is obtained by Galerkin's method. It is demonstrated that critical loads are influenced by the initial slope, and hence the linear portion, of the interface force-slip relation but the post-buckling response, which in some sense resembles that of plastic buckling, is affected by the entire interface constitutive relation. Imperfection buckling is analyzed in a similar manner by assuming a slight initial curvature of the rod. Sensitivity of the response to imperfection magnitude is discussed as well.     

含有多个涂层压电纤维复合材料的平面问题研究

压电纤维在未来的复合材料结构健康监测中具有重要作用．本文基于横观各向同性压电材料位移和应力连续条件以及经典的复势函数理论,讨论了同时受到平面内机械载荷和出平面电载荷作用时含有多个带涂层压电纤维的无限大线弹性基体的平面力学问题．首先将线弹性基体、涂层和压电纤维的应力场、位移场表示成复势函数,然后通过横观各向同性压电材料和线弹性材料的位移和应力连续条件确定复势函数表达式．将得到的复势函数表达式代入线弹性基体、涂层和压电纤维的的应力场、位移场公式可确定其应力场和位移场．最后,通过定量的案例讨论了涂层的材料属性对线弹性基体应力场的影响．案例分析表明涂层的材料属性对压电复合材料的应力场有重要的影响．     

等边角钢四肢方阵式格构柱截面直接设计法

本文考虑剪切变形影响,将等边角钢四肢方阵式格构柱分为缀板式和缀条式两种,分别导出截面直接设计表达式,符合现行《钢结构设计规范》ＧＢＪ１７－８８的要求和习惯,便于工程设计应用．     

Retention time and effective separation factor in series-coupled columns with different stationary phases

Basic expressions are derived for both the retention time and the effective separation factor in serially coupled GC columns. The retention time is determined by two main parameters. The first is the fractional time spent by an unretarded solute in each column which, in turn, is determined by the relative column lengths and flow velocities through each column. The second parameter is the relative mass distribution coefficient of a particular solute in each column; a variable that can be adjusted by changing the relative temperatures of the columns. The expression for the effective separation factor relates the measured separation factor for the series combination to the separation factors on the individual columns, the fractional time spent by an unretarded peak in each column, as well as the relative values of the mass distribution coefficients of a particular solute on the different columns.     

Nonseparating trees in 2-connected graphs and oriented trees in strongly connected digraphs

Mader (2010) conjectured that for every positive integer $k$ and every finite tree $T$ with order $m$, every $k$-connected, finite graph $G$ with $\delta \left(G\right)\ge \lfloor \frac{3}{2}k\rfloor +m-1$ contains a subtree $T^{\prime }$ isomorphic to $T$ such that $G-V\left(T^{\prime }\right)$ is $k$-connected. The conjecture has been verified for paths, trees when $k=1$, and stars or double-stars when $k=2$. In this paper we verify the conjecture for two classes of trees when $k=2$.For digraphs, Mader (2012) conjectured that every $k$-connected digraph $D$ with minimum semi-degree $\delta \left(D\right)=min\{{\delta }^{+}\left(D\right),{\delta }^{-}\left(D\right)\}\ge 2k+m-1$ for a positive integer $m$ has a dipath $P$ of order $m$ with $\kappa (D-V\left(P\right))\ge k$. The conjecture has only been verified for the dipath with $m=1$, and the dipath with $m=2$ and $k=1$. In this paper, we prove that every strongly connected digraph with minimum semi-degree $\delta \left(D\right)=min\{{\delta }^{+}\left(D\right),{\delta }^{-}\left(D\right)\}\ge m+1$ contains an oriented tree $T$ isomorphic to some given oriented stars or double-stars with order $m$ such that $D-V\left(T\right)$ is still strongly connected.     

The e-exchange basis graph and matroid connectedness

Let $M$ be a matroid and $e\in E\left(M\right)$. The $e$-exchange basis graph of $M$ has vertices labeled by bases of $M$, and two vertices are adjacent when the bases labeling them have symmetric difference $\{e,x\}$ for some $x\in E\left(M\right)$. In this paper we show that a connected matroid is exactly a matroid with the property that for every element $e\in E\left(M\right)$, the $e$-exchange basis graph is connected.     

Coarser connected metrizable topologies

We show that every metric space, X, with w(X)?c has a coarser connected metrizable topology.     

Quotients of Incidence Algebras and the Euler Characteristic

In this note, we show that, if A ? kQ _A /I _A is a schurian strongly simply connected algebra given by its normed presentation, and Σ is the unique poset whose Hasse quiver coincides with Q _A , then A ? kΣ if and only if I _A has a generating set consisting of exactly χ(Q _A ) elements, where χ(Q _A ) is the Euler characteristic of Q _A . We also prove that a quotient of an incidence algebra A = kΣ/J is strongly simply connected if and only if A is simply connected and kΣ is strongly simply connected.     

On the Quasi-Stratified Algebras of Liu and Paquette

Liu and Paquette defined a class of artin algebras, more general than the standardly stratified ones, called quasi-stratified algebras. Not only is the Cartan Determinant Conjecture (CDC) true for these algebras, so is its converse. This article shows that this class of algebras is preserved under “pruning” sources and sinks from the left quiver. It compares the classes of quasi-stratified and left serial algebras, as well as quasi-stratified and gentle algebras. Holm has shown that the CDC holds for gentle algebras; the converse is also established. It is shown when a Yamagata family of algebras of large finite global dimension yield quasi-stratified ones and constructs quasi-stratified elementary algebras from smaller ones.