Natural vibrations of a strip made of a composite material with a locally curved structure

The possibility of using the finite-element method for investigating two-dimensional problems on natural vibrations in the mechanics of composite materials with curved structures is considered. With the example of a hinge-supported strip made of a composite material with a locally curved structure, the influence of geometrical and mechanical parameters of the strip on its eigenfrequencies is examined. It is established that the presence of local curving in the structure of strip material decreases the magnitude of eigenfrequencies.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 71–78, January–February, 2005.     

André-Quillen cohomology and rational homotopy of function spaces

We develop a simple theory of André-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent CW-complexes. This puts certain results of Sullivan in a more conceptual framework.     

基于混合状态变量的中厚板条形传递函数解

基于Mindlin板理论和改进的混合能量变分原理,建立了矩形区域中厚板问题的条形传递函数解法。该方法将矩形板在一个方向上离散为多个条形单元,而条形单元状态变量的解在单元的横向采用多项式插值,在单元的纵向直接解析求解。通过定义结点变量,并利用结点位移连续和力平衡条件,将多个简单子区域的解进行组装,可构造出分析复杂形状、复杂边界条件中厚板的条形传递函数解。数值算例表明,条形传递函数方法具有很高的计算精度。     

DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL

The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.     

非均质材料梯度多墙结构非线性屈曲特性

非均质、各向异性材料梯度多墙结构充分利用了材料性质连续、渐进、变化的物理力学性能,现已广泛应用于飞行机翼结构和汽车轻量化结构．在层合板屈曲理论的基础上,针对梯度多墙结构这一具体结构形式,采用当量刚度方法,建立了相应的本构关系和非线性屈曲控制方程,求解得到不同复杂边界条件及组合载荷下的屈曲临界载荷,通过试验分析验证,计算结果可以较好地满足工程设计．研究结果表明:梯度材料能有效地减小界面中的应力集中,减弱材料中初始缺陷的作用,从而不同程度地提高了材料的强度和韧性．     

分次反单本原根

本文给出分次情形的反单本原根SJGG,当群G满足|G|<∞,证明了SJG=SJref=SJG,其中SJref和SJG分别表示反射反单本原根和限制反单本原根.而且讨论了SJG的分次补根.     

分次环的分次根

给出了建立分次环根的一般方法．作为其应用，建立了分次环的分次Brown—McCoy根，并给出了Brown—McCoy半单分次环的结构定理．     

Compact DG modules and Gorenstein DG algebras

When the base connected cochain DG algebra is cohomologically bounded, it is proved that the difference between the amplitude of a compact DG module and that of the DG algebra is just the projective dimension of that module. This yields the unboundedness of the cohomology of non-trivial regular DG algebras. When A is a regular DG algebra such that H(A) is a Koszul graded algebra, H(A) is proved to have the finite global dimension. And we give an example to illustrate that the global dimension of H(A) may be infinite, if the condition that H(A) is Koszul is weakened to the condition that A is a Koszul DG algebra. For a general regular DG algebra A, we give some equivalent conditions for the Gorensteiness. For a finite connected DG algebra A, we prove that D^c(A) and D^c(A ^op) admit Auslander-Reiten triangles if and only if A and A ^op are Gorenstein DG algebras. When A is a non-trivial regular DG algebra such that H(A) is locally finite, D^c(A) does not admit Auslander-Reiten triangles. We turn to study the existence of Auslander-Reiten triangles in D_lf^b(A) and D_lf^b (A ^op) instead, when A is a regular DG algebra. This work was supported by the National Natural Science Foundation of China (Grant No. 10731070) and the Doctorate Foundation of Ministry of Education of China (Grant No. 20060246003)     

On the structure of graded <Emphasis Type="Italic">λ</Emphasis>-Hopf algebras

Let G be an abelian group, B the G-graded λ-Hopf algebra with A being a bicharacter on G. By introducing some new twisted algebras （coalgebras）, we investigate the basic properties of the graded antipode and the structure for B. We also prove that a G-graded λ-Hopf algebra can be embedded in a usual Hopf algebra. As an application, it is given that if G is a finite abelian group then the graded antipode of a finite dimensional G-graded A-Hopf algebra is invertible.     

一类广义Heisenberg-Virasoro代数的导子

主要研究了一类非有限分次的广义Heisenberg-Virasoro代数HV,并给出了HV导子的具体结构.为了计算HV的导子Der HV,可以把它分解成内导子adHV和阶为零次的导子(Der HV)_0之和.