流形元法固定边界约束处理研究

在数值流形方法中,对于材料的固定边界,一般采用罚函数的方法进行处理,即在固定边界上设置刚性弹簧约束其位移来实现固定约束条件的近似满足。罚函数法在理论上不是严格的固定约束处理方法,罚弹簧的布置与弹簧刚度的大小对模拟的效果都会产生影响。基于流形单元上位移函数的组成提出了流形方法固定边界约束处理的新方法,在组成流形单元的物理覆盖上,通过取消相应的覆盖函数在流形单元位移函数中的组成来实现双向固定的约束条件,通过使用只包含单方向位移的覆盖函数使x向固定约束条件和y向固定约束条件得到实现,推导了相应固定约束条件下的流形单元刚度矩阵的数值计算格式。该方法严格满足固定约束的物理意义,简化了固定边界的处理,并经算例证明是有效和准确的,有利于数值流形方法的程序实现和工程应用。     

工程施工路径相关性的数值仿真

本文将损伤理论与时变力学耦联，形成用于模似施工的损伤时变力学方法，文中推导了基本方程和数值化算式。利用时变分析法对某地下煤层开采过程进行计算机仿真分析，给出了三种不同路径下开采引起地表沉陷的时空演化图，并进行对比分析。对体现出的位移、损伤与施工路径相关现象进行了探讨，并定量给出损伤时变分析下不同开采路径造成的最终力学状态的差别。本文中损伤时变力学方法为施工过程分析提供了一种新方法与手段。     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Reasearch and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972∼), Doctor (E-mail: xiegming@mech.pku.edu.cn)     

声焦散线及其与应力强度因子的关系

 根据焦散线的形成原理，以及含I型裂纹试件受力前后光程差与 声程差表达式的相似性，提出了声焦散线的概念，得到了声焦散线沿 横向最大尺寸与应力强度因子的关系，为通过声焦散线法确定应力强 度因子打下了基础.     

识别求解路径上奇异点的一个计算方法

提出一个在路径跟踪计算中识别分支点和极值点的实用方法，给出了算例。     

动态裂纹扩展中的分形效应

假设裂纹顶端沿着分形轨迹运动，建立了裂纹扩展的分形弯折（ｋｉｎｋｉｎｇ）模型来描述裂纹的动态扩展。根据这个模型，我们推导了分形裂纹扩展对劝态应力强度和裂纹速度的影响．动态应力强度因子与表观应力强度因子之比Ｋ（ｌ（ｔ），Ｖ）／Ｋ（Ｌ（ｔ），Ｏ）是表观裂纹速度Ｖ＿Ｏ，材料微结构参数（ｄ／Δａ），分维Ｄ和裂纹扩展路径的弯折角θ的函数。本文研究结果表明：在分形裂纹扩展中，表观（或量测）的裂纹速度Ｖ＿Ｏ很难接近Ｒａｙｌｅｉｇｈ波速Ｃ＿ｒ．动态断裂实验中Ｖ＿Ｏ明显低于Ｃ＿ｒ的原因可能是分形裂纹扩展效应所致。材料的微结构，裂纹扩展路径的分维和弯折角均很强地影响动态应力强度因子和裂纹扩展速度。     

一维非线性黏弹体和黏塑性体中的最优应变路径

得出了一维非线性黏弹体和黏塑性体中最优应变路径方程，并揭示了它们的某些特性，如：（１）当非线性黏弹本构方程中的黏性部分与应变的关系具有上凸形式时，相应的最优应变路径具有下凸性质；（２）对于过应力和Ｂｏｄｎｅｒ－Ｐａｒｔｏｎ黏塑性体，它们的最优应变路径是塑性应变为线性形式，即塑性应变率为常数，而弹－黏塑性体的最优应变路径则不同。     

Mathematical Modeling for One New Method of Breaking Ice Cover

The spatial problem of determining the stress-strain state of an ice plate of finite thickness broken by a patented method is solved using the theory of small elastoplastic strains and a proven numerical method. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 139–146, March–April, 2006.     

Effects of timber skidding on chemical characteristics of herbaceous cover, forest floor and topsoil on skidroad in an oak (Quercus petrea L.) forest

This paper examines the effects of timber harvesting by skidding on some soil properties (sand, silt, clay, pH, organic carbon, bulk density and compaction), herbaceous cover (unit mass) and forest floor (unit weight) properties. Also N (%), P, K, Na, Ca, Mg, Fe, Zn, Cu and Mn (ppm) were determined in all herbaceous cover, forest floor and two soil depth (0–5 cm and 5–10 cm) on skidroad of an oak (Quercus petrea L.) stand in Istanbul Belgrad Forest – Turkey. In this study, obtained results are; the forest floor and the herbaceous cover amount on the skidroad have been found considerably lower than undisturbed area. There were some crucial changes in the characteristics of the soil which has been investigated down to 10 cm depth. Soil bulk density was found quite high in the samples taken from the skidroad subject to compaction compared to the ones on the undisturbed area. Nevertheless, no important difference had been detected between the skidroad and the undisturbed area at both soil depths in terms of organic carbon contents. Moreover, the soil acidity (pH) values showed noteworthy differences in the analysis of soil samples taken from both soil depths on the skidroad and on the undisturbed area. Fe and Cu contents of herbaceous samples on skidroad were significantly higher than undisturbed area. Forest floor on skidroad had significantly higher K content, and significantly lower Zn, Mn and N content compared to undisturbed area. P, Fe, Zn and Mn contents were found significantly lower in 0–5 cm soil depth on skidroad than undisturbed area. In 5–10 cm soil depth, concentrations of N, P, Fe, Zn and Mn were significantly lower, while Mg and Cu contents were significantly higher than undisturbed area. Results indicate that long-term harvest using skidding techniques on these sites had adversely affected soil cation concentrations, physical soil conditions and mass of herbaceous cover and forest floor.     

Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids

We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite type. This generalises a result of Matsumoto and Matui from the irreducible to the general case. We also prove that a pair of one-sided shift spaces of finite type are continuously orbit equivalent if and only if their groupoids are isomorphic, and that the corresponding two-sided shifts are flow equivalent if and only if the groupoids are stably isomorphic. As applications we show that two finite directed graphs with no sinks and no sources are move equivalent if and only if the corresponding graph $C^{?}$-algebras are stably isomorphic by a diagonal-preserving isomorphism (if and only if the corresponding Leavitt path algebras are stably isomorphic by a diagonal-preserving isomorphism), and that two topological Markov chains are flow equivalent if and only if there is a diagonal-preserving isomorphism between the stabilisations of the corresponding Cuntz–Krieger algebras (the latter generalises a result of Matsumoto and Matui about irreducible topological Markov chains with no isolated points to a result about general topological Markov chains). We also show that for general shift spaces, strongly continuous orbit equivalence implies two-sided conjugacy.