复合Logistic映射中的逆分岔与分形

利用分岔图，揭示出复合Logistic映射可按倍周期分岔走向混沌，且混沌区中存在混沌危机及逆分岔现象．同时，分析了复合Logistic映射临界点的轨道，给出了复合Logistic映射Mandelbrot-Julia集(简称M-J集)的定义，推广了Welstead和Cromer所提出的周期点查找技术，并利用该技术，构造出一系列复合Logistic映射的M-J集．在此基础上，研究了M-J集的对称性；探索了M集周期区域分布的拓扑不变性；通过定性地建立M集上J集的整体刻画，发现M集包含了J集构造的大量信息．     

嵌岩桩桩端承载力探讨

以往嵌岩桩的试验资料表明,当上覆岩土层较薄、嵌岩桩的入岩深度较小时,嵌岩桩的极限端承力对桩的承载能力起主导作用。为求出桩端极限承载力的表达式,本文将嵌岩段以上岩土层自重视为作用在基岩半平面上的均布荷载,把桩端合力分解为相对简单的荷载作用于基岩平面上,利用滑移线理论并通过叠加的方法分析出桩端基岩破坏时的最危险点。然后根据Mindlin课题求出该点的应力,运用Griffith准则的Murrell推广导出桩端极限承载力的公式,并指出了此公式的适用范围。最后结合工程实际进行了对比分析,表明本文方法具有一定的实用性。     

多点碰撞动力学的规范求解

物体间的碰撞是工程技术中一个重要研究课题．大多数的研究工作都是集中在多刚体系统碰撞动力学问题的研究．在多刚体系统中，两个刚体之间是用一个铰连接的．但是，还存在另一类型的碰撞系统，在这类碰撞系统中，相碰的物体间没有铰存在．物体可能是自由的，也可能是被其周围环境约束的，但在物体之间没有铰的联系，这种碰撞问题称作为“分离式碰撞问题”，物体间的相互联系和相互作用仅仅在碰撞过程中存在．本文对这类“分离式碰撞问题”进行了研究，并且给出了一组解决这类问题的通用公式．这些公式可以方便地编程和计算，从而实现了多物体间的多点碰撞的动力学求解     

滑动最小二乘插值函数配点法

给出了利用滑动最小二乘法构造加权残值法中试函数的方法，对试函数中的基函数以及权函数的选取提出了建议；该试函数适用于任何定解问题，采用配点法求出试函数中的系数，进而可得到定解问题的近似解，利用该试函数对简支板的挠曲，悬臂梁的弯曲，以及中心具有小圆孔的大板的均匀拉伸等三个例子进行了数值计算，并与理论结果进行对比，同时还检验了该法的精度对结点数，配点数，以及结点影响半径的依赖情况，结果表明，该试函数适用于多种边值问题，且精度高，该法简化了选择试函数的过程，尤其适用于工程中的各种数值计算。     

Dynamical analysis of cavitation for a transversely isotropic incompressible hyper-elastic medium: Periodic motion of a pre-existing micro-void

In this paper, the dynamical cavitation behavior is analyzed for a sphere composed of a class of transversely isotropic incompressible hyper-elastic materials, where there is a pre-existing micro-void in the interior of the sphere. A second-order non-linear ordinary differential equation that governs the motion of the initial micro-void is obtained by using the boundary conditions. On analyzing the qualitative properties of the solutions of the differential equation, some interesting conclusions are proposed. It is proved that the number of equilibrium points of the differential equation depends on the values of the material parameters, and that the phase diagrams of the equation are closed, smooth and convex trajectories. For any prescribed surface tensile dead-loads, the motion of the initial micro-void undergoes a non-linear periodic oscillation. The dependence of the periodic motion of the initial micro-void on material parameters and the radius of the initial micro-void is examined, and numerical results are also provided. It is worth pointing out that the conclusions in this paper can be used to describe approximately the physical implications of the dynamical formation of a cavity in the sphere.     

Gelation study of high processability and high reliability ternary systems based on benzoxazine, epoxy, and phenolic resins for an application as electronic packaging materials

 Fourier transform mechanical spectroscopy technique (FTMS) is utilized as a powerful tool to study the sol-gel transition of covalent bonded polymeric network. Winter and Chambon criteria resulting from the fractal-geometry characteristic of the gel networks allow the determination of the gel point with only single experiment using this technique. The gelation behaviors of low melt viscosity ternary systems of benzoxazine, epoxy, and phenolic resins are investigated and analyzed by the technique in order to study the effect of epoxy diluent on the rheological property development before and after the gel points. The gel time at 140 °C ranges from 5 min to 30 min and less than 5 min at 180 °C for all tested ternary system compositions. The gelation of the ternary mixture shows an Arrhenius-type behavior and the gel time can be well-predicted by the Arrhenius equation. Received: 23 November 1999 Accepted: 2 January 2001     

Positive Solutions of Boundary Value Problems for Second-Order Singular Nonlinear Differential Equations

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｈａｌｌｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｓｉｎｇｕｌａｒｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ (ＢＶＰ)ｕ″ ｇ(ｔ)ｆ(ｕ) =0 ,　　 0 <ｔ<1 ,αｕ(0 ) -βｕ′(0 ) =0 ,　　γｕ(1 ) δｕ′(1 ) =0 ,(1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,ρ:=βγ αγ αδ>0 ,ｆ∈Ｃ([0 ,∞ ) ,[0 ,∞ ) ) ,ｇｍａｙｂｅｓｉｎｇｕｌａｒａｔｔ=0ａｎｄ/ｏｒｔ=1 .Ｔｈｉｓｐｒｏｂｌｅｍａｒｉｓｅｓｎａｔｕｒａｌｌｙｉｎｔｈｅｓｔｕｄｙｏｆｒａｄｉａｌｌｙｓｙｍｍｅｔ…     

Supersonic flow past a wedge on a flat plate. Laminar boundary layer separation and reattachment

Supersonic laminar flow past a two-dimensional “flat-plate/wedge“ configuration is numerically investigated. The pressures at the boundary layer separation and reattachment points are calculated over wide Mach and Reynolds number ranges. The minimum angles of the wedge surface inclination at which a return flow occurs are determined. The results are presented in the form of generalized Mach-number-dependences of the theoretical pressure on the wedge surface initiating boundary layer separation and the pressure at the boundary layer reattachment point.     

Insight into the physics of foam densification via numerical simulation

Foamed materials are increasingly finding application in engineering systems on account of their unique properties. The basic mechanics which gives rise to these properties is well established, they are the result of collapsing the foam microstructure. Despite a basic understanding, the relationship between the details of foam microstructure and foam bulk response is generally unknown. With continued advances in computational power, many researchers have turned to numerical simulation to gain insight into the relationship between foam microstructure and bulk properties. However, numerical simulation of foam microscale deformation is a very challenging computational task and, to date, simulations over the full range of bulk deformations in which these materials operate have not been reported. Here a particle technique is demonstrated to be well-suited for this computational challenge, permitting simulation of the compression of foam microstructures to full densification. Computations on idealized foam microstructures are in agreement with engineering guidelines and various experimental results. Dependencies on degree of microstructure regularity and material properties are demonstrated. A surprising amount of porosity is found in fully-densified foams. The presence of residual porosity can strongly influence dynamic material response and hence needs to be accounted for in bulk (average) constitutive models of these materials.     

A numerical approach to spherical indentation techniques for material property evaluation

In this work, some inaccuracies and limitations of prior indentation theories, which are based on experimental observations and the deformation theory of plasticity, are investigated. Effects of major material properties on the indentation load-deflection curve are examined via finite element (FE) analyses based on incremental plasticity theory. It is confirmed that subindenter deformation and stress-strain distribution from deformation plasticity theory are quite dissimilar to those obtained from incremental plasticity theory. We suggest an optimal data acquisition location, where the strain gradient is the least and the effect of friction is negligible. A new numerical approach to indentation techniques is then proposed by examining the FE solutions at the optimal point. Numerical regressions of obtained data exhibit that the strain-hardening exponent and yield strain are the two key parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides a stress-strain curve and material properties with an average error of less than 3%.