Homogeneous monotropic elastic rods: Normal uniform configurations and universal solutions

A number of simple solutions are obtained which are universal for an homogeneous monotropic elastic rod whose theory is based on a Cosserat-type model.

---

Sommario Si ottengono alcune soluzioni semplici che sono universali per una trave omogenea monotropica la cui teoria è basata su un modello alla Cosserat.

     

Multi-scale and multi-order singularity approach to non-equilibrium mechanics: Coupling of atomic-micro-macro damage

Offered in this work is the development of a macro/meso/micro model that covers the lineal scale of 10⁻¹¹ to 10⁰ by application of the volume energy density function. Boundary constraints and defect geometries are shown to play a role at the smaller scale in the same way as those at the macroscopic scale. Different orders of stress (or energy density) singularities are used to describe the defect geometry and prevailing constraint via the boundary conditions in a way similar to singularity adopted in classical fracture mechanics. Two classes of singularities have been identified in addition to classical one without violating the finiteness conditions of the local displacement and energy density. Still the connection of results from the different scales is no small task and is made possible by application of a scale multiplier. It is determined by considering the interactive effects of the parameters at the different scales from the atomic to the macroscopic. Unlike the classical boundary value problem approach, application of the scale multiplier has led to closed-form asymptotic multiscale solutions that otherwise would not have been made possible. The procedure is demonstrated for the anti-plane shear of a macro-micro-atomic model that accounts for imperfection at the different scales Published in Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 3–22, January 2006.     

深部土高压卸载变形结构性量化参数确定及本构模型

用取自山东巨野矿区埋深300～600m的深部粘土样,在三轴伺服仪上进行原状和重塑土的高压三轴卸载试验,对比分析其变形特点;提出一种描述深部土高压卸载变形与强度连续变化的土结构性参数的方法,并根据三轴卸载试验结果,确定了巨野矿区深部土高压卸载变形结构性参数,建立了描述巨野矿区深部土高压卸载结构性本构模型。     

基于数字图像的土、岩和混凝土内部结构定量分析和力学数值计算的研究进展

土、岩及混凝土是一种内部结构极其复杂的材料,内部细观组成和结构决定了它们在外力作用下内部应力和应变等物理场的分布状态,在很大程度上控制了它们的宏观力学响应和破坏机理和过程。自1995年以来,数字图像处理技术作为一种材料细观空间结构及几何形态的精确量测和数字表述手段快速地被应用于沥青混凝土、水泥混凝土、土和岩体材料细观结构定量分析中来。本文在研究相关文献的基础上,分析和研究了数字图像技术在土、岩及混凝土内部结构定量分析和力学数值计算中的发展过程和研究成果,内容包括:单个骨料颗粒形态特征定量分析;土、岩和混凝土内部结构定量分析;岩体结构定量分析中的应用;基于数字图像处理的土、岩和混凝土细观结构力学计算。在此基础上,本文进一步对数字图像技术在岩土领域中的应用进展及未来的发展趋势进行了探讨,认为数字图像作为一种空间分布测量手段和数字表述方法使得它具有巨大的潜力,特别是在岩土领域的纵深发展过程中,它可能实现考虑细微观结构性的岩土力学和工程分析和预测的、新的方法和理论。     

On the existence of self-similar solutions of the equations governing unsteady flow through a porous medium

In this paper the conditions for the existence of self-similar solutions of the equations governing unsteady flows through a porous medium are presented and discussed. The first two sections deal with the case of non-Newtonian fluids of power-law behavior; the third section analyzes the case of non-Darcy gas flows. The boundary and initial conditions occuring currently in a large class of fluid mechanics problems, of practical interest in engineering, are considered.     

Stress Concentration at Interacting Spherical Inclusions in a Transversely Isotropic Body

An elastic-equilibrium problem is rigorously solved for a transversely isotropic body containing a finite number of arbitrarily arranged and oriented transversely isotropic spherical inclusions or an infinite periodic array of such inclusions. The solution is found based on the superposition principle for general solutions of single-particle problems and the addition theorems for partial vector solutions of the elastic equilibrium equations. The numerical results presented allow assessing the influence of matrix anisotropy on the stress concentration between inclusions     

Exact solutions of some general nonlinear wave equations in elasticity

A similarity analysis of a nonlinear wave equation in elasticity is studied; in particular, one with anharmonic corrections. The symmetry transformation give rise to exact solutions via the method of invariants. In some cases, graphical figure of the solutions are presented. Furthermore, we consider some cases wherein the velocities of the longitudinal and transversal plane waves are variable. Finally, a brief discussion on how a symmetry analysis on a perturbation of the elasticity equation can be pursued.     

Traveling Waves of a Singularly Perturbed System of Integral–Differential Equations Arising from Neuronal Networks

A nonlinear nonlocal model arising from synaptically coupled neuronal networks with two integral terms is considered. The existence and stability of several traveling wave solutions are established by using ideas in differential equations and functional analysis. Steady-state solutions of some inhomogeneous integral–differential equations are also investigated. We consider several types of kernel functions: (I) positive functions, such as and , where ρ>0 is a constant; (II) nonnegative kernels with compact supports, for examples, (i) 1$$" align="middle" border="0"> , and (ii) {\pi\over 2}$$" align="middle" border="0"> ; (III) Mexican hat type kernel functions, such as and , where A>B>0 and a>b>0 are constants.Dedicated to Professor Yulin Zhou and Professor Boling Guo on the Occassions of their birthdays.     

Improved operator comfort and off-road capability through pendulum arm technology

The Nordic forest industry requires just-in-time wood deliveries. Operations must continue regardless of season, weather and terrain. Soil compaction and deep ruts must be avoided while providing high performance and a reasonable working environment for operators.The Xt28 pendulum arm forwarder is a full-size concept forwarder with six hydrostatic propelled wheels on pendulum arms built on a three-piece frame connected with two articulation joints. The Xt28 concept machine was tested according to Skogforsk standard machine tests. Rut depth test focused on soil interaction where rut depth was measured related to number of passes. Machine dynamics were measured using standardized test track with focus on operator comfort.The project proved the potential of pendulum arm technology in off-road transportation. Automatic pendulum arm levelling, equalized ground pressure between wheels and improved operator comfort through reducing adverse vibrations and roll angles, simultaneously reducing dynamic forces transferred to the forest floor. Pendulum arm technology improves travel speed in adverse terrain, providing unparalleled side slope capability and enhanced productivity.     

Overwinter changes to near-surface bulk density, penetration resistance and infiltration rates in compacted soil

Previous studies at Yakima Training Center (YTC), in Washington State, suggest freeze-thaw (FT) cycles can ameliorate soil compacted by tracked military vehicles [J. Terramechanics 38 (2001) 133]. However, we know little about the short-term effects of soil freezing over a single winter. We measured bulk density (BD), soil penetration resistance (SPR), and steady-state runoff rates in soil newly tracked by an Abrams tank and in uncompacted soil, before and after a single winter at YTC. We similarly measured BD, SPR and saturated hydraulic conductivity (k_fs) in simulated tank tracks at another site near Lind Washington. Average BD was significantly greater in tank ruts at YTC and in simulated tracks at the Lind site than in uncompacted soil soon after tracking and did not change significantly during the winter of 1997–1998. Measurements of SPR were strongly influenced by soil moisture. When soil was moist or tracks were newly formed, SPR was significantly higher in tank ruts than in uncompacted soil from the surface to a depth of about 10–15 cm. The greatest average SPR in compacted soil was observed between 4 and 6 cm depth. We observed less difference in SPR between tank ruts and uncompacted soil near-surface at YTC as the time after trafficking increased. We observed highest SPR ratios (compacted rut:undisturbed) in fresh tracks near the surface, with lower ratios associated with increasing track age or soil depth, indicating that some recovery had occurred at YTC near-surface. However, we did not observe a similar over-winter change in SPR profiles at the Lind site. Rainfall simulator data from YTC showed higher steady-state runoff rates in tank ruts than over uncompacted soil both before and after winter. However, more time was required to reach steady-state flow in tank ruts and the proportion of runoff was slightly lower in May 1998 than in August 1997. At the Lind site, k_fs was lower in newly compacted soil than in one-year old compacted soil or uncompacted soil. Our data suggest that indices of water infiltration such as steady-state runoff rates or k_fs, are more sensitive indicators of soil recovery after compaction than are BD or SPR.