尖锥头长杆弹侵彻的界面击溃分析

在Alekseevski-Tate模型基础上, 理论分析了尖锥头长杆弹的界面击溃过程, 分别给出在锥头侵蚀阶段和弹身侵蚀阶段的弹体速度下降及质量侵蚀计算公式; 随后分析弹体的动能损失, 讨论半锥角对弹体动能损失的影响. 通过分析小子弹撞击陶瓷/金属复合靶板的例子, 验证了该理论的正确性, 并对比分析了尖锥头长杆弹与小子弹及平头长杆弹在界面击溃中动能损失之间的差异.      

理论力学教材的发展趋势

从历史发展的角度讨论理论力学教材的发展趋势．列举一些近50年来的优秀教材，并总结出理论力学教材内容改进的4种趋势：即突出分析力学、理论体系的几何化、加强动力系统与动力系统定性理论和突出变换群与不变量理论．并且提出了一些作为基础教材改革的一些设想，还附带了一个改革内容的简要提纲．     

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.     

《理论力学》学习中常见错误分析之一──动量矩定理的应用

《理论力学》学习中常见错误分析之一──动量矩定理的应用谢正桐，杨海兴（上海交通大学，上海２０００３０）本文根据一道具体习题的求解过程，指出动量矩定理应用中一个应注意的问题：不论是对定点还是对动点，应用动量矩定理必须取一般点而不能取特殊点。习题质量为ｍ...     

在理论力学教学中引入与自行车有关的力学分析

在理论力学教学中引入与自行车有关的力学分析李文玲，刘元懿（西安建筑科技大学基础部，西安７１００５５）（合肥工业大学，合肥２３０００９）理论力学课程在工程和现代科技中有广泛应用，它还可以应用于丰富多彩的文娱、体育，以及日常生活中．如踢足球、打高尔夫球、...     

分析和综合方法在理论力学中的应用

剖析了分析和综合方法在理论力学学科体系的建立及研究方法中的应用,理解这些应用,对于提高教学和学习效果大有裨益．     

风沙运动的沙粒带电机理及其影响的研究进展

土壤风蚀以及沙尘暴是人类面临的重大自然环境灾害之一,它直接关系着人类的生存环境和生活质量.许多国家和政府以及科学家们对此一直十分关注并开展了大量研究.由于大气和地表条件的多样性以及地表沙粒的运动与风场作用的相互耦合,导致风沙运动问题研究的复杂性.除此之外,伴随着对风沙运动机理的研究和对沙尘暴的观测,人们发现在风沙跃移运动和沙尘暴中的沙粒带有电荷并形成风沙电场.沙粒的运动不仅导致沙粒带电和风沙电场形成,而且也直接受到沙粒带电和风沙电场的影响.为了弄清风沙电的起因以及揭示其影响规律,研究人员对此进行了野外观测、实验室测量和理论推测等.本文将就这一问题重点介绍有关风沙运动中沙粒带电的机理、风沙电场分布规律、沙粒带电对风沙运动的微宏观物理量以及沙尘暴中沙粒带电对电磁波散射的影响等方面的实验和理论研究的基本概况和进展以及作者等人在此方面的研究工作.主要包含内容有:沙粒带电及其电场的基本实验测量,粒带电对风沙运动的影响,沙尘暴对电磁波衰减的影响研究以及有关风沙起电的机理研究等.同时,对这一研究领域中目前关注与存在的主要问题给予评述.图6参81      

粘弹层合板的自由振动和横向应力

Based on Reddy＇s layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of simply supported viscoelastic sandwich plate, showing good agreement with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lower-frequency free vibration, and the transverse normal stress is the main one in higher-frequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress＇s maximum value and the in-plane stress＇s maximum-value is obtained. The results show that the proposed method, and the adopted equations and programs are reliable.     

结构分析的光塑性法

本文围绕光塑性的模型理论、模型材料和应力—光学规律等基本问题的研究工作进行论述,提出一个可供实际应用的结构分析的光塑性方法,并在实际中作了初步应用。     

弯曲动脉壁非线性弹性力学性质的理论分析

血管壁非线性力学特性是探索心血管中的血液流动规律及脉搏波传播现象的一个重要前提．在血管力学研究中,直管动脉壁的本构方程已有相当深人的研究,唯独象主动脉弓那样的弯管动脉壁本构方程;至今还没有建立一个理论模型．文中在已有的直管动脉壁本构方程研究基础上,提出一个理论方法来分析弯曲动脉壁的非线性弹性力学性质,在弯曲动脉壁被模拟为均质、正交各向异性、不可压缩材料的前提下,作者从理论上建立了一个表达弯管动脉壁非线性弹性性质的三维ｅ指数型本构方程文中还探讨了弯曲动脉壁内的残余应变分析．     

Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

In the last decade, three dimensional discontinuous deformation analyses (3D DDA) has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block deformation. In this paper, 3D DDA is coupled with tetrahedron finite elements to tackle these two problems. Tetrahedron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topology shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Validation is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demonstrates the robustness and versatility of the coupled method.     

三维连续与非连续变形分析

将石根华博士所提出的二维非连续变形分析——Discontinuous Deformation Analysis（DDA）方法扩展到三维情况,并对三维不连续块体进行有限元网格剖分,即块体之间的接触采用DDA描述,块体内部的位移场和应力场则采用有限单元法描述,从而将三维DDA与有限元方法结合起来,增强了DDA方法与有限元方法解决实际工程问题的能力,实现了三维连续与非连续变形分析.给出了基本公式的推导过程和各子矩阵的形式.典型接触、碰撞算例证明了所提出方法的有效性和正确性.     

Explicit formulations for evaluation of velocity gradients using boundary‐domain integral equations in 2D and 3D viscous flows

In this paper, explicit boundary‐domain integral equations for evaluating velocity gradients are derived from the basic velocity integral equations. A free term is produced in the new strongly singular integral equation, which is not included in recent formulations using the complex variable differentiation method (CVDM) to compute velocity gradients (Int. J. Numer. Meth. Fluids 2004; 45 :463–484; Int. J. Numer. Meth. Fluids 2005; 47 :19–43). The strongly singular domain integrals involved in the new integral equations are accurately evaluated using the radial integration method (RIM). Considerable computational time for evaluating integrals of velocity gradients can be saved by using present formulation than using CVDM. The formulation derived in this paper together with those presented in reference (Int. J. Numer. Meth. Fluids 2004; 45 :463–484) for 2D and in (Int. J. Numer. Meth. Fluids 2005; 47 :19–43) for 3D problems constitutes a complete boundary‐domain integral equation system for solving full Navier–Stokes equations using primitive variables. Three numerical examples for steady incompressible viscous flow are given to validate the derived formulations. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic 3D axisymmetric problems in continuously non-homogeneous piezoelectric solids

The meshless local Petrov-Galerkin (MLPG) method is used to analyze transient dynamic problems in 3D axisymmetric piezoelectric solids with continuously inhomogeneous material properties. Both mechanical and thermal loads are considered here. A 3D axisymmetric body is created by rotation of a cross section around an axis of symmetry. Axial symmetry of geometry and boundary conditions reduces the original 3D boundary value problem into a 2D problem. The cross section is covered by small circular sub-domains surrounding nodes randomly spread over the analyzed domain. A unit step function is chosen as test function, in order to derive local integral equations on the boundaries of the chosen sub-domains, called local boundary integral equations (LBIE). These integral formulations are either based on the Laplace transform technique or the time-difference approach. The local integral equations are non-singular and take a very simple form, despite of inhomogeneous and anisotropic material behaviour across the analyzed structure. Spatial variation of all physical fields (or of their Laplace transforms) at discrete time instants are approximated on the local boundary and in the interior of the sub-domain by means of the moving least-squares (MLS) method. The Stehfest algorithm is applied for the numerical Laplace inversion, in order to retrieve the time-dependent solutions.     

三维非连续变形分析方法碰撞分析及其应用

将具有完备动力学理论的非连续变形分析(DDA)方法应用于块体碰撞研究。基于三维DDA(3D DDA)方法,按时步输出块体碰撞过程速度变化和接触嵌入量,进而得到块体碰撞恢复系数、冲量、冲击力。以此为参考指标,采用斜抛、面-面对心等碰撞模型,验证3D DDA方法模拟块体碰撞的有效性,并将3D DDA方法应用于多米诺骨牌倾倒、滚石边坡成灾及防护等算例分析,探讨了多米诺骨牌倾倒机制、滚石启动及运动行为、滚石灾害防护方案。结果表明:多米诺骨牌间距越大,同一块体被碰撞时间越迟,其最终稳定时间也越迟,与下一块体碰撞的动能越大;滚石运动呈侧向平动及转动三维运动特征,每一次碰撞,均引起动能、轨迹或状态的显著变化;滚石拦挡设施弹簧刚度越大,越先达到最大冲击力,最大冲击力随弹簧刚度的增加而减小;可结合树木阻挡效应,耗散滚石动能,降低滚石飞跃高度,使滚石灾害减轻或控制在防护范围以内。     

Effect of 2D Image Resolution on 3D Stochastic Reconstruction and Developing Petrophysical Trend

Multi-resolution digital rock physics (DRP) makes it possible to up-scale petrophysical properties from micron size to core sample size using two-dimensional (2D) thin section images. Resolution of 3D images and sample size are challenging problems in DRP where high-resolution images are acquired from small samples using inefficient and expensive micro-CT facilities. Three-dimensional stochastic reconstruction is an alternative approach to overcome these challenges. In this paper, we use multi-resolution images and investigate effect of 2D image resolution on 3D stochastic reconstruction and development of petrophysical trends for our two sandstone and carbonate original representative volume elements (RVEs). The proposed method includes three steps. In the first step, the spatial resolution of our original RVEs is decreased synthetically. In the second step, stochastic RVEs are realized for each resolution using two perpendicular images, correlation functions, and phase recovery algorithm. In the reconstruction method, a full set of two-point correlation functions (TPCFs) is extracted from two perpendicular 2D images. Then TPCF vectors are decomposed and averaged to realize 3D stochastic RVEs. In the third step, petrophysical properties like relative and absolute permeability as well as porosity and formation factor are computed. The output is used to develop trends for petrophysical properties in different resolutions. Experimental results illustrate that the proposed method can be used to predict petrophysical properties and reconstruct 3D RVEs for resolutions unavailable in the acquired 2D or 3D data.     

Stochastic estimation and proper orthogonal decomposition: Complementary techniques for identifying structure

The Proper Orthogonal Decomposition (POD) as introduced by Lumley and the Linear Stochastic Estimation (LSE) as introduced by Adrian are used to identify structure in the axisymmetric jet shear layer and the 2-D mixing layer. In this paper we will briefly discuss the application of each method, then focus on a novel technique which employs the strengths of each. This complementary technique consists of projecting the estimated velocity field obtained from application of LSE onto the POD eigenfunctions to obtain estimated random coefficients. These estimated random coefficients are then used in conjunction with the POD eigenfunctions to reconstruct the estimated random velocity field. A qualitative comparison between the first POD mode representation of the estimated random velocity field and that obtained utilizing the original measured field indicates that the two are remarkably similar, in both flows. In order to quantitatively assess the technique, the root mean square (RMS) velocities are computed from the estimated and original velocity fields and comparisons made. In both flows the RMS velocities captured using the first POD mode of the estimated field are very close to those obtained from the first POD mode of the unestimated original field. These results show that the complementary technique, which combines LSE and POD, allows one to obtain time dependent information from the POD while greatly reducing the amount of instantaneous data required. Hence, it may not be necessary to measure the instantaneous velocity field at all points in spacesimultaneously to obtain the phase of the structures, but only at a few select spatial positions. Moreover, this type of an approach can possibly be used to verify or check low dimensional dynamical systems models for the POD coefficients (for the first POD mode) which are currently being developed for both of these flows.The authors wish to thank DRET Grant # 90/171, the French Embassy Chateaubriand Fellowship (CIES) program for L. Ukeiley, NASA/Lewis GSRP for D. Cole, NASA/Ames Dryden, NASA/Langley and NSF/CNRS through the international travel grants program for funding various portions of this work.     

Modeling rock failure using the numerical manifold method followed by the discontinuous deformation analysis

A complete rock failure process usually involvesopening/sliding of preexisting discontinuities as well as fracturing in intact rock bridges to form persistent failure surfaces and subsequent motions of the generated rock blocksThe recently developed numerical manifold method(NMM)has potential for modelling such a complete failure processHowever,the NMM suffers one limitation,i.e.,unexpectedmaterial domain area change occurs in rotation modellingThis problem can not be easily solved because the rigidbody rotation is not represented explicitly in the NMM.Thediscontinuous deformation analysis(DDA) is specially developed for modelling discrete block systems.The rotationinduced material area change in the DDA modelling canbe avoided conveniently because the rigid body rotation isrepresented in an explicit form.In this paper,a transitiontechnique is proposed and implemented to convert a NMMmodelling to a DDA modelling so as to simulate a completerock failure process entirely by means of the two methods,in which the NMM is adopted to model the early fracturingas well as the transition from continua to discontinua,whilethe DDA is adopted to model the subsequent motion of thegenerated rock blocks.Such a numerical approach also improves the simulation efficiency greatly as compared with acomplete NMM modelling approach.The fracturing of arock slab with pre-existing non-persistent joints located ona slope crest and the induced rockfall process are simulated.The validity of the modelling transition from the NMM tothe DDA is verified and the applicability of the proposed numerical approach is investigated.     

A note on the reservoir routing problem

The reservoir routing problem has been recognized and managed for quite some time, but this paper presents a consistent mathematical approach by applying only the mass conservation principle (instead of various ‘ad hoc’ approaches). Application of the mass conservation principle facilitates the presentation of integral and differential formulations based on either the water volume or the water level of an arbitrarily-shaped reservoir. For the solution, new functions with a clear physical meaning are introduced. An error analysis is performed using a new approach based on spectral operators (traditionally, Richardson extrapolation has been used). It becomes evident that the integral formulations are more advantageous in terms of stability; however, they take more time to program and to calculate. The calculations in the examples are based on actual data from an artificial water reservoir (lake) Botonega in Croatia using the authors’ computer program that was created in the Mathcad environment.