考虑Reissner效应的表面裂纹的非线性线弹簧模型

本文在非经典板的弯曲理论基础上,对应力-应变关系满足ε/ε_o=σ/σ_o α(σ/σ_o)~n的幂硬化材料的表面裂纹的弹塑性断裂分析,建立了非线性线弹簧模型,计算了表面裂纹的应力强度因子及其最大深度点的J积分值,研究了幂硬化指数n和系数α以及波桑比ν对J积分值的影响。     

用云纹干涉法测定表面复合材料层板面内位移及其导数场

本文针对含表面裂纹的C/E复合材料层板,运用云纹干涉法测定了层板表面的面内位移及其导数场,提出了一种四次曝光直接错位的位移导数测量方法。与有限元计算结果对照,表明实验条纹图与计算条纹图基本是一致的.     

用赝势方法计算贵金属的弹性常数

利用我们在文献[1]中提出的贵金属赝势与重迭能形式计算了Cu、Ag和Au在OK的二阶弹性常数的压力导数与三阶弹性常数。五个待定参数用零温零压下晶体的总能、三个二阶弹性常数以及晶格常数的实验值确定。理论计算与实验的比较表明,本文对于Au的计算结果比其他作者的计算结果更接近于实验值。     

圆钢管K型弯管锥头节点轴向刚度曲线参数化分析

K型弯管锥头节点核心区由节点管、空心切头锥两部分组成。本文采用ANSYS参数化分析了节点管外径及其壁厚、弦管外径及其壁厚、腹管外径及其壁厚、腹管轴线与节点管轴线夹角?、屋面坡度i、弦管轴力与其屈服荷载的比值σz/fy对节点轴向刚度的影响。分析表明:减小弦管1与节点管外径之比、增加腹管的壁厚会降低节点的轴向刚度,屋面坡度对节点轴向刚度的影响不大,腹管受拉的节点轴向刚度优于腹管受压的节点轴向刚度;弦管承受轴拉力的节点轴向刚度优于弦管承受轴压力的。引入两个量纲归一化参数,即节点轴向刚度因子η和节点轴力因子ω,根据有限元计算的η-ω曲线,通过多元线性回归拟合了η-ω曲线的计算公式,该计算公式为钢管结构的分析及设计提供了节点刚度计算模型。     

基于分数导数本构的粘弹性土层—隧洞衬砌系统的稳态动力响应

将混凝土衬砌材料视为具有分数导数本构的粘弹性体,在频率域研究了深埋圆形隧洞粘弹性土的稳态动力响应。利用衬砌的内边界条件和混凝土衬砌与土体界面处的连续性条件,得到了粘弹性土体和衬砌稳态振动的应力和位移解析解。进行了隧洞衬砌厚度、土体阻尼比、本构阶数、材料参数比等对土体的位移和应力幅值影响的算例分析,结果表明:材料参数比对系统动力特性有较大影响,随着材料参数比的增加,位移和应力幅值减小;随着土体的阻尼比、衬砌厚度的增加,位移和应力幅值减小;当材料参数比Tσ/Tε=3时,随着分数导数阶数增大,响应幅值减小。     

对Grüneisen系数高压渐近行为的讨论

P_x为冷压,K_ο和K_ο~1分别为零压体积模量及其对P_x的一次导数,α为随采用物理模型而异的一个参数(α=0,slater公式;α=2/3,Dugdale-MacDonald公式;α=4/3,自由体积公式)。实际的计算结果表明:用上述各模型计算的γ值,对于一般金属材料,大约在兆巴数量级的冷压下彼此趋于接近。     

爆轰产物组成和爆轰参数计算方法的理论研究

为实现爆轰产物组成和爆轰参数的计算,采用拉格朗日乘数法和牛顿迭代的方法预测爆轰产物组成,利用BKW状态方程预测爆轰参数,在0~600 GPa和300~15 000 K压力温度范围内选取金刚石作为碳的生成相;对爆轰产物系统采用最小自由能原理,结合牛顿迭代法求解爆轰产物的化学平衡方程组;对BKW状态方程参数提出修订,取α=0.5,β=0.298,θ=6 620,κ=9.50;采用自编程序实现计算过程。使用此方法和Hugoniot关系计算密度为1.77 g/cm3的PETN爆轰CJ点爆轰参数验证计算精度,结果显示计算与实验结果的误差均小于1%。利用此方法结合Hugoniot关系预测出爆轰CJ点的产物密度为2.43 g/cm3。     

α铁晶界熵及表面张力的分子动力学模拟

晶界也是一种界面。表面张力是晶界的一个重要的热力学量。本文采用计算机分子动力学模拟(CMD)方法计算 α-Fe,∑=9 的晶界在不同温度和压力下的表面张力,结果与实验值的比较是满意的。发现熵对晶界的表面张力的贡献是很小的,通常可以忽略不计。     

不变变分问题 (此文献给F.Klein,为博士研究50周年纪念日作)

研究Lie意义下的允许连续群的变分问题.基于形式变分学方法与Lie群理论方法的联系,得到以下两个定理.定理1:如果积分I=∫…∫f(x,u,au/ax2,…)dx相对某有限连续群Dρ是不变的,则Lagrange表示ψ的ρ个线性独立组合将变为散度;反之,由后一条件得到积分,相对某群Dρ的不变性.对无限多个参数的极限情形,定理也对.定理2:如果积分,相对无限连续群D∞ρ是不变的,在此群中会出现直至σ阶导数的导数,那幺Lagrange表示ψ及其至σ阶导数之间有ρ个恒等关系成立;这里反述也对.定理1在ψ=0时给出ρ个第积分.定理2表明,Lagrange方程总数中的ρ个方程是其余方程的结果.     

岩石强度随中间主应力变化规律

1.引言 Murrell、Handin等及茂木等,从围压下的压缩实验与拉伸实验的莫尔包线的显著差异发现了中间主应力对岩石强度有相当大的影响.Weibols和Cook,在岩石的强度取决于有效畸变能的某一最大值的假设之下,根据有限单元法的计算结果指出了在某一恒σ_3作用下当σ_2=σ_3增加到σ_2=σ_1时,岩石强度有一个逐渐增大到最大值后便又逐渐下降到大于常规三轴压缩强度的某一个值的规律     

The divergence of nearby trajectories in soft-sphere DEM

The n-body instability is investigated with the soft-sphere discrete element method. The divergence of nearby trajectories is quantified by the dynamical memory time. Using the inverse proportionality between the dynamical memory time and the largest Lyapunov exponent, the soft-sphere discrete element method results are compared to previous hard-sphere molecular dynamics data for the first time. Good agreement is observed at low concentrations and the degree of instability is shown to increase asymptotically with increasing spring stiffness. At particle concentrations above 30%, the soft-sphere Lyapunov exponents increase faster than the corresponding hard-sphere data. This paper concludes with a demonstration of how this case study may be used in conjunction with regression testing and code verification activities.     

纵向参数激励下平动刚-液耦合系统稳定性

纵向参数激励下液体晃动稳定性是航天器动力学中一个广受关注的问题,然而在以往的研究中没有考虑液体晃动与航天器运动之间的耦合作用对系统参数振动稳定性的影响. 建立了用液体晃动等效单摆模型描述的纵向激励下平动刚-液耦合系统的Mathieu方程,采用摄动法确定了耦合系统1/2亚谐波振动和谐波振动的激励幅-频稳定性边界. 研究发现,液体晃动与主刚体横向运动的耦合作用扩大了参数振动不稳定区, 并使其向高频移动,影响的程度随等效晃动质量的减小而减小;液体晃动模态阻尼对1/2亚谐波振动不稳定区的缩小作用远弱于对谐波振动不稳定区的缩小作用. 对耦合系统第1阶液体晃动模态1/2亚谐波振动响应的研究表明:当纵向激励参数在不稳定区内时,可能引起主刚体的纵横耦合振动现象.      

DYNAMIC SIMULATION OF ROTATING SHELLS COUPLED WITH LIQUID

The dynamic behaviors of rotating shells coupled with liquid are shown. The shell under consideration has arbitrary boundary conditions and a complex shape. A modified boundary element method and finite strip technique are used to improve the computing efficiency and to guarantee the continuity conditions on the liquid-shell interaction plane. The effects of various parameters such as shell's thickness and liquid depth are investigated. Dynamic simulations are applied to several typical shell-liquid systems, and the natural frequencies, mode shapes and response of vibration are calculated numerically. Project supported by the National Natural Science Foundation of China (No. 19702004).     

Molecular models for simulation of rarefied gas flows using direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is a technique for the numerical simulation of the rarefied gas flows by employing simulated molecules in simulated physical spaces. In the procedures involved in DSMC, the accuracy of the simulation of intermolecular collisions depends on the collision model adopted in the collision routine. The simplest molecular model is the hard-sphere model. In order to improve the accuracy of the simulations, more and more refined collision models were introduced for the use in DSMC. Thus, the variable hard-sphere, the variable soft-sphere, the generalised hard-sphere, the generalised soft-sphere and the variable sphere models were put forward by various researchers. And, all these models have met with varying degrees of success. Meanwhile, the Borgnakke-Larsen model, statistical inelastic cross-section models for both continuous and discrete internal energy and the dynamic molecular collision model were proposed for the treatment of polyatomic molecules in which transfer of energy among translational, rotational and vibrational degrees of freedom is possible. This paper gives a brief introduction to the intermolecular potentials based on which the molecular models have been constructed. Then the various models are introduced in the chronological sequence; finally concluding with a brief summary of the progress that has been made so far in this area.     

AUTOMATIC IDENTIFICATION OF MESOSCOPIC PARAMETERS OF DISCRETE ELEMENTS OF SAND MATERIAL 1)

本文依照四川大学某理论力学教学班实际教学改革的经验,通过具体举例说明计算机技术在理论力学教学中尚未开发的巨大潜力,减小数学运算使学生重点关注理论力学基本原理,批量求解使学生提前接触实际应用案例,普适性求解使学生深化对处理多变量问题的认识。同时本文还探讨了理论力学教学改革的方向和目的,即把教学重点放在普适的教学方法上,借助计算机求解多刚体、多变量问题,以期有助于理论力学教材更好地适应时代发展。     

液封液桥内热毛细对流的数值模拟

建立了液封液桥(不相溶混的双层同轴液柱)内热毛细对流的物理数学模型，采用涡量-流 函数法、利用有限差分格式对微重力条件下液封液桥内热毛细对流进行了数值模拟，得到了 双层液柱主流区的温度场和流场，证实了液封技术能削弱液桥主流区的热毛细对流，从而提 高浮区晶体生长质量，找出了液封厚度以及内、外层流体物性参数比对液桥内热毛细对流的 影响规律.     

OBSERVATIONS OF BUBBLE SELF-ORGANIZATION IN LASER-MATTER INTERACTIONS

Bubbles generated in laser–metal interactions (LMI) at the transition from planar-to-volume boiling behave like hard (and soft) spheres. Micrographic analysis indicates that the surface layer of vaporizing metal, which comprises small microscale bubbles, behaves like a two-dimensional granular system. Bubble collision leads to bubble self-organization which changes with laser power density Q_p, and falls into (i) the kinetic regime, (ii) the clustering regime, or (iii) the regime of inelastic collapse (when bubbles form chain-like clusters), in analogy with the results of numerical simulations of hard-sphere dynamics. At a certain power density, shock waves that travel over the surface become strong enough, so that the system of bubbles behaves like horizontally and vertically shaken granular material. Since bubbles in the vibrational process are decelerated, hydrodynamic forces deform them, causing them to stay coalesced after the collision, forming a cluster with plateau borders, which is actually metal foam. The results presented show the existence of various complexity levels in the self-organization of bubbles, their sensitivity to the variation of interaction parameters, and finally, they indicate some universal features of bubble system dynamics.     

HYDROELASTIC VIBRATION OF A CIRCULAR CONTAINER BOTTOM PLATE USING THE GALERKIN METHOD

The free vibration of a flexible thin plate placed into a circular hole and elastically connected to the rigid bottom slab of a circular cylindrical container filled with fluid having a free surface is studied. The liquid is assumed to be incompressible, inviscid and irrotational. The effect of the free surface wave is also taken into account in the analysis. First of all, the exact expression of velocity potential of the liquid movement is derived by a combination of the superposition method and the method of separation of variables. With the help of the Fourier–Bessel series expansion, part of the unknown coefficients in the solution is determined by the consistency condition between the liquid movement and the plate vibration, in the form of integrals associated with the dynamic deflection of the plate. Then, the Galerkin method is applied to derive the eigenfrequency equation of the fluid–plate interaction. Finally, the effects of various parameters and the free surface wave on eigenfrequencies of the fluid–plate system are discussed. As a consequence, the accuracy of the nondimensional added virtual mass incremental (NAVMI) factor solution has also been evaluated by comparing with the more accurate Galerkin solution. It is shown that the proposed method is also applicable to the vibration analysis of circular plates in contact with an infinite liquid by only taking a finite but larger size of liquid to replace the infinite liquid in the computation.     

Exact solution for capillary interactions between two particles with fixed liquid volume

The capillary interactions, including the capillary force and capillary suction, between two unequal-sized particles with a fixed liquid volume are investigated. The capillary interaction model is used within the Young-Laplace framework. With the profile of the meridian of the liquid bridge, the capillary suction, and the liquid volume as state variables, the governing equations with two-fixed-point boundary are first derived using a variable substitution technique, in which the gravity effects are neglected. The capillary suction and geometry of the liquid bridge with a fixed volume are solved with a shooting method. In modeling the capillary force, the Gorge method is applied. The effects of various parameters including the distance between two particles, the ratio of particle radii, and the liquid-solid contact angles are discussed.     

自旋液体晃动研究

对旋转对称中心贮箱内的自旋液体晃动问题，提出了一个直接对Ｅｕｌｅｒ方程进行Ｇａｌｅｒｋｉｎ离散的近似方法，并分析了方法的近似性。